A Hydraulic Actuated Thermal Management System for Large Displacement Engine Cooling Systems Peyton Frick Clemson University, [email protected]

A Hydraulic Actuated Thermal Management System for Large Displacement Engine Cooling Systems Peyton Frick Clemson University, Fpeyton@Clemson.Edu

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8-2007 A Hydraulic Actuated Thermal Management System For Large Displacement Engine Cooling Systems Peyton Frick Clemson University, [email protected]

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Recommended Citation Frick, Peyton, "A Hydraulic Actuated Thermal Management System For Large Displacement Engine Cooling Systems" (2007). All Theses. 191. https://tigerprints.clemson.edu/all_theses/191

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A HYDRAULIC ACTUATED THERMAL MANAGEMENT SYSTEM FOR LARGE DISPLACEMENT ENGINE COOLING SYSTEMS ______

A Thesis Presented to the Graduate School of Clemson University ______

In Partial Fulfillment of the Requirements for the Degree Master of Science Mechanical Engineering ______

by Peyton Matthew Frick August 2007 ______

Accepted by: Dr. John R. Wagner, Committee Chair Dr. Darren Dawson Dr. Laine Mears

ABSTRACT

The performance of automotive cooling systems can be improved by replacing the traditional mechanically driven radiator fan and water pump assemblies with computer controlled components. The introduction of electric servo-motors to drive the cooling components can improve temperature tracking, which should increase fuel efficiency and decrease tailpipe emissions. However, the power requirement for these electric motors increases with greater cooling demands if the radiator surface area remains constrained.

For heavy-duty applications, where engines are subjected to significant cooling loads, electric motors may become impractical due to their increased size and power requirements; in these situations, hydraulic-based components are advantageous due to their high power density. The off-road equipment industry currently uses hydraulic radiator fan drives for cooling applications, while the coolant pump remains mechanically driven. Therefore, an opportunity exists to integrate the radiator fan and coolant pump into hydraulic circuits to actively meet cooling demands.

In this research project, an automotive thermal management system, which features a computer controlled hydraulically actuated fan and coolant pump, was investigated. A series of analytical mathematical models were derived for the hydraulic and thermal system components. An experimental test bench was constructed, which implements a hydraulic based radiator fan and water pump, as well as electric immersion heaters to simulate the heat of engine combustion. The test bench was used to validate the mathematical models and study the proposed cooling system’s ability to regulate engine

temperature. Classical control methods have been applied to control the coolant temperatures by integrating the temperature, shaft speed, and hydraulic pressure feedback information. Further, the performance of two types of hydraulic flow control valves has been studied to offer design engineers insight into actuator behavior.

The dynamic hydraulic and thermal system models displayed good correlation with data obtained from the experimental test bench (steady-state errors below 1.6%).

Additionally, the experimental system demonstrated excellent temperature tracking results (maximum 0.20 K steady-state set point deviation) when using servo-solenoid valves to control the speed of the hydraulic motor driven radiator fan and water pump.

However, when using the more cost effective solenoid poppet valves, the system exhibited limited temperature tracking abilities (maximum 2.48 K steady-state set point deviation). Still, each valve displayed minimal power usage (by the pump and fan motors) with the servo valves consuming on average 58-160 Watts and the poppet valves consuming on average 66-128 Watts.

The hydraulic actuated thermal management system has the ability to effectively regulate engine temperatures while offering the potential for power minimization.

Despite their higher cost, servo-solenoid hydraulic control valves may be a good choice for controlling actuator speeds and regulating engine temperatures. Solenoid poppet valves offer a lower cost alternative to the servo-solenoid valves, but temperature tracking performance may be sacrificed. To study the power saving potential of hydraulic based thermal management systems, future experiments should include on-vehicle comparisons of the traditional and hydraulic based thermal management approaches.

iii

DEDICATION

I dedicate this work to my Dad, Bernard Frick, who taught me the value of hard work. Without him this thesis would not have been possible.

ACKNOWLEDGEMENTS

There are several people to whom I would like to express my utmost gratitude for their assistance and continuous support throughout this endeavor. I would like to thank

Dr. John R. Wagner for providing the resources necessary to complete this research project, as well as for his guidance in hydraulic and electrical theory. In addition, I am grateful to my committee members, Dr. Darren Dawson and Dr. Laine Mears.

Next, I would like to thank my parents for their financial support, as well as moral guidance. Also, I would like to extend thanks to my sister and brother-in-law, as well as to my girlfriend and her family for their continued emotional support and inspiration.

Additionally, I would like to extend special thanks to both Tom Mitchell and

Mohammad Salah for their assistance in integrating system components and in the coding of control strategies, respectively. Lastly, thanks to Michael Justice and Jamie Cole for their craftsmanship and mechanical abilities.

TABLE OF CONTENTS

Page

TITLE PAGE ...... i

ABSTRACT ...... ii

DEDICATION ...... iv

ACKNOWLEDGEMENTS ...... v

LIST OF TABLES ...... viii

LIST OF FIGURES ...... ix

NOMENCLATURE ...... xv

CHAPTER

1. INTRODUCTION ...... 1

Literature Review ...... 4 Research Objective and Goals ...... 7 Thesis Organization ...... 8

2. MATHEMATICAL MODELING AND CONTROL ...... 9

Linearized Electro-Hydraulic Model ...... 9 Nonlinear Hydraulic and Thermal Model ...... 22 Control Strategy ...... 26

3. EXPERIMENTAL TEST BENCH AND ACTUATOR CHARACTERIZATION ...... 28

Test Bench ...... 28 Actuator Characterization ...... 33

4. NUMERICAL AND EXPERIMENTAL RESULTS ...... 37

Linearized Electro-Hydraulic Simulation Results ...... 37 Nonlinear Hydraulic and Thermal Model Validation ...... 43 Experimental Results for Servo-Solenoid Valves ...... 48

Table of Contents (Continued)

Page

Experimental Results for Solenoid Poppet Valves ...... 55

5. CONCLUSIONS AND RECOMMENDATIONS ...... 61

Conclusions ...... 61 Recommendations ...... 62

APPENDICES ...... 63

A. Servo-Solenoid Valve Test Results ...... 64 B. Solenoid Poppet Valve Test Results ...... 74 C. Matlab/Simulink Modeling Algorithms ...... 84 D. Matlab/Simulink Control Algorithms ...... 95 E. Empirical Regressions ...... 103

BIBLIOGRAPHY ...... 104

vii

LIST OF TABLES

Table Page

4.1 Simulation parameter values used in the linearized electro-hydraulic and radiator models ...... 38

4.2 Simulation parameter values used in the reduced order nonlinear hydraulic and thermal models ...... 44

4.3 Test results using Proportional-Integral-Derivative (PID) controlled servo-solenoid valves for fixed and sinusoidal temperature profiles ...... 50

4.4 Test results using Proportional-Integral-Derivative (PID) controlled solenoid poppet valves for fixed and sinusoidal temperature profiles ...... 55

viii

LIST OF FIGURES

Figure Page

1.1 A traditional automotive thermal management system featuring a thermostat valve, mechanical water pump, and mechanically driven radiator fan...... 2

1.2 Proposed hydraulic actuated thermal management system featuring a hydraulically driven radiator fan and water pump...... 8

2.1 Schematic of hydraulic control valve ...... 11

2.2 Hydraulic model schematic with radiator fan and coolant pump motors ...... 24

2.3 Thermal model schematic ...... 25

3.1 Data acquisition board and computer ...... 30

3.2 Experimental test bench: (a) Hydraulic side; and (b) Thermal side ...... 31

3.3 Hydraulic flow control valves (a) Servo-solenoid valve and (b) Solenoid cartridge/poppet valves ...... 32

3.4 Hydraulic components (a) Hydraulic power unit; and (b) Hydraulic gear type motor ...... 33

3.5 Steady state actuator speeds versus valve displacements for different supply pressures ...... 34

3.6 Actuator response to valve input of πt + 5)2sin(3 [Volts] ...... 36

4.1 Hydraulic valve spool displacement for a step input of 10 VDC to the valve’s solenoid ...... 39

4.2 Hydraulic motor supply and return pressure for step response in valve spool position ...... 39

4.3 Hydraulic motor speed for step valve input ...... 40

List of Figures (Continued)

Figure Page

4.4 Air speed across cross flow radiator versus hydraulic valve spool position ...... 41

4.5 Water temperature at radiator outlet versus air speed using ε-NTU and Nusselt methods...... 42

4.6 Water temperature at intervals along radiator for different air velocities using Nusselt method ...... 43

4.7 Measured and simulated response to an 8 VDC step input to the control valve for the (a) Fan speed; and (b) Pump speed ...... 45

4.8 Measured and simulated response to an 8 VDC step input to the control valve for the (a) Fan load pressure; and (b) Pump load pressure ...... 47

4.9 Thermal response for warm-up condition and step input to the hydraulic actuators at t = 300 seconds to remove heat ...... 48

4.10 Results from Test 1 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance ...... 51

4.11 Initial Δt = 500 sec of Test 1 to display details of the (a) Coolant temperatures; and (b) Actuator speeds ...... 53

4.12 Results from Test 8 with a sinusoidal engine reference temperature, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph ...... 54

4.13 Results from Test 11 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance ...... 57

4.14 Results from Test 19 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance ...... 58

4.15 Phase lag in temperature tracking from Test 12 ...... 60

List of Figures (Continued)

Figure Page

A.1 Results from Test 1 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance ...... 64

A.2 Results from Test 2 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , constant

heat input, Qin = 12 kW, and no disturbance ...... 65

A.3 Results from Test 3 with a fixed engine reference temperature, Tref = 322°K, and heat disturbance, Qd = 4 kW ...... 66

A.4 Results from Test 4 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , and heat

disturbance, Qd = 4 kW ...... 67

A.5 Results from Test 5 with a fixed engine reference temperature, Tref = 322°K, and ram air disturbance, Vram = 35 kph ...... 68

A.6 Results from Test 6 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , and ram

air disturbance, Vram = 35 kph ...... 69

A.7 Results from Test 7 with a fixed engine reference temperature, Tref = 322°K, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph ...... 70

A.8 Results from Test 8 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , heat

disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph ...... 71

A.9 Results from Test 9 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance ...... 72

List of Figures (Continued)

Figure Page

A.10 Results from Test 10 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , constant

heat input, Qin = 8 kW, and no disturbance ...... 73

B.1 Results from Test 11 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance ...... 74

B.2 Results from Test 12 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , constant

heat input, Qin = 12 kW, and no disturbance ...... 75

B.3 Results from Test 13 with a fixed engine reference temperature, Tref = 322°K, and heat disturbance, Qd = 4 kW ...... 76

B.4 Results from Test 14 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , and heat

disturbance, Qd = 4 kW ...... 77

B.5 Results from Test 15 with a fixed engine reference temperature, Tref = 322°K, and ram air disturbance, Vram = 35 kph ...... 78

B.6 Results from Test 16 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , and ram air

disturbance, Vram = 35 kph ...... 79

B.7 Results from Test 17 with a fixed engine reference temperature, Tref = 322°K, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph ...... 80

B.8 Results from Test 18 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , heat

disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph ...... 81

xii

List of Figures (Continued)

Figure Page

B.9 Results from Test 19 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance ...... 82

B.10 Results from Test 20 with a sinusoidal engine reference 2π temperature, Tref = sin11.1 (300 )+ 322 °Kt , constant

heat input, Qin = 8 kW, and no disturbance ...... 83

C.1 Linearized electro-hydraulic model, 1st level ...... 84

C.2 Solenoid dynamics, 2nd and 3rd levels ...... 84

C.3 Spool dynamics, 2nd level ...... 85

C.4 Solenoid dynamics, flow 1, 3rd level ...... 86

C.5 Solenoid dynamics, flow 2, 3rd level ...... 86

C.6 Valve flow, 2nd level ...... 86

C.7 Motor dynamics, 2nd level ...... 87

C.8 Rotation, 3rd level ...... 87

C.9 Nonlinear hydraulic and thermal system model, 1st level ...... 90

C.10 Plant, 2nd level ...... 90

C.11 Flow, fan and pump, 3rd level ...... 91

C.12 Rotation, fan and pump, 3rd level ...... 91

C.13 Air flow, 3rd level ...... 91

C.14 Coolant flow, 3rd level ...... 92

C.15 Radiator thermal dynamics, 3rd level ...... 92

C.16 Engine thermal dynamics, 3rd level ...... 92

xiii

List of Figures (Continued)

Figure Page

D.1 Servo-solenoid valve control, 1st level ...... 95

D.2 Bosch valve control, 2nd level ...... 96

D.3 RPM acquire fan and pump, 2nd level ...... 96

D.4 Frequency counting fan and pump, 3rd level ...... 97

D.5 Subsystem 1, 4th level ...... 97

D.6 Subsystem 1a, 5th level ...... 97

D.7 Hydraulic pump valves, 2nd level ...... 98

D.8 Pressure reading, 2nd level ...... 98

D.9 Temperature sensing/flow rate, 2nd level ...... 99

D.10 Solenoid poppet valve control, 1st level ...... 100

D.11 Valve control, 2nd level ...... 101

D.12 Hydraulic pump valves, 2nd level ...... 101

E.1 Linear regression for air velocity versus fan speed ...... 103

E.2 Linear regression for coolant flow versus pump speed ...... 103

xiv

NOMENCLATURE

Symbol Units Description

A m2 area

2 Aa m annular fan area

2 Aeff m effective fin surface area

2 Afin m fin surface area

2 At,i m tube inner surface area

2 At,o m tube outer surface area a mm solenoid contact length

Bm N-s/cm motor damping b m fin separation distance bv N-s/mm valve damping

C, C′ W/K thermal capacity rate cc J/kg·K specific heat of coolant ca J/kg·K specific heat of air cp J/kg·K specific heat cp,c J/kg·K specific heat of cold fluid cp,h J/kg·K specific heat of hot fluid

Cd - damping Coefficient

Ce kJ/K engine thermal capacity

Cmin W/K minimum heat capacity rate

Cmax W/K maximum heat capacity rate

Nomenclature (Continued)

Symbol Units Description

Cr - ratio heat capacity rate

Crad kJ/K radiator thermal capacity

3 Dm cm /rev motor displacement

Dh m hydraulic diameter e(t) K temperature tracking error

Fs N force generated by the solenoid

Fss N steady state fluid force on the solenoid

Ftr N transient fluid force on the solenoid h W/m2·K heat transfer coefficient

2 ha W/m ·K air-side heat transfer coefficient

2 hc W/m ·K coolant-side heat transfer coefficient

2 hL W/m ·K avg. heat transfer coefficient over flat plate i A solenoid current

2 Jf kg-cm fan inertia

2 Jp kg-cm pump inertia

K W/m·K thermal conductivity

KD - PID derivative gain

Kf,p - controller intensity factor

KI - PID integral gain

KP - PID proportional gain

xvi

Nomenclature (Continued)

Symbol Units Description kt W/m·K thermal conductivity of tube material kf W/m·K thermal conductivity of fin material kv N/mm valve spring constant

L m length

Lf m core depth along the fin for unlouvered fins

Ln H coil inductance

Ld mm damping length lg mm reluctance gap

m& a kg/s air mass flow rate

m& c kg/s coolant mass flow rate

m& h kg/s mass flow rate of hot fluid ms g spool mass

N - # of turns on solenoid coil

NTU - number of transfer units

Nu - Nusselt number

Pavg W average power consumed

Pr - Prandtl number

PL kPa load pressure

PS kPa supply pressure

PT kPa tank pressure

xvii

Nomenclature (Continued)

Symbol Units Description

PA kPa hydraulic motor supply pressure

PB kPa hydraulic motor return pressure

Q W heat transfer rate

3 Qa cm /s volumetric flow rate of air

Qd W disturbance heat

Qin W heat input

Qout W heat lost to random airflow

QL L/min load flow

Qmax W maximum heat transfer rate

R Ohms coil resistance

Rt,cond K/W conduction resistance of tube wall

'' 2 R ,cf K·m /W cold fluid side fouling resistance

'' 2 R ,hf K·m /W hot fluid side fouling resistance

Rw K/W tube wall conduction resistance

Re - Reynold’s number

5 Ri N·s/cm internal leakage resistance

Sf,p V control signal

Tar N-cm torque due to air resistance

Tc,i K cold fluid inlet temperature

Te K engine temperature

xviii

Nomenclature (Continued)

Symbol Units Description

Tr K radiator temperature

Tref K engine reference temperature

Th,i K hot fluid inlet temperature

Th,o K hot fluid outlet temperature

T∞ K ambient air temperature t sec time

U W/m2·K overall heat transfer coefficient

V V voltage

Va m/s air velocity

Vram kph air velocity for ram air disturbance

3 Vt cm volume of compressed fluid w mm2/mm area gradient of orifice xv mm valve spool displacement

βe kPa bulk modulus of hydraulic fluid

δf m fin thickness

ε - heat exchanger effectiveness

ηf - plate fin efficiency

ηo - overall finned surface efficiency

θ K temperature

θj rad jet angle

xix

Nomenclature (Continued)

Symbol Units Description

μ N·s/m2 viscosity

μ0 H/mm Solenoid armature permeability

ρ kg/m3 density

τ N-m hydraulic motor torque

ω rad/s actuator speed

CHAPTER 1

INTRODUCTION

In most passenger and commercial vehicles, liquid cooling systems manage the engine’s thermal needs by regulating the coolant temperature (Chastain and Wagner,

2006). An ethylene-glycol mixture is circulated through the engine block and cylinder heads to absorb heat from the combustion process. Typically, a cross flow heat exchanger transfers the coolant heat to the atmospheric air. In addition to the radiator, there are three other components integral to the cooling system: the thermostat, water pump, and radiator fan (refer to Figure 1.1). The thermostat is a temperature sensitive wax-based valve that regulates the coolant temperature by directing fluid flow to the bypass and/or then radiator. The water pump provides the pressure to maintain the coolant flow through the engine, radiator, thermostat valve, and hoses. The radiator fan draws air through the radiator fins for forced convection heat transfer. The topic of interest in this project is the radiator fan and water pump assemblies.

Traditionally, automotive cooling systems have relied on mechanically driven components (i.e., radiator fan and water pump). In this arrangement, the components are attached either directly to the engines crankshaft or are coupled to the crankshaft through a belt and pulley. Often, a thermostatically controlled viscous clutch is utilized to regulate a mechanically driven fan’s speed. This type of clutch allows the fan to turn at slower speeds for cooler temperatures, which in turn consumes less engine power.

Intake Thermostat Valve Manifold Mechanically Driven Radiator Fan Cylinder Heads Hoses

Engine Block

Mechanically Driven Water Pump Cross Flow Accessory Belt Radiator Drive

Figure 1.1: A traditional automotive thermal management system featuring a thermostat valve, mechanical water pump, and mechanically driven radiator fan

However, mechanically driven components have limitations. One example is the lack of versatility when it comes to packaging. Since mechanical fans rely on the rotation of the crankshaft for power, the radiator placement must be close to the engine and geometrically aligned with the crankshaft output. Another disadvantage is that both the fan and pump speeds are dependent on the engine speed. Thus, the radiator fan and water pump may be running faster than what is required by the cooling system and in turn wasting power, decreasing fuel efficiency, and increasing pollution (Drummond, 2005).

One alternative to the traditional mechanically driven fan and pump assemblies involves using an electric servo-motor to drive the cooling system components (Allen and

Lasecki, 2001). Another strategy uses hydraulic motors to power the variable speed components. Both of these can be extremely efficient methods because they allow for computer control of the pump and fan speed. Therefore, the cooling elements will operate only when needed and only as fast as necessary to meet the cooling demands. In addition, these methods offer greater design flexibility because they are decoupled from the engine allowing the radiator and/or water pump to be mounted at other locations in the vehicle.

Both systems can also be programmed to reverse direction on demand. This is useful in fan applications for off-road machinery since it allows the fan to switch directions and blow air through the radiator removing debris that may have accumulated (Drummond,

2005). However, for larger engine sizes and increased cooling demands (i.e. cooling oil, transmission fluid, and any other fluids in addition to the engine coolant), the power requirements for the pump and fan increase.

The electric motors required to meet these requirements can be quite large and heavy. Further, they also produce a great deal of heat. In comparison, hydraulic motors can generate large amounts of power in a small and compact package while emitting very little heat. This attribute along with their packaging versatility make hydraulic drives a good choice for cooling systems used in off-road vehicles and machinery. This has lead to an increase in the use of hydraulically driven fans in off-road applications as well as the development of stand alone hydraulic fan drive systems which can be retrofit for

specific applications. However, despite the recent interest in hydraulic fan drives, there are still limited amounts of literature available on the subject.

Literature Review

For years, automotive thermal management systems remained unchanged (Allen and Lasecki, 2001). Most systems consisted of a radiator with a fan driven by the engines crankshaft, a wax based thermostat, and a water/coolant pump also driven by the engines crankshaft. However, Hall and Claussen (1985) proposed a cooling system featuring a hydraulic radiator fan drive which was intended to provide greater efficiency over traditional cooling systems. Their system consisted of an engine driven hydraulic pump which drove the hydraulic fan motor, a wax based thermostatic pilot valve, and a two way switching valve. The thermostatic valve worked similar to a traditional wax based thermostat. However, it opened when subjected to cold coolant temperatures and closed when subjected to warm coolant temperatures. Consequently the resulting flow was inversely proportional to the coolant temperature. The switching valve was driven by the amount of fluid flowing from the thermostatic valve; this allowed a proportional amount of output oil flow from the hydraulic pump to be diverted to the tank bypassing the hydraulic motor. Thus, the fan speed became a function of coolant temperature.

More recently, thermal management systems which utilize computer controlled components are being investigated and implemented. Allen and Lasecki (2001) outline the evolution of the thermal management system. Though they focus mostly on computer controlled pumps and valves, they explain how computer controlled components can

reduce the amount of parasitic drag on an engine which can in turn increase horsepower to the wheels, increase fuel efficiency, and decrease emissions. Hamamoto et al. (1990) developed an electronically or computer controlled hydraulic cooling fan system for use on (Toyota) passenger cars. They claim the following benefits over the traditional engine- driven fan and electric motor fan: reduced fan noise, improved fuel economy, and small size and light weight. They also speak of the benefits of using pressure control over flow control for control of the fan speed using a hydraulic motor. Essentially, when using flow control the fan speed can vary with the temperature of the hydraulic oil because a rise in oil temperature leads to a decrease in the volumetric efficiency of the motor. However, with pressure control, fan speed is kept almost constant since the flow rate will change to match the desired pressure difference regardless of the volumetric motor efficiency.

Chalgren and Allen (2005) studied the effects of an advanced thermal management system on light duty diesel applications. More specifically, they replaced a typical mechanical cooling system on a light duty truck with an electric cooling system.

The test platform used was a Ford Excursion with a 242 kW (325 hp) 6.0 liter diesel engine. Testing revealed reductions in cooling system power consumption as well as increases in fuel economy. Though Chalgren and Allen (2005) utilize electric cooling components, they mention the fact that increased cooling loads may necessitate higher voltage requirements than the standard 12 V system. For this reason, hydraulically driven components may be beneficial in off road applications where cooling loads can be very large.

An article in Diesel Progress (2005) explains the demands of current off road engines and the benefits of using a commercially available hydraulically driven radiator fan. Today’s off road engines must operate within relatively tight temperature constraints to meet emission requirements, yet they are typically used in a broad range of climates from the scorching desert to the frigid arctic. The cooling systems for these off road vehicles face a growing number of other cooling loads (e.g., engine oil, hydraulic oil, air conditioning refrigerant, charge-air cooling, transmission cooling). A primary benefit of hydraulic driven fans is speed independent of the engine speed, which accomplishes a vehicle’s cooling demands as efficiently as possible. Further, little space is required inside the engine compartment in contrast to mechanically driven fans which require complicated belt and pulley mechanisms, and hydraulic fans allow a tighter tolerance radiator shroud fit.

An important issue in this study of hydraulically driven cooling components is the development of a system model. This involves mathematically modeling the hydraulic valves and motors as well as the radiator, pump, and fan. Merritt (1967) offers a wealth of knowledge about modeling hydraulic components such as a servo-valve and motor.

Both linear and nonlinear differential equations are presented which describe steady state and transient responses of hydraulic servo-valves and motors. Vaughan and Gamble

(1996) present a nonlinear dynamic model of a high speed direct acting solenoid valve similar to the valve used in this research project that offers good correlation with experimental results.

Although there is a wealth of industry literature available on the benefits and applications of hydraulically driven radiator fans, very little work has been published on system modeling and control. In addition, none of the aforementioned research investigates alternative configurations which may include using a hydraulically driven coolant pump along with the fan for cooling systems. This research project addresses these issues by implementing a hydraulic-based thermal management system with system models and control strategies.

Research Objective and Goals

The objective of this research project is to study the performance of a computer controlled hydraulic-based thermal management system (refer to Figure 1.2). To accomplish this, the four goals of modeling, fabricating, testing, and controlling a hydraulic-based thermal management system will be undertaken. First, a mathematical model of the system should be developed. The model will be used to simulate the dynamic response of the system, design an experimental setup, and develop an efficient and robust control strategy. Second, an experimental test-bench should be constructed.

The test-bench should consist of a hydraulic-based thermal management setup including a hydraulic pump and fan, a heat input (simulating an engine), and a heat exchanger or radiator. In addition, the test-bench should be capable of real time control and data acquisition. The last phase involves testing and control of the experimental setup. This includes obtaining experimental data to characterize the system and validate the mathematical system model as well as testing control algorithms and comparing the system performance to that of other thermal-management systems.

Figure 1.2: Proposed hydraulic actuated thermal management system featuring a hydraulically driven radiator fan and water pump

Thesis Organization

This thesis is divided into five chapters. Chapter 1 introduces the problem while also providing a review of the available literature on the subject. Chapter 2 presents both linear and non-linear models of the system along with control strategies for two types of hydraulic control valves. Chapter 3 provides a detailed explanation of the experimental setup. Chapter 4 includes simulation results as well as experimental data to demonstrate the performance of the control valves. Finally, the fifth chapter summarizes the findings and discusses recommendations for future research.

CHAPTER 2

MATHEMATICAL MODELING AND CONTROL

In this study, two mathematical models for a hydraulic-based automotive thermal management system were developed. The first one is a complete linearized electro- hydraulic model coupled with two corresponding heat exchanger models. This analytical model offers a full dynamic response of all the system components due to voltage inputs applied to the servo-solenoid control valves. The second lumped parameter model, a modified version of the first one, was developed to be compatible with control algorithms and the experimental system hardware.

Linearized Electro-Hydraulic Model

Servo-Solenoid Hydraulic Control Valve

To describe the dynamics of the control valve, the forces acting on the valve spool

(e.g., solenoid, fluid flow, centering spring, and damping) must be considered. In Figure

2.1, a schematic of the valve is displayed showing these forces. The solenoid force generated is proportional to the square of applied current. The solenoid circuit can be represented by a resistor in series with an inductor (Vaughn and Gamble, 1996) so that the current differential equation becomes

di 1 −= iRV )( (2.1) Ldt n

The force generated by the solenoid is then given by

⎛ 1 2 μ aN ⎞ ⎜ 0 ⎟ 2 Fs = i (2.2) ⎜ 4 l ⎟ ⎝ g ⎠

where N, μ0, a, and lg denote the solenoid’s number of coil turns, armature permeability, contact length, and reluctance gap respectively.

The fluid flow forces arise due to acceleration of the hydraulic fluid. The steady state component of these forces is due to a jet force caused by the acceleration of fluid as it enters and exits the valve chambers through the small openings or orifices between the spool and the valve body. As a result of the symmetry of the valve ports around the spool, only the component of the jet force acting parallel to the spools longitudinal axis affects spool dynamics. This force always acts in a direction to close the orifice. The magnitude of the steady state force is described by

ss = 2 d wCF θ j − 21 ))(cos( xPP (2.3)

where Cd, w, and θj denote the damping coefficient, area gradient, and jet angle respectively. The variable P1 is the fluid pressure in the chamber the fluid is leaving (PS or

PB), and P2 denotes the fluid pressure in the chamber the fluid is entering (PA or PT). If the valve orifice is rectangular and the peripheral width is large compared with its axial length, then the flow can be considered two-dimensional and LaPlace’s equation can be solved to determine the jet angle, θj, assuming the flow is irrotational, nonviscous, and incompressible (Merritt, 1967). Von Mises performed this solution and θ was found to be

69° when there is no radial clearance between the valve spool and sleeve.

θj

Figure 2.1: Schematic of hydraulic control valve

The transient fluid force is caused by the acceleration of the fluid in the valve chamber (Watton, 1989). For this to occur, there must be a pressure drop in the valve chamber. This means that the pressure on one land will be greater than the pressure on an adjacent land which translates into a force acting on the spool. The direction of this force can be visualized by examining a slug of fluid as shown in Figure 2.1. Examining a fluid slug between the lands A and B, the pressure on the left hand side of the slug must be less that the pressure on the right hand side in order for it to accelerate to the left. This means that the pressure on the face of the right land (land B) is greater than the pressure on the face of the left land (land A) and the force will act to the right. The magnitude of this transient force is defined by

⎛ dx ⎞ (2.4) = ddtr wCLF ρ − PP 21 )(2 ⎜ ⎟ ⎝ dt ⎠

Knowing the forces acting on the valve spool, the equation describing the motion of the spool can now be found using Newton’s Law and summing forces on the spool in the axial direction so that

2 xd 1 ⎡ ⎛ dx ⎞⎤ FFFFF (2.5) 2 ⎢ sss ss 21 tr −++−= tr12 )()( −− bxk vv ⎜ ⎟⎥ dt m s ⎣ ⎝ dt ⎠⎦

where Fss1 is the steady state force due to fluid exiting the main valve chamber to port A.

The variable Fss2 is the steady state force due to fluid exiting port B to tank, and Ftr1 is the transient force due to acceleration of the fluid between lands A and B when the spool is displaced to the left in Figure 2.1. Finally, the variable Ftr2 is the transient force due to fluid acceleration to the right of land B when the spool is displaced to the left.

Hydraulic Motor

Hydraulic motors are broadly classified as fixed displacement (e.g. vane motors or gear motors) and variable displacement motors (e.g. axial piston motors). Each class includes several types to suit specific power, flow rate and operating pressure requirements. For instance, gear motors are common in low flow rate applications, while their operating pressures are relatively higher than vane motors. The flow rate is mainly dictated by the motor displacement, which is the fluid volume displaced per unit of angular rotation, while the operating pressure depends mainly on the internal clearances imposed by the design or achieved during manufacturing. Those clearances have also a

crucial effect on the internal loses and hence the overall motor efficiency. In the case of the used gear motor, and assuming a perfect incompressible fluid, loses are mainly contributed to the clearances between the internal gears and the motor housing. The flow continuity can be used to derive the following equation which relates the load pressure,

PL, load flow, QL, and motor speed, ω, such that

1 mL ω += PDQ L (2.6) Ri

The load flow and valve spool position, x, are related as

= qL − PKxKQ Lc (2.7)

where Kq is the valve flow gain and Kc is the valve flow-pressure coefficient.

In addition to the flow losses mentioned above, there are also other factors influencing the dynamic response of the motor. In this case, the three main factors are load inertia, Jf, internal damping, Bm, and linear torsional loads, TL. The effect of these can be found by summing torques on the motor. The dynamic equation is expressed as

dω 1 (2.8) = ()P mmL ω −− TBD L Jdt f

It is also important to note that there are torsional loads due to internal friction and fluid shear. However, for a linearized analysis such as this, they must be neglected due to their nonlinear dependence on velocity (Merrit, 1967).

Effectiveness-NTU Method Radiator Model

When analyzing a heat exchanger, in which the fluid inlet and outlet temperatures are known or can be determined, the overall heat transfer rate can be determined by calculating Log Mean Temperature Difference (LMTD). When the outlet temperatures are unknown, determining the LMTD requires an iterative procedure. In this case, a better technique is the effectiveness-NTU (ε-NTU) method, described in Incropera and DeWitt

(1990) which determines the effectiveness of the heat exchanger through a relationship to the number of transfer units (NTU). The effectiveness is simply the ratio of the heat exchanger’s actual heat transfer rate to the heat transfer rate obtained with a counter flow heat exchanger of infinite length or the maximum possible heat transfer rate. The NTU can be described as the capacity, or ability, of the heat exchanger to transfer heat from one fluid to the other or the ability of the heat exchanger to change the temperature of the fluid which experiences the largest temperature change.

To apply the ε-NTU method, it is necessary to determine the maximum heat transfer (MHT) rate based on each fluid. The MHT rate is the smaller of the two heat capacity rates multiplied by the difference in inlet temperatures between the two fluids so that

Qmax = − TTC ,,min icih )( (2.9)

The effectiveness of the radiator may be defined as

ε = / QQ max (2.10)

where Q is the heat transfer rate. It can also be described as a function of the number of transfer units, NTU, and the ratio of minimum to maximum heat capacity rate, Cr

(Incropera and DeWitt).

For a cross flow heat exchanger with both fluids unmixed, the effectiveness becomes

⎡⎛ 1 ⎞ ⎤ ⎜ ⎟ 22.0 78.0 ε −= exp1 ⎢⎜ ⎟ NTU )( {}[]− r NTUCEXP −1)( ⎥ (2.11) ⎣⎝ Cr ⎠ ⎦

UA Cmin where NTU and Cr are given by NTU = and C = , respectively. The product Cmin r Cmax

UA defines the overall heat transfer coefficient for the radiator. With the effectiveness known, equation (2.10) can be used to solve for the actual heat transfer rate, which in turn can be used to determine the coolant outlet temperature as

Q = & − TTcm ,,, ohihhph )( (2.12)

An important part of the analysis is determining the overall heat transfer coefficient for the heat exchanger. This is found by summing thermal resistances such that

11 R′′,cf R′′,hf 1 += Rw ++ + (2.13) 0hAUA c ηη 0 A c 0 )()()( h ηη 0hAA )( h

The subscripts h and c correspond to the hot and cold fluids, respectively. The first and last values in the sum represent the resistances due to convection of the cold and hot

fluids respectively. The R f and Rw terms denote the thermal resistances which account

for fouling and the conduction resistance. The ηo term is the overall surface efficiency of the finned surface and A is the total surface area. The overall surface efficiency can be calculated as

A η fin −−= η )1(1 (2.14) 0 A f

mL)tanh( where Af is the fin surface area, η f = mL is the fin efficiency, = /2 kthm , and t is the fin thickness.

The most significant terms in equation (2.13) are the air side convection coefficients which define the heat transfer rate changes with respect to the fan speed. To determine an average air side convection coefficient, the relationship for laminar flow over a flat plate was selected

L Lh 3/12/1 uN L =≡ L PrRe664.0 (2.15) k

The assumption of laminar flow over the entire surface was verified by calculating the

Reynolds numbers, Re, at the trailing edge of the tubes and fins on the radiator. Though the Reynolds number depends on air velocity, an average of approximately 40,000 was

found for air velocities 0

Remark #1: The Reynolds and Prandtl numbers may be computed as

LV pa ν Re L = ν and Pr = α , respectively.

The coolant side convection coefficient was determined using the relationship

Sieder and Tate (1936).

14.0 hD ⎛ μ ⎞ (2.16) h 3/15/4 ⎜ ⎟ Nu D =≡ D PrRe027.0 ⎜ ⎟ k ⎝ μ s ⎠

for fully developed turbulent flows where ≤≤ 700,16Pr7.0 , ≥ 000,10Re , and L ≥ 10 . For D Dh the radiator tubes, these criteria are met over the majority of the tube length. Estimations for both the hydrodynamic and thermal entry length are between 4 to 24 centimeters.

Thus, at L/2 or 34.3 centimeters the flow should be fully developed. This point will be used to calculate the coolant side convection coefficient since it should be representative of an average convection coefficient for the entire tube.

Remark #2: The radiator dimensions correspond to a 6.8L engine

radiator for a Ford spark ignition engine.

Nusselt Method Radiator Model

In this method, the heat exchange between two fluids in cross flow is considered on a differential basis. The resulting fluid temperature differential equations calculate an average exiting temperature for each fluid stream. These differential equations, and the

accompanying integral solution, were developed by and attributed to Nusselt for pure cross flow. As with the preceding method, representations of heat transfer for the coolant and air as well as the heat transfer through the tube wall are needed to create the model.

Coolant Heat Transfer Coefficient

The flow of coolant in the radiator has been assumed to correspond to internal pipe flow. The value of the heat transfer coefficient, hc, depends on the Reynold’s number, Re, associated with this flow. The heat transfer model includes the following provisions for the three possible types of internal flow regimes. For Re<2100, the flow is considered laminar, and a Nusselt correlation attributed to Stephan (Hausan, 1983) is employed

1.33 ⋅ h L)/DRe(Pr0677.0 (2.17) c 66.3Nu += 0.83 ⋅⋅+ h L)/DPr(Re0.11

For 2100

8.0 3.0 0.89 (2.18) c = − +− h )L)/D(1)(8.0Pr8.1)(230(Re0235.0Nu

For Re>4,000, the flow is considered turbulent, and the Gnielinski correlation (Incropera and DeWitt) is used

f − Pr)1000)(Re8/( Nu = (2.19) c + f 3/25.0 − )1(Pr)8/(7.121

where f = (0.79 −1.64)Reln −2 for smooth tubes.

Air Heat Transfer Coefficient

The air-side heat transfer is characterized by an outer tube surface with attached plate fins. Heat transfer coefficients for plate fin surfaces are obtained using the Colburn factor, jh, where

3/2 h ⎛ c μ ⎞ a ⎜ p ⎟ jh = ⎜ ⎟ (2.20) ρ cV pa ⎝ k ⎠

The Colburn factor can be determined from representative plots of jh versus Re (Bejan and Kraus, 2003), or approximated using an adapted equation for heat transfer from a flat plate (Beard and Smith, 1971) as

− 2/1 2 ⎛ VL ρ ⎞ f a (2.21) jh = ⎜ ⎟ 3 ⎝ μ ⎠

where Lf is the core depth along the fin for unlouvered fins, and the distance between each louver for louvered fins.

The efficiency of the plate fins is given by

)mb5.0tanh( η = (2.22) f mb5.0

1/2 where m = () k/h2 f δ fa . Consequently, the effective surface area for heat transfer on the air side of the radiator becomes a weighted average of the primary tube surface and the effective fin surface, given by

eff = ot, + η f AAA fin (2.23)

Heat Transfer through Tube Wall

The resistance to conduction through a tube wall of rectangular cross section is calculated by integrating the relationship for resistance of a wall with arbitrary cross section, so that

1 s2 ds R = (2.24) condt, ∫ t s)(Ak s1 where s denotes the spatial variable, and A(s) is the corresponding heat transfer area.

Overall Heat Transfer Coefficient

The overall heat transfer coefficient for the radiator is calculated using a sum of resistances in series for the coolant, tube wall, and air heat transfer contributions.

1 1 1 R condt, ++= (2.25) UA Ah it,c ot,a +η f fin )AA(h

The amount of heat transfer provided by the radiator is then determined by calculating a mean temperature difference between the coolant and air.

Radiator Model

The required differential equations obtained after evaluating the heat exchange in cross flow over a differential area of a tube are

∂θ ∂θ ′ = ′ −θθ and −= θθ ′ (2.26) ∂ξ ∂ξ ′ where θ and θ′ represent temperatures of the coolant and air flows, respectively. The variables ξ and ξ′ are dimensionless and given as

LU ′ UL ξ = x and ξ ′ = x′ (2.27) C C′

where C and C′ are thermal capacity rates of the coolant and air flows, respectively. The coordinates x and x′ represent the tube length along directions of the coolant and air flows.

The resulting simplified solutions to equations (2.26) and (2.27) become

′ ⎡ 2 3 ′ n2 2 ′ 1-n ⎤ − θθ 1 -()+ξξ ′ ξ ξ ⎛ ξ ⎞ ξ ⎛ ξ ′ ξ ⎞ (2.28) 1 −= e ⎢ξ ()1 ++ ξ′ ⎜1 ++ ξ′ + ⎟ ⎜1 ++ ξ′ + ... + ⎟⎥ − θθ ′ 2! 3! ⎜ 2! ⎟ n! ⎜ !2 − !1n ⎟ 11 ⎣⎢ ⎝ ⎠ ⎝ ()⎠⎦

⎡ 2 2 n ⎛ 2 n ⎞ ⎤ ′ − θθ 1′ -()+ξξ ′ ξ ⎛ ξ ′ ⎞ ξ ⎜ ξ ′ ξ ′ ⎟ 1 −= e ⎢1 ξ ()1 ++ ξ ′ ⎜ 1 ++ ξ ′ + ⎟ ⎜ 1 ++ ξ ′ + ... ++ ⎟ ⎥ (2.29) − θθ ′ 2! ⎜ 2! ⎟ n! ⎜ !2 n! ⎟ 11 ⎣⎢ ⎝ ⎠ ⎝ ⎠ ⎦⎥

The average exit temperatures of the coolant and air flows are then determined by integrating equations (2.28) and (2.29) according to the relationships shown in (2.30) and

(2.31).

C′ CUA/ ′ UA θ = ′ ,d ξξθ = (2.30) 2 ∫ UA 0 C

C / CUA UA θ ′ = d , ξξθ ′′ = 2 ∫ (2.31) UA 0 C′

Subsequently, the amount of heat transferred by the heat exchanger becomes

′ ′ ′ Q = C(θ1 − θ 2 ) = C ( − θθ 12 ) (2.32)

In other words, the variable Q represents the amount of radiator heat dissipated which can regulate the engine’s thermal performance for particular operating conditions. For example, θ1>θ2 indicates a heat loss from the coolant to the air and q is then the available engine cooling for the particular operating condition.

Nonlinear Hydraulic and Thermal Model

The servo solenoid valves used in this research project were driven by amplifier cards which featured built in control to ensure correct displacement of the valve solenoid.

Thus, when a voltage signal is sent to the valve’s amplifier card, the valve spool will be displaced an amount proportional to the voltage signal. In this case, a 0 VDC signal corresponds to the valve being fully closed, while a 10 VDC signal corresponds to the valve being fully opened. Consequently, when developing a system model for control purposes (refer to Figure 2.2), the valve’s spool displacement can be assumed to be proportional to the applied voltage. This allows the solenoid and spool dynamics presented in Equations (2.1-2.5) to be eliminated from the hydraulic model.

Hydraulic Model

Removal of the solenoid and spool dynamics (equations (2.1)-(2.5)) allowed more emphasis to be placed on modeling the hydraulic flow. Specifically, a load pressure rate term was added to the motor flow continuity equation (2.6) to yield

⎛ 1 ⎞ ⎛ V ⎞ ⎜ ⎟ ⎜ t ⎟ (2.33) DQ mL ω += ⎜ ⎟PL + ⎜ ⎟P&L ⎝ Ri ⎠ ⎝ 2β e ⎠

while the nonlinear form of the valve flow continuity equation (2.7) was maintained as

⎛ − PP )( ⎞ = ⎜ wCQ Ls ⎟x (2.34) ⎜ dL ⎟ v ⎝ ρ ⎠

Note that equation (2.8), which was used to describe the rotational dynamics of the actuators, remains unchanged with no added terms or nonlinearities. In addition to the modifications to the flow equations, a transient thermal model was implemented to simulate the temperature response of the engine and radiator.

Figure 2.2: Hydraulic model schematic with radiator fan and coolant pump motors

Thermal Model

To describe the cooling system’s thermal dynamics, a two-node lumped capacitance heat transfer model was selected (refer to Figure 2.3). The radiator was represented by one node while the engine, or in this case a block of heating coils, was represented by the second node. An energy balance may be performed on the block of heaters and the radiator to realize

dT e (2.35) Ce & −−= TTmcQ reccin )( dt

dT r (2.36) Crad & −−+−= ε & eaareccout −TTmcTTmcQ ∞ )()( dt

where & c = fm (ω p ) and & a = fm (ω f ) . The relationship between pump speed, ωp, and

coolant mass flow rate, m& c , as well as the relationship between the fan speed, ωf, and air

mass flow rate, m& a , can be determined empirically by collecting velocity or flow rate values at various actuator speeds and fitting a regression to the acquired data (Refer to

Appendix E). In equation (2.35), Qin represents the heat input by the heating coils

whileQout , in equation (2.36), represents the heat lost due to uncontrollable airflow.

Heating Coils T∞ Qin Qout

Radiator m& a Te

Water m& c Pump

Figure 2.3: Thermal model schematic

Control Strategy

With the development of both a linear and nonlinear system model, there were many options available for controlling the engine temperature. Though some advanced control methods (optimal and model predictive) were considered, simulation results revealed that good performance could be achieved using a classical Proportional-Integral-

Derivative (PID) controller.

Servo-Solenoid Valves

Control of the fan and pump via the servo-solenoid valves was accomplished using a classic PID controller in the form

⎡ tde )( ⎤ , = , ⎢ Ppfpf )( + I eKteKKS )( + Kdtt D ⎥ (2.37) ⎣ ∫ dt ⎦

where te )( is the temperature tracking error, S , pf is 0-10 V signal sent to the valve

controlling either the pump or the fan, and K , pf is an intensity factor which can be changed to allow the effects of the controller to be more or less intense for each actuator.

Additional modifications to equation (2.37) included adding a lower saturation on the integrator to prevent integrator windup in situations where the measured temperature is well below the reference. This was necessary due to the limited control over how fast the system warms. Even with the fan off and the pump running at minimum speed (315

RPM), the heaters may take a significant amount of time (Δt = 200 sec) to bring the temperature up to the set-point. In addition, a transfer function with unity gain was used

as a low pass filter on the derivative term so that any large and high frequency rates of change due to noise in the temperature measurement were filtered out.

Solenoid Poppet Valves

The controller used on the solenoid poppet valves is the same controller presented in equation (2.37). However, poppet valves are intended to be used in an on/off fashion so it was necessary to develop a method for energizing the solenoid so that the actuators could operate at variable speeds. Initial attempts at having the valve “float” using Pulse

Width Modulation (PWM) failed. Nevertheless, it was determined that the fan speed could be controlled by using PWM and varying the duty cycle of a one Hz pulse applied to the solenoid. By varying the duty cycle, or width of the electrical pulse, the length of time that the valve is open is also varied. The longer the valve is open the higher the speed the fan can reach before the valve is closed and flow is shut off to the hydraulic motor. Furthermore, the fan’s inertia along with the addition of a check valve allowed the fan to spin freely while the valves were off. Thus, the fan speed was controlled using a

PID controller with the duty cycle of a one hertz pulse being the control signal. The upper and lower saturations for the duty cycle signal were fixed at 0% and 100% respectively.

Nevertheless, the heat load (12 kW) applied in the experimental tests only required operation in a duty cycle range of about 0%-30%. With that said, controlling the coolant pump in the same manner is not practical due to its lack of inertia. Consequently, the poppet valves providing flow to the pump’s motor were left open allowing the pump to maintain a constant speed of 600 RPM.

CHAPTER 3

EXPERIMENTAL TEST BENCH AND

ACTUATOR CHARACTERIZATION

To validate concepts and investigate control methods, an experimental setup was created. Although actual on-engine testing would be ideal, the assembled thermal test bench allowed for a controlled testing environment. Computer controlled actuators and data acquisition were used for optimal repeatability. This chapter outlines the test bench components and operation while also presenting a brief characterization of the hydraulic actuators.

Test Bench

A data acquisition system (refer to Figure 3.1) and experimental test bench (refer to Figure 3.2) have been assembled to validate the system models and control strategies in addition to performing data logging for system characterization. This system offers a flexible, rapid, repeatable, and safe testing environment. The test bench features a hydraulic-based automotive radiator fan, hydraulic-based water pump, hydraulic valves, and electric immersion heaters. Additionally, numerous sensors have been integrated to monitor the fluid temperatures, flow rates, and pressures as well as the rotational shaft speeds.

The radiator inlet (engine) and radiator outlet temperatures are measured using two K type thermocouples, while the ambient temperature is measured by a single J type thermocouple. All thermocouple signals are isolated, amplified, and linearized via Omega

OM5-LTC signal conditioners. In addition, two Monarch Instruments ROS-W optical sensors (6180-056) are responsible for measuring the rotational speed of the actuators, while a turbine flow meter (model TR-1110) from the AW Company records the coolant flow rate. Finally, Honeywell (Sensotec) A-5 pressure transducers are employed to measure the hydraulic supply and return pressures.

Data acquisition and control is accomplished using a dSPACE 1104 controller board. Analog-to-Digital Conversion (ADC) is achieved through either a single 16-bit channel which accommodates four multiplexed input signals, or one of four 12-bit channels which accommodate one input signal each. Additionally, there are 8 parallel channels available for Digital-to-Analog Conversion (DAC) as well as 20 digital input/output’s. The controller board interfaces with Matlab’s Simulink allowing for real- time execution of control strategies. The coding in Simulink is flexible allowing for implementation of C code, Matlab M-files, and Simulink block diagrams. In addition, dSPACE’s “Control Desk” software is used to set up and monitor experiments while also capturing experimental results.

Figure 3.1: Data acquisition board and computer

The experimental setup utilizes a series of 6 Temco (TSPO2084) 110 VAC immersion heater coils to heat water circulating within the system. This heat transfer process simulates that of an internal combustion engine and its associated coolant. This configuration can provide up to 12 kW of energy (6 heaters, 2 kW each) and is setup such that individual heaters may be switched on/off to provide fluctuations in the heat input.

Hydraulic Control Valves

Immersion Radiator/Fan B Heaters Assembly

Water Hydraulic Pump Motors

Figure 3.2: Experimental test bench: (a) hydraulic side; and (b) thermal side

Once heated, the water is circulated via a hydraulically driven water pump through a radiator (6.8L capacity) where forced convection is provided by a hydraulically driven fan. Both the water pump and fan are driven by hydraulic gear type motors (refer to Figure 3.4b). The centrifugal pedestal mount water pump (model # 3704-95) is from

AMT and is capable of delivering up to 58 GPM of water. It is driven by a Haldex model

4F655 hydraulic motor with a displacement of 6.36 cm3/rev, while the fan utilizes a

Haldex model 4F659 motor with a displacement of 11.65 cm3/rev. Hydraulic flow to the motors is controlled using either 2 servo-solenoid proportional control valves (BOSCH

NG 6, refer to Figure 3.3a) or 4 solenoid operated cartridge/poppet valves (Parker B09-2-

6P, refer to Figure 3.3b). The servo solenoid valves are driven by Bosch PL 6 amplifier cards which feature built in PID position control. This allows for spool displacements which are proportional to a 0-10 VDC input signal.

A B

Figure 3.3: Hydraulic flow control valves (a) Servo-solenoid valve, and (b) Solenoid cartridge/poppet valves

Supply pressure for the hydraulic components is provided through a hydraulic power unit (refer to Figure3.4a). The unit consists of a 7.5 hp Baldor industrial electric motor spinning a Bosch Hydraulic pump with a volumetric displacement per revolution of 16.39 cm3/rev. A Bosch hydro-pneumatic accumulator is used for energy storage and

two Bosch directional control valves allow separate pressure supplies to the two actuators.

A B

Figure 3.4: Hydraulic components (a) Hydraulic power unit; and (b) Hydraulic gear type motor

Actuator Characterization

Once the fabrication of the test bench was complete, some tests were executed to examine the characteristics of the hydraulic actuators when using the servo solenoid valves. In Figure 3.5, the actuator’s steady state speed at various valve positions and at different values of supply pressure has been presented. A mildly non-linear relationship has been observed between steady state actuator speeds and spool positions. Note that the fan motor may be undersized for on-vehicle applications as evident by the upper fan speed values. Nevertheless, the fan motor is sufficient for the given experimental application. Additionally, the pump reaches higher speeds than the fan at lower supply

pressures. Consequently, the pump requires less effort from the engine and in turn consumes less power. This fact may be used when designing control strategies to minimize power by intensifying the pump’s control signal and allowing it to exert more cooling effort than the fan.

1200 500 psi 750 psi 1000 1000 psi

800

600

Fan Speed (RPM) 400

200 a

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.94 1 Spool Position (x/x ) max

2000 250 psi 1800 500 psi 750 psi 1600

1400

1200

1000

800 Pump Speed (RPM) 600

400 200 b 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Spool Position (x/x ) max

Figure 3.5: Steady state actuator speeds versus valve displacements for different supply pressures. (a) Fan response for pressure supply of [3,450; 5,170; 6,890] kPa; and (b) Pump response for pressure supply of [1,720, 3,450; 5,170] kPa;

The transient actuator response to a 1 Hz sinusoidal valve input of πt)2sin(3 + 5

[VDC] is shown in Figure 3.6. It can be observed, that a small time lag, Δt = 0.08 seconds, exists for the pump while the fan displays a Δt = 0.23 second lag. This may be

2 attributed to the inertia for the fan assembly ( Jf = 1/2·M·R , M = 4.53 kg, R = 24.13 cm,

2 so that Jf = 1319 kg·cm ). In many control applications, the time lag may be significant.

However, for temperature control, this difference will probably be irrelevant due to the fact that the response for both actuators is extremely fast in relation to the system’s thermal dynamics.

1400

1200

1000

800

600 Fan Speed (RPM)

400

200 System Response a Test trajectory input in terms of fan speed 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.54 5 Time (sec)

1400

1200

1000

800

600 Pump Speed (RPM) 400

200 System Response Test trajectory input in terms of pump speed b 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec)

Figure 3.6: Actuator response to valve input of sin(3 πt)2 + 5 [Volts]. (a) Fan response for supply pressure of 6,890 kPa; and (b) Pump response for supply pressure of 3,450kPa;

CHAPTER 4

NUMERICAL AND EXPERIMENTAL RESULTS

The hydraulic and thermal system dynamic responses were simulated using the analytical models presented in Chapter 2. The experimental hydraulic driven thermal management system outlined in Chapter 3 was used to validate the set of reduced-order nonlinear mathematical models. In addition, a variety of laboratory experiments were conducted to demonstrate the performance of the integrated thermal management system components and linear control strategies from Chapter 2. This chapter presents the numerical and experimental test results.

Linearized Electro-Hydraulic Simulation Results

The differential equations developed to describe the transient response of the hydraulic system were solved numerically using Matlab/SimulinkTM. All solutions were generated using a fourth order Runge–Kutta integration method. The valve model parameters used correspond to a Bosch NG6 servo solenoid control valve. The motor modeled is a Haldex gear type motor with a volumetric displacement per revolution of

6.36 (cm3/rev). To estimate coolant temperatures, the steady state outputs from the hydraulic models were used as inputs for the radiator fan model and both heat exchanger models. The fan and heat exchanger parameters are based on the aforementioned radiator and fan assembly. The parameter values used for the simulations are shown in Table 4.1.

Table 4.1: Simulation parameter values used in the linearized electro-hydraulic and radiator models

Symbol Value Units Symbol Value Units Symbol Value Units

A 12.06 m2 K 0.011 cm4/s '' 2 m2·K/W c c R ,cf A 0.7 m2 K 494.2 cm5/(N·s) '' 2 m2·K/W fin q R ,hf 2 5 Ah 5.96 m kf 200 W/(m·K) Ri 400 (N·s)/cm 2 2 At,i 0.079 m kt 100 W/(m·K) Rw 0 m ·K/W 2 At,o 0.080 m kv 52.5 N/mm Tc,i 295.15 ˚K a 1 cm L 5.72 cm Th,i 360 ˚K Bm 0.82 N·s/cm Lf 5.72 cm TL 0 N·cm b 9.5 mm Ln 0.02 H V 10 Volts 2 bv 7 N·s/mm Ld 12.7 mm w 3.62 cm /cm Cd 0.63 - lg 1 mm ηo,c 0.5 - cp,c 1 kJ/(kg·K) ms 146 kg ηo,h 0.5 -

cp,h 4.2 kJ/(kg·K) N 1600 - θj 1.2 rad -4 2 Dh 4 mm Ps 13.8 MPa μ 3.7·10 N·s/ m 3 -7 Dm 1.01 cm /rad PT 0 kPa μ0 4.9·10 H/cm 2 3 Jf 11.3 kg·cm R 4.3 Ohms ρ 900 kg/ m

A step input of 10VDC applied to the valve solenoid with a hydraulic supply pressure of 13,790 kPa was modeled and the resulting responses are shown in Figures 4.1 through 4.3. Referring to Figure 4.1, the model predicts the valve spool to quickly reach a steady state displacement of about 3.69 mm. Correspondingly, Figure 4.2 shows the motor supply pressure quickly settling at about 1,200 kPa above half of the overall supply pressure while the motor return pressure settles about 1,200 kPa below half of the overall supply pressure. Figure 4.3 displays a steady state motor speed of approximately 1016

RPM resulting from the 10VDC input applied to the valve.

4.5

3.5

2.5

Displacement, x [mm] Displacement, 1.5

0.5

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [sec]

Figure 4.1: Hydraulic valve spool displacement for a step input of 10 VDC to the valve’s solenoid

8500

8000 Motor Supply Pressure Motor Return Pressure 7500

7000 Pressure [kPa] Pressure 6500

6000

5500 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [sec]

Figure 4.2: Hydraulic motor supply and return pressure for step response in valve spool position

1200

1000

800

600

Motor Speed [RPM] Speed Motor 400

200

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [sec]

Figure 4.3: Hydraulic motor speed for step valve input

The velocity of the air flowing across the radiator was found as a function of the hydraulic valve position and the corresponding relationship is shown in Figure 4.4. Since the motor/fan speed is proportional to the valve displacement, and the air velocity is proportional to the fan speed, the resulting relationship between valve position and air velocity is linear.

3.5

3 (m/s) a

2.5

1.5

1 Air Velocity Across Radiator, V 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Valve Spool Displacement, x (mm)

Figure 4.4: Air speed across cross flow radiator versus hydraulic valve spool position

Fluid temperatures were estimated using both the effectiveness-NTU method and

Nusselt method radiator models. Water was used as the coolant with a mass flow rate of

0.41 kg/s. The water temperature at the inlet of the radiator was fixed at 360°K. Radiator water temperatures are plotted for air velocities ranging from 0 to 4 m/s.

The effectiveness-NTU and Nusselt methods were used to predict radiator outlet temperatures for the given conditions as shown in Figure 4.5. The models predict a temperature change of approximately 9°K for the modeled hydraulic systems maximum air velocity of Va = 4 m/s. Differences in the temperature profile given by these two models can be attributed to the different approach used in each model. Specifically, the ε-

NTU method uses a lumped representation of the radiator while the Nusselt method incorporates a differential representation of the radiator.

360 ε-NTU 359 Nusselt

358 (K)

h,o 357

356

355

354

353

Coolant Outlet Temperature, T 352

351

350 0 0.5 1 1.5 2 2.5 3 3.5 4 Air Velocity, V (m/s) a

Figure 4.5: Water temperature at radiator outlet versus air speed using ε-NTU (solid) and Nusselt (dashed) methods

The Nusselt Method radiator model was used to predict temperature profiles along the length of the radiator for the given conditions. As shown in Figure 4.6, the temperature profiles are linear with a temperature drop of about 9°K for the modeled hydraulic systems maximum air velocity of Va = 4 m/s.

360 V = 1 m/s a 359 V = 2 m/s a V = 3 m/s 358 a V = 4 m/s a 357

356

355

354 Water Temperature,(K)

353

352

351 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Distance Along Radiator, (m)

Figure 4.6: Water temperature at intervals along radiator for different air velocities using Nusselt method

Nonlinear Hydraulic and Thermal Model Validation

After completion of the experimental test bench, the reduced-order nonlinear system models were validated. An experiment was created to investigate the system’s response to a step input in the hydraulic control valve. The test data obtained from this experiment was compared to the numerical results acquired from the simulated system model response. This allowed the dynamic model to be “tuned” so that its outputs adequately predicted the experimental behavior. The parameter values used in the simulations are shown in Table 4.2.

Table 4.2: Simulation parameter values used in the reduced order nonlinear hydraulic and thermal models

Symbol Value Units Symbol Value Units Symbol Value Units

3 B , fm 0.82 N·s/cm D , fm 1.85 cm /rad T , fL 0 N·cm 3 B , pm 0.15 N·s/cm D , pm 1.01 cm /rad T , pL 0 N·cm 2 3 ca 1.0057 kJ/(kg·˚C) J f 1.13 kg·cm V , ft 36,871 cm 2 3 cc 4.179 kJ/(kg·˚C) J p 0.904 kg· cm V , pt 119,626 cm 2 Cd 0.63 - P , fs 6895 kPa w 3.62 cm /cm

Ce 90.69 kJ/˚C P , ps 3447 kPa βe 689.48 MPa 5 Ri 400 (N·s)/cm Qin 12 kW ε 0.69 - 3 Cr 34.18 kJ/˚C Qout 1.054 kW ρ 900 kg/m

Fan and Pump Rotational Response

The speed of the radiator fan and water pump generated from a step input to the hydraulic control valve of 8 VDC (valve 80% open) was measured. Figure 4.7a shows the measured fan speed plotted against its simulated response, and Figure 4.7b displays the measured pump speed with its simulated response. In Figure 4.7a, it can be observed that the model does a good job in predicting the response of the radiator fan. The steady state error between the modeled fan speed and the measured fan speed is approximately 1.6%.

In Figure 4.7b, the modeled pump speed response is not as accurate as the fan’s speed response. Nevertheless, most of the deviation occurs during the transient portion and the steady state error is actually slightly more accurate for the pump (1.0%). For this study, the steady state actuator speed is much more important than the transient. This is due to the fact that the actuator’s response is on the order of twenty times faster than the

temperature response. In other words, the thermal dynamics essentially damp out fast changes in actuator speeds. Thus, the thermal response to the simulated and experimental pump behavior in Figure 4.7b would be similar.

1000

900 Measured Output Simulated Output 800

700

600

500

400 Fan Speed [RPM] Speed Fan 300

200 100 a

0 0 5 10 15 20 25 4 30 Time [sec]

1400

1200 Measured Output Simulated Output 1000

800

600 Pump Speed [RPM] 400

200 b 0 0 5 10 15 20 25 30 Time [sec]

Figure 4.7: Measured and simulated response to an 8 VDC step input to the control valve for the (a) Fan speed; and (b) Pump speed

Fan and Pump Hydraulic Pressure Response

The hydraulic load pressure for the pump and fan motor was also experimentally studied. Figure 4.8 shows the modeled load pressure along with the measured load pressure for both the fan and pump motors due to an 8 VDC step input to the control valve. The simulated response for both the fan and pump load pressures show excellent steady state correlation with the measured pressures. The steady state error in the fan response is approximately 0.3% while the steady state error in the pump response is about

0.2%. However, there are notable errors (up to 8%) in the transient portion of the pressure responses. Although these errors may be eliminated by further revising the system model, they were deemed acceptable for the purposes of this research project.

Additionally, as with the speed response, the transient portion of the pressure response is not as significant as the steady state portion due to its quickness relative to the thermal response.

3000

Measured Load Pressure 2500 Simulated Load Pressure

2000

1500

1000 Fan PressureLoad [kPa]

500 a

0 5 10 15 20 25 4 30 Time [sec]

1400

1200 Measured Load Pressure Simulated Load Pressure 1000

800

600

400 Pump Pressure Load [kPa]

200 b 0 5 10 15 20 25 30 Time [sec]

Figure 4.8: Measured and simulated response to an 8 VDC step input to the control valve for the (a) Fan load pressure; and (b) Pump load pressure

Engine and Radiator Temperatures

The system’s experimental thermal response was also observed and compared to the dynamic model. Figure 4.9 shows the engine and radiator temperature response to a step input of 8 VDC applied to both control valves with a constant heat input of 12 KW.

With the step occurring at t = 300 seconds, the first part of the plot represents a warm up condition in which the pump is running at a minimum speed (450 RPM, 2 VDC valve input) and the radiator fan is off. From Figure 4.9, it can be observed that the modeled thermal response is a good predictor of the actual system response. The maximum error for both the engine and radiator temperature is roughly 1.6°K.

335 Measured Engine Temp., T e Measured Radiator Temp., T 330 r Simulated Engine Temp., T e Simulated Radiator Temp., T r 325

320 Temperature [K] 315

310

305 0 200 400 600 800 1000 Time [sec]

Figure 4.9: Thermal response for warm-up condition and step input to the hydraulic actuators at t = 300 seconds to remove heat. (Note that the pump is operating for 0 ≤ t ≤ 300 sec @ 450 RPM)

Experimental Results for Servo-Solenoid Valves

To test the performance of the Proportional-Integral-Derivative (PID) controlled

(refer to Chapter 2) servo-solenoid valves on the hydraulic system, ten test scenarios were

studied. Table 4.3 summarizes the scenarios and results. The tests which utilize a fixed set point for the reference temperature (1,3,5,7,9) were run for Δt = 2,000 seconds

(approximately 33 minutes). The set point tests also included a warm up period in which the pump is running at minimum speed (e.g., 315 RPM) and the system is allowed to warm up to the operating temperature or set point (322°K). The tests which employ a sinusoidal reference temperature (2,4,6,8,10) were run for Δt = 3,000 seconds (50 minutes) and begin with the engine temperature at or just below its initial reference (Te ≤

322°K). The test duration, disturbance duration, and initial engine temperature were chosen to allow the system to reach steady state before, during, and after the application of the disturbance.

The air temperature within the test cell varied with the heat rejected by the radiator, but was kept within 300 ≤ T∞ ≤ 305°K for the ten tests shown in Table 4.3. The fixed set point for the engine temperature was 322°K while the sinusoidal reference

2π temperature can be described as Tref = sin11.1 (300 )+ 322 °Kt . The air velocity for the ram air disturbance was approximately 35 kph, while the heat disturbance was the equivalent of 2 heaters (2 KW a piece or 4 KW). Table 4.3 shows that the Proportional-

Integral-Derivative (PID) controlled servo-solenoid valves perform well in all ten tests.

The valves and their associated controller achieve steady state set point tracking errors below 0.2°K and steady state sinusoidal tracking errors below 1.3°K. The average power

1 T consumed was calculated by, P = ⋅+⋅ )()()()( dttQtPtQtP , where PL avg T ∫ , fL , fL , pL , pL t0

and QL are the hydraulic load pressures and flows respectively. The results for all ten tests can be found in Appendix A.

Table 4.3: Test results using Proportional-Integral-Derivative (PID) controlled servo- solenoid valves for fixed and sinusoidal temperature profiles

Test Reference Heat Disturbance Error (°K), Average Power No. Temperature , Input e(t) Consumed (W) Tref (kW) Fixed Sine Qin Heat, Ram Air, ess emax Pavg Qd = 4 kW Vram= 35 kph 1 X - 12 - - 0.15 4.8 159.13 2 - X 12 - - 1.20 4.1 160.47 3 X - 8 X - 0.17 3.9 82.18 4 - X 8 X - 1.30 3.0 95.15 5 X - 12 - X 0.20 4.7 111.18 6 - X 12 - X 1.20 4.0 134.15 7 X - 8 X X 0.20 3.6 79.94 8 - X 8 X X 1.20 3.4 84.26 9 X - 8 - - 0.18 3.4 57.64 10 - X 8 - - 1.20 4.3 72.18

Test One

Test 1 demonstrates the proposed thermal management system’s ability to track a fixed reference temperature (Tref = 322°K) with a constant heat input of Qin = 12 kW.

Figure 4.10 presents graphs for coolant temperatures, tracking error, actuator speeds, and total power consumption. It may be observed that the system and its associated controller nicely regulate the engine temperature to within 0.15°K of the set point. Note the fluctuations in the fan and pump speeds are proportional to each other. This results from

1 the controller intensity factor, K , pf , being equal for both actuators . Although this strategy may not be optimal for power minimization, it yields satisfactory temperature tracking results. Thus, some tradeoff may be established between power consumption and tracking performance.

330 1200 Set Point Temperature, T sp Fan Speed, ωf e Engine Temperature, T T e Pump Speed, ωp 325 Radiator Temperature, T 1000 r Pump 320 800 K] °

315 600 Tr Fan Temperature [ 310 400 Actuator Speed [RPM]

305 200

12 kW, 0 kph a 12 kW, 0 kph b 300 0 0 200 400 600 800 1000 1200 1400 1600 18004 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

5 250

200 0 K] °

150

-5

100 Total Power [Watts] Power Total

-10 Temperature Tracking Error [ c 50 d 12 kW, 0 kph 12 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure 4.10: Results from Test 1 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance. (a) Temperatures; (b) Actuator speeds; (c) Tracking error; and (d) Total power consumption

______

1 The PID controller gains for both actuators were, Kf , p = 0.4, KI = 0.025, KP = 0.65, and KD = 1.1

One cause of concern may be the maximum temperature error which occurs due to the engine temperature’s initial overshoot of its reference. Figure 4.11 presents the temperatures and actuator speeds for the initial Δt = 500 seconds of Test 1. In Figure

4.11a, there is approximately a Δt = 15 second delay between the engine temperature reaching its set point (t = 200 sec) and the activation of the radiator fan (t = 215 sec).

This delay is caused by integrator wind up in the Proportional-Integral-Derivative (PID) controller. Though its effect may be minimized by adding saturations to the integrator, it is an inherent limitation of the controller and one cause for the initial (4.8°K) overshoot of the reference temperature.

In addition, the engine temperature, Te, is not affected by the cooling system until the radiator temperature, Tr, is cooled to at least 8°K below Te. For Test 1, this takes about Δt = 15 seconds and is accompanied by a 2.5°K increase in the engine temperature which only adds to the overshoot. Even so, this behavior may be eliminated by incorporating a thermostat valve into the system. A thermostat valve would allow the coolant to circulate within the engine during warm up without affecting the radiator temperature. Thus, when the fan and pump are activated and coolant begins to flow through the radiator, it should immediately begin to decrease the engine temperature.

330

325 a 4

320 K] °

315 Temperature [ 310

Set Point Temperature, T 305 sp Engine Temperature, T e Radiator Temperature, T r 300 0 50 100 150 200 250 300 350 400 450 500 Time [Sec]

1200 Fan Speed, ωf b Pump Speed, ω 1000 p 4

800

600

400 Actuator Speed [RPM]

200

0 0 50 100 150 200 250 300 350 400 450 500 Time [Sec]

Figure 4.11: Initial Δt = 500 sec of Test 1 to display details of the (a) Coolant temperatures; and (b) Actuator speeds

Test Eight

Test 8 presents a scenario in which a combined heat (4 kW) and ram air (35 kph) disturbance is applied to the system for 1,000 ≤ t ≤ 3,000 seconds and the desired

temperature profile is sinusoidal. In Figure 4.12a, the controller readily rejects the disturbances while maintaining the engine temperature within 2.5°K of the reference.

Figure 4.12b shows the power consumption increase (~ 45 W) during the application of the disturbance. This result may be attributed to the heat disturbance adding more heat than the ram air can reject. Thus, the actuators must exert more effort (i.e., consume power) to maintain the desired temperature profile.

330 1200 Fan Speed ωf a Te b Pump Speed ω 325 1000 p

320 800 Pump K] °

315 600

Tr Sinusoidal Reference, T Temperature [ ref 310 400 Engine Temperature, T Actuator Speed [RPM] e Radiator Temperature, T r Fan 305 200

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

5 250 c d 200 0 K] °

150

-5

100 Total Power [Watts] Power Total

-10 Temperature Tracking Error [ 50

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure 4.12: Results from Test 8 with a sinusoidal engine reference temperature, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph. (a) Temperatures; (b) Actuator speeds; (c) Tracking error; and (d) Total power consumption

Experimental Results for Solenoid Poppet Valves

The ten tests presented in Table 4.3 were repeated using Proportional-Integral-

Derivative (PID) controlled2 solenoid poppet valves to regulate flow to the hydraulic motors. The results are shown in Table 4.4 Tests 11-20. It can be observed that the poppet valves perform well for certain test profiles (fixed reference and maximum heat) while offering only adequate performance in others (sinusoidal and reduced heat). The poppet valves and their associated controller allow steady state set point tracking errors up to 2.48°K and steady state sinusoidal tracking errors of up to 3.47°K.

Table 4.4: Test results using Proportional-Integral-Derivative (PID) controlled solenoid poppet valves for fixed and sinusoidal temperature profiles

Test Reference Heat Disturbance Error (°K), Average Power No. Temperature , Input e(t) Consumed (W) Tref (kW) Fixed Sine Qin Heat, Ram Air, ess emax Pavg Qd = 4 kW Vram= 35 kph 11 X - 12 - - 0.19 3.8 122.52 12 - X 12 - - 2.20 4.1 127.89 13 X - 8 X - 2.42 2.5 74.64 14 - X 8 X - 3.40 4.6 100.07 15 X - 12 - X 0.40 3.8 93.36 16 - X 12 - X 2.42 4.6 113.12 17 X - 8 X X 2.40 2.6 69.35 18 - X 8 X X 3.37 3.6 88.29 19 X - 8 - - 2.48 2.5 65.85 20 - X 8 - - 3.47 3.6 83.74

______

2 -4 The PID controller gains used for the fan were, Kf , p = 1, KI = 7.6·10 , KP = 0.02, and KD = 0.04

Test Eleven

Test 11 parallels Test 1 in the previous section. It demonstrates the poppet valves’ ability to track a fixed reference temperature with a constant heat input of 12 kW. For this test profile, the poppet vales offer comparable performance to the servo-valves. In fact, comparing the results to Test 1 in Table 4.3, it can be shown that the maximum error and average power consumption have been reduced. Note that in Figure 4.13b there is an upper and lower bound plotted for the fan speed. This is a result of the control method used with the poppet valves. Opening the valves at a rate of 1 Hz causes the fan to operate in a band of approximately 250 RPM. Varying the duty cycle, or length of time for which the valves are open, effectively moves the band up or down in the RPM range.

A larger duty cycle corresponds to a higher speed, while a smaller duty cycle corresponds to a lower speed.

Further examinations of Figure 4.13b, as well as the corresponding plot for the servo valve testing (Figure 4.10b), reveals that the reduction in power consumption is most likely due to the pump running at a constant speed. The pump speed for the servo valve system operates at speeds around 800 RPM while the pump speed for the poppet valve system is held at a constant 600 RPM. Additionally, the average fan speed for the poppet valve system (553 RPM) appears to be slightly lower than the fan speeds reached by the servo-valve system (600 RPM). Thus, it appears that the fan can efficiently control the engine temperature without the added effort from the pump.

330 1200 Set Point Temperature, T sp Fan Speed (Upper Bound) Engine Temperature, T Te e Fan Speed (Lower Bound) 325 Radiator Temperature, T 1000 Pump Speed r

320 800 K] ° Fan Upper

315 600 Pump Tr Temperature [ 310 400 Actuator Speed [RPM] Fan Lower 305 a 200 b 12 kW, 0 kph 12 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 18004 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

5 250

200 0 K] °

150

-5

100

-10 [Watts] Power Total Average Temperature Tracking Error [ 50 c d 12 kW, 0 kph 12 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure 4.13: Results from Test 11 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin= 12 kW, and no disturbance. (a) Temperatures; (b) Actuator speeds with upper and lower fan bounds; (c) Tracking error; and (d) Average total power consumption

Test Nineteen

The two main deficiencies of the poppet valves in comparison to the servo- solenoid valves are their tendency to overcool and their sensitivity to error in temperature measurement. The overcooling effect is demonstrated in the results from Test 19 shown in Figure 4.14. In Figure 4.14, it may be observed that once the fan is activated it eventually cools the engine below its set point and cuts off (t = 510 sec). Subsequently,

the radiator must warm to within 2°K of the engine before the engine temperature will begin to rise back to its set point. At this point (t = 600 sec), the fan is again activated and the cycle repeats itself.

330 1200

Te 8 kW, 0 kph 325 1000 a b Fan Speed (Upper Bound) Fan Speed (Lower Bound) 320 4 800 Pump Speed K] ° Pump 315 600

r Set Point Temperature, T T sp Temperature [ Engine Temperature, T Fan 310 e 400 Actuator Speed [RPM] Radiator Temperature, T r

305 200

8 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

5 250 c d 200 0 K] °

150

-5

100

-10 [Watts] Power Total Average Temperature Tracking Error [ 50

8 kW, 0 kph 8 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure 4.14: Results from Test 19 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance. (a) Temperatures; (b) Actuator speeds with upper and lower fan bounds; (c) Tracking error; and (d) Average total power consumption

Two factors were identified that may be influencing the overcooling behavior.

The first is the absence of a thermostat valve. As previously mentioned, integration of a

thermostat would allow part of the coolant flow to bypass the radiator. This would permit the engine to warm without the associated increase in radiator temperature. The second deals with the control strategy. In Figure 4.14, it appears that the problem could be reduced, or possibly eliminated, by reducing the proportional gain or increasing the derivative gain in the controller. However, further investigation revealed that the control signal was only operating in the lowest portion of its range. In other words, the shortest pulse detectable by the valves was allowing fan speeds of up to 350 RPM. This coupled with the fact that the pump speed is maintained at a constant 600 RPM was causing the system to overcool with only minimal control effort.

The second deficiency mentioned was sensitivity to temperature measurement error. Since the control signal for the fan is the percentage or fraction of a second for which the poppet valves are activated, noise or small fluctuations in the input signal tend to have a large affect on the fan speed. This attribute (sensitivity to noise) limited the amount of derivative action which could be applied to the controller. Too much derivative action allowed the effects of noise in the temperature measurement to be seen in the control signal and as a result decreased system performance. Thus, a significant phase lag was present when attempting to track a sinusoidal reference using the poppet valves (refer to Figure 4.15). Note that a low pass filter (transfer function with unity gain) was used to reduce noise in the temperature signal while the derivative controller signal was also filtered.

330

325 K]

° 320

315 Temperature [

Sinusoidal Reference, T 310 ref Engine Temperature, T e Radiator Temperature T r 305 0 500 1000 1500 2000 2500 3000 Time [Sec]

Figure 4.15: Phase lag in temperature tracking from Test 12

CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

This chapter summarizes the research that has been completed and includes conclusions which were drawn to illustrate the findings of the project. In addition, this section provides guidance and contains recommendations for future work.

Conclusions

A hydraulic-actuator based thermal management system has been developed and implemented to successfully control engine coolant temperatures. System performance was demonstrated by a variety of experimental tests. The results obtained from these tests show that to achieve optimal performance, cost-effectiveness may be compromised.

Initially, mathematical models and control strategies were developed to simulate the thermal management system and to control engine coolant temperatures, respectively.

A test bench was built which featured hydraulic actuated components and electrical immersion heaters to emulate an engine’s heat of combustion. The test bench was used to experimentally validate mathematical models and study the performance of two types of hydraulic control valves.

The two types of hydraulic flow control valves used to control actuator speeds were servo-solenoid and solenoid poppet valves. The servo-solenoid valves displayed excellent temperature tracking for both fixed and sinusoidal temperature profiles; however, the increased cost of the valves may limit practicality. The solenoid poppet valves exhibited satisfactory performance for certain test profiles, while displaying

limited performance in others. While cost-effective, the practicality of these valves will be determined by the allowable error in engine temperature control.

Recommendations

Future laboratory testing should be done in a temperature controlled environment so that ambient temperatures can be chosen and maintained throughout test durations.

This would create a more realistic testing environment while also allowing tests to be executed at extreme ambient temperatures (i.e. desert and arctic climates). Additionally, a thermostat valve should be integrated to allow for quick warm-up times and to prevent overcooling. Although temperature tracking improvements may be achieved with a traditional wax-based thermostat valve, a controllable “smart” valve would likely yield the best results by allowing computer control over the amount of coolant flow through the engine and radiator.

Furthermore, the increased temperature tracking performance of modern model- based control methods should be investigated. A model-based controller should be capable of predicting and compensating for future changes in the system states. This would eliminate the lag associated with classical controllers. Nevertheless, performance will ultimately depend on the accuracy of the model. The most favorable experimental scenario would include integration of a hydraulic actuated thermal management system on an actual vehicle. Testing could be done to compare the power consumption and temperature tracking abilities of traditional cooling systems to those of hydraulically actuated systems. A direct comparison should clarify the advantages and disadvantages of traditional and hydraulic-based thermal management systems.

APPENDICES

Appendix A

Servo-Solenoid Valve Test Results

330 1200 Set Point Temperature, T sp Fan Speed, ωf Engine Temperature, T e Pump Speed, ωp 325 Radiator Temperature, T 1000 Engine r Pump 320 800 K] °

315 Radiator 600 Fan Speed [RPM] Temperature [ 310 400

305 200

12 kW, 0 kph 12 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

12 kW, 0 kph 12 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200 1000 Fan

150 800 Pump 600 100 Power [Watts] Power Pressure [kPa] Pressure

400

50 200 12 kW, 0 kph 12 kW, 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure A.1: Results from Test 1 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance.

330 1200 Fan Speed ωf Pump Speed ω 325 Engine 1000 Pump p

320 800 K] °

315 600 Sinusoidal Reference, T Radiator ref Speed [RPM]

Temperature [ Engine Temperature, T 310 e 400 Fan Radiator Temperature, T r

305 200

12 kW, 0 kph 12 kW, 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0.4 K] ° -5 0.3 Error [

0.2 Coolant Flow [kg/sec]

-10

0.1

12 kW, 0 kph 12 kW, 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 Pump Load Pressure, P 250 L,p Fan Fan Load Pressure, P 1200 L,f

200 1000

800 150

600 Power [Watts] Power

Pressure [kPa] Pressure Pump 100

400

50 200 12 kW, 0 kph 12 kW, 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure A.2: Results from Test 2 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , constant heat input, Qin = 12 kW, and no disturbance.

330 1200 Set Point Temperature, T sp Fan Speed, ωf Engine Temperature, T e Pump Speed, ωp 325 Radiator Temperature, T 1000 Engine r Pump 320 800 K] °

315 600 Radiator Speed [RPM] Temperature [ 310 400

305 200 Fan

8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000

150 800 Pump

600 100 Power [Watts] Power Pressure [kPa] Pressure

400 Fan

50 200 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure A.3: Results from Test 3 with a fixed engine reference temperature, Tref = 322°K, and heat disturbance, Qd = 4 kW.

330 1200 Fan Speed ωf Pump Speed ω 325 1000 p Engine Pump

320 800 K] °

315 600

Sinusoidal Reference, T [RPM] Speed Radiator ref Temperature [ 310 Engine Temperature, T 400 e Radiator Temperature, T r 305 200 Fan 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0.4 K] ° -5 0.3 Error [

0.2 Coolant Flow [kg/sec]

-10

0.1

8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f Fan 200 1000

150 800 Pump

600 100 Power [Watts] Power Pressure [kPa] Pressure

400

50 200 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure A.4: Results from Test 4 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 + 322 °Kt , and heat disturbance, Qd = 4 kW.

330 1200 Set Point Temperature, T sp Fan Speed, ωf Engine Temperature, T e Pump Speed, ωp 325 Radiator Temperature, T 1000 Engine r

320 800 K]

° Pump

315 Radiator 600 Speed [RPM]

Temperature [ Fan 310 400

305 200

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000 Fan

150 800 Pump 600 100 Power [Watts] Power Pressure [kPa] Pressure

400

50 200 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure A.5: Results from Test 5 with a fixed engine reference temperature, Tref = 322°K, and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed ωf Pump Speed ω 325 Engine 1000 p Pump 320 800 K] °

315 600 Radiator

Sinusoidal Reference, T [RPM] Speed ref Temperature [ 310 Engine Temperature, T 400 e Fan Radiator Temperature, T r 305 200

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0.4 K] ° -5 0.3 Error [

0.2 Coolant Flow [kg/sec]

-10

0.1

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f Fan 200 1000

150 800

600 100 Power [Watts] Power Pressure [kPa] Pressure Pump 400

50 200 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure A.6: Results from Test 6 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , and ram air disturbance, Vram = 35 kph.

330 1200 Set Point Temperature, T sp Fan Speed, ωf Engine Temperature, T e Pump Speed, ωp 325 Radiator Temperature, T 1000 Engine r

320 800 K]

° Pump 315 Radiator 600 Speed [RPM] Temperature [ 310 400 Fan 305 200

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000

150 800 Pump 600 100 Power [Watts] Power Pressure [kPa] Pressure Fan 400

50 200 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure A.7: Results from Test 7 with a fixed engine reference temperature, Tref = 322°K, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed ωf Pump Speed ω 325 Engine 1000 p

320 800 Pump K] °

315 600

Sinusoidal Reference, T Radiator ref Temperature [ 310 Engine Temperature, T 400 e Actuator Speed [RPM] Radiator Temperature, T r 305 200 Fan 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000

150 800 Pump

600 100 Pressure [kPa] Pressure Total Power [Watts] Power Total 400 Fan 50 200 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure A.8: Results from Test 8 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 + 322 °Kt , heat disturbance, Qd = 4 kW,

and ram air disturbance, Vram = 35 kph.

330 1200 Set Point Temperature, T sp Fan Speed, ωf Engine Temperature, T e Pump Speed, ωp 325 Radiator Temperature, T 1000 Engine r

320 800 K] °

315 600 Radiator Pump Temperature [ 310 400 Actuator Speed [RPM]

305 200 Fan

8 kW, 0 kph 8 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 kW, 0 kph 8 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000

150 800 Pump 600 100 Pressure [kPa] Pressure

Fan [Watts] Power Total 400

50 200 8 kW, 0 kph 8 kW, 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure A.9: Results from Test 9 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance.

330 1200 Fan Speed ωf Pump Speed ω 325 Engine 1000 p

320 800 K] ° Pump 315 600 Radiator Speed [RPM] Temperature [ 310 Sinusoidal Reference, T 400 ref Engine Temperature, T e Radiator Temperature, T 305 r 200 Fan

8 kW, 0 kph 8 kW, 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0.4 K] ° -5 0.3 Error [

0.2 Coolant Flow [kg/sec]

-10

0.1

8 kW, 0 kph 8 kW, 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000 Pump 150 800

600 100 Power [Watts] Power Pressure [kPa] Pressure

400 Fan 50 200 8 kW, 0 kph 8 kW, 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure A.10: Results from Test 10 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , constant heat input, Qin = 8 kW, and no disturbance.

Appendix B

Solenoid Poppet Valve Test Results

330 1200 Set Point Temperature, T sp Fan Speed (Upper Bound) Engine Temperature, T e Fan Speed (Lower Bound) 325 Radiator Temperature, T 1000 Pump Speed Engine r

320 800 K] ° Fan Upper

315 600 Radiator Pump Temperature [ 310 400 Actuator Speed [RPM] Fan Lower

305 200

12 kW, 0 kph 12 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

12 kW, 0 kph 12 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000 Fan

150 800

600 Pump 100 Pressure [kPa] Pressure

400 Average Total Power [Watts] 50 200 12 kW, 0 kph 12 kW, 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure B.1: Results from Test 11 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 12 kW, and no disturbance.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 Fan Upper K] °

315 600

Radiator Sinusoidal Reference, T ref Speed [RPM]

Temperature [ Engine Temperature, T 310 e 400 Radiator Temperature T r 305 200 Fan Lower

12 kW, 0 kph 12 kW, 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

12 kW, 0 kph 12 kW, 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

50 200 12 kW, 0 kph 12 kW, 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure B.2: Results from Test 12 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , constant heat input, Qin = 12 kW, and no disturbance.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] ° Pump 315 600 Radiator Set Point Temperature, T sp

Engine Temperature, T Speed [RPM] Temperature [ e Fan 310 400 Radiator Temperature, T r

305 200

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

Figure B.3: Results from Test 13 with a fixed engine reference temperature, Tref = 322°K, and heat disturbance, Qd = 4 kW.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] °

315 600 Radiator

Sinusoidal Reference, T Speed [RPM] Temperature [ ref 310 400 Engine Temperature, T e Radiator Temperature T r 305 200

8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

50 200 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 0 kph 8 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure B.4: Results from Test 14 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 + 322 °Kt , and heat disturbance, Qd = 4 kW.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] °

315 600 Pump

Radiator Set Point Temperature, T

sp Speed [RPM] Temperature [ Engine Temperature, T 310 e 400 Radiator Temperature, T Fan r

305 200

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

Figure B.5: Results from Test 15 with a fixed engine reference temperature, Tref = 322°K, and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] °

315 600 Radiator Sinusoidal Reference, T ref Speed [RPM]

Temperature [ Engine Temperature, T 310 e 400 Radiator Temperature T r

305 200

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

50 200 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 12 (kW), 0 kph 12 (kW), 35 kph 12 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure B.6: Results from Test 16 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] ° Pump 315 Radiator 600

Set Point Temperature, T Speed [RPM] sp Temperature [ Fan 310 Engine Temperature, T 400 e Radiator Temperature, T r 305 200

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

Figure B.7: Results from Test 17 with a fixed engine reference temperature, Tref = 322°K, heat disturbance, Qd = 4 kW, and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] °

315 600 Radiator

Sinusoidal Reference, T Speed [RPM] ref Temperature [ 310 Engine Temperature, T 400 e Radiator Temperature T r 305 200

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

50 200 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 8 (kW), 0 kph 12 (kW), 35 kph 8 (kW), 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure B.8: Results from Test 18 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 + 322 °Kt , heat disturbance, Qd = 4 kW,

and ram air disturbance, Vram = 35 kph.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] ° Pump 315 Radiator 600

Set Point Temperature, T

Temperature [ sp 310 400

Engine Temperature, T Actuator Speed [RPM] e Fan Radiator Temperature, T r 305 200

8 kW, 0 kph 8 kW, 0 kph 300 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 kW, 0 kph 8 kW, 0 kph -15 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Total Power [Watts] 50 200 8 kW, 0 kph 8 kW, 0 kph 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time [Sec] Time [Sec]

Figure B.9: Results from Test 19 with a fixed engine reference temperature, Tref = 322°K, constant heat input, Qin = 8 kW, and no disturbance.

330 1200 Fan Speed (Upper Bound) Fan Speed (Lower Bound) 325 Engine 1000 Pump Speed

320 800 K] °

315 Radiator 600 Sinusoidal Reference, T ref Speed [RPM]

Temperature [ Engine Temperature, T 310 e 400 Radiator Temperature T r

305 200

8 kW, 0 kph 8 kW, 0 kph 300 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

0.5

0 K] ° 0.4

-5 0.3

0.2 Coolant Flow [kg/sec]

-10 Temperature Tracking Error [

0.1

8 kW, 0 kph 8 kW, 0 kph -15 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

1400 250 Pump Load Pressure, P L,p Avg. Fan Load Pressure, P 1200 L,f 200

1000

150 800

600 100 Pressure [kPa] Pressure

400 Average Power [Watts]

50 200 8 kW, 0 kph 8 kW, 0 kph 0 0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 Time [Sec] Time [Sec]

Figure B.10: Results from Test 20 with a sinusoidal engine reference temperature, 2π Tref = sin11.1 ()300 322 °+ Kt , constant heat input, Qin = 8 kW, and no disturbance.

Appendix C

Matlab/SimulinkTM Modeling Algorithms

Linearized Electro-Hydraulic Model

v oltageSolenoid Force Fsol PL x x PL V PL Solenoid dynamics QL QL PL Thetadot omega Input Voltage Spool dynamics si m o u t Valve flow Motor dynamics QL T o Wo rksp a ce x

Figure C.1: Linearized electro-hydraulic model, 1st level

1 Voltage Current current Opening f orce 1 voltage Solenoid Force Subsystem Subsystem1

V 1 i 1 1/L 1 s Voltage Current Inductance

Resistance Subsystem

2 1 u 1/4 N^2 mu a 1/l_g 1 current Opening force Current Squared Constant Coils Squared permeability "a" gap Subsystem1

Figure C.2: Solenoid dynamics, 2nd and 3rd levels

x 1

ks x

s 1

level xdot nd s 1 bs

zterm zterm zdot term

zdot term flow 1

flow 2

(P_s-P_ms) 1/M_s (P_mr-P_t) |u|

Abs |u| Abs1

Figure C.3: Spool dynamics, 2

P_s P_t 1 Fsol

Subsystem1 Subsystem PL P_mr

PL P_ms

2 PL

1 |u| 2*rho sq rt l*C_d*w 1 (P_s-P_ms) zdot term

2 C_d*w cos(phi) 2 zterm

Figure C.4: Solenoid dynamics, flow 1, 3rd level

1 |u| 2*rho sq rt l*C_d*w 1 (P_mr-P_t) zdot term

2 C_d*w cos(phi) 2 zterm

Figure C.5: Solenoid dynamics, flow 2, 3rd level

1 kq 1 x QL

2 kc PL

Figure C.6: Valve flow, 2nd level

1 1 (4*Beta)/Vt Cim QL s 1 PL

PL Thetadot 2 Thetadot D_m Rotation

Figure C.7: Motor dynamics, 2nd level

1 Thetadot

1 D_m 1 1 PL 1/Jm s s

Bm G Tl

Figure C.8: Rotation, 3rd level

Linearized Electro-Hydraulic Model M-file

% This Program gives the inputs for the model of the Bosch NG 6 % solenoid controlled servo valve clear all clc t_f = 5;

%%%%%%%%%%%%%%%%%%%%%%%% SOLENOID CONSTANTS %%%%%%%%%%%%%%%%%%%%%%%%%%% V=10; % Supply Voltage (Volts) L=0.02; % Coil inductance (H) R=4.3; % Coil Resistance (Ohms) N=1600; % Number of coil turns mu=4*pi*10^-7; % Solenoid armature permeability (Henries/inch) a=.394; % Solenoid contact length (in) l_g=0.0393; % Reluctance gap (in)

%%%%%%%%%%%%%%%%%%%%%% VALVE/SPOOL CONSTANTS %%%%%%%%%%%%%%%%%%%%%%%%%% C_d=0.61; % contraction/flow coefficient w=1.963; % (guess) Area gradient of orifice(in^2/in) M_s=10; % (estimate from Gamble pg 124) Mass of the spool (lbm) bs= 40; % (estimate from Gamble pg 124)spool damping (lbs*s/in) ks= 300; % (estimate from Gamble pg 124)spool spring constant (lbs/in) phi=69*pi/180; % flow angle (rad) l=.5; % distance between lands (in)

%%%%%%%%%%%%%%%%%%%%%%%%% FLUID PROPERTIES %%%%%%%%%%%%%%%%%%%%%%%%%%%% rho=0.03251; % fluid density (lbm/in^3) Beta=2.2*10^5; % Bulk modulus (lbs/in^2) mu2=2*10^-6; % absolute viscosity (lb*s/in^2)

%%%%%%%%%%%%%%%%%%%%%%%%%% PUMP CONSTANTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%% P_s = 2000; % Supply Pressure (psi) P_t=0; % Return (tank) pressure (lb/in^2)

%%%%%%%%%%%%%%%%%%%%%%%%% Motor Constants %%%%%%%%%%%%%%%%%%%%%%%%%%%%% kq=0.07*C_d*w*sqrt(P_s/rho) % (guess) valve flow gain kc=0.07*pi*w*.0002^2/(32*mu2) % (guess) valve flow pressure coefficient Vt = 2250; % Total compressed volume (in^3) Cim =1/9506.97; % Internal motor leakage coefficient (in^5/(lb*s)); D_m=.388/(2*pi); % Motor Displacement (in^3/rad) Jm =.01; % Motor Inertia Bm = 0.47; % Motor Damping G=0; % Motor Spring Coefficent Tl=0; % Torque Load on motor %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sim('Valveloadedit',t_f); PL=simout(:,1);

Speed=simout(:,2).*2.5; QL=simout(:,3); z=simout(:,4); speed = Speed./(2*pi); %%%%%%%%%%%%%%%%%%%%%%%%%%% PLOTTING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% rpm = speed*60; figure plot(tout,rpm) grid on % title('Motor Speed vs. Time') xlabel('Time [sec]') ylabel('Motor Speed [RPM]') x_mm = z.*25.4; figure plot(tout,x_mm) % title('Spool Position vs. Time') grid on xlabel('Time [sec]') ylabel('Displacement, x [mm]')

P_s_kpa = P_s.*6.894757; PL_kpa = PL.*6.894757; P_ms_kpa=(P_s_kpa+PL_kpa)./2; P_mr_kpa=(P_s_kpa-PL_kpa)./2;

P_ms=(P_s+PL)./2; P_mr=(P_s-PL)./2; figure plot(tout, P_ms_kpa,'--',tout,P_mr_kpa) grid on xlabel('Time [sec]') ylabel('Pressure [kPa]') legend('Motor Supply Pressure','Motor Return Pressure')

Nonlinear Hydraulic and Thermal System Model

Te Control Signal si m o u t Tr Step T o Wo rksp a ce Plant

Figure C.9: Nonlinear hydraulic and thermal system model, 1st level

Fan Dynamics

Thetadot PL PL Thetadot_f xv_f Thetadot_f m_dot_a 1 Flow fan Rotation fan air flow Te Te

1 m_dot_a Tr m_dot_w Control Signal Thermal dynamics RADIATOR Pump Dynamics 2 Tr Thetadot Tr PL PL Thetadot_p Te xv_p Thetadot_p m_dot_w m_dot_w Flow pump Rotation pump Thermal dynamics coolant flow ENGINE

Figure C.10: Plant, 2nd level

2 xv_f

Product Cd*w sq rt 1/rho P_s_f

Math Ps Function

1 2*beta_f/Vt_f 1 1 Dm_f s PL PL Thetadot Integrator

Cim

Figure C.11: Flow, fan and pump, 3rd level

1 Thetadot_f

1 Dm_f 1 1/Jm_f PL s

TL Bm_f

Figure C.12: Rotation, fan and pump, 3rd level

m_dot_air 1 1/(2*pi) 0.2 3.28084 rho_a*A_r 1 Thetadot_f m_dot_a (rad/s) m/s ft/s Hz ft/s1

Figure C.13: Air flow, 3rd level

m_dot_water 1 60/(2*pi) 0.01124 0.002228 rho_w 1 Thetadot_p m_dot_w (rad/s) RPM gpm ft^3/s

1.6749

Figure C.14: Coolant flow, 3rd level

1 Tr Tr_dot 1 Tr 1/C_r cp_w Qo s Integrator Gain Gain1 Product

1 3 Te m_dot_w

e*cp_a

Tinf Gain2 Product1 Constant1 2 m_dot_a

Figure C.15: Radiator thermal dynamics, 3rd level

1 Te

2 m_dot_w Te_dot 1 Te Qin 1/C_e cp_w s Product Qin Gain1 Integrator 1 Gain Tr

Figure C.16: Engine thermal dynamics, 3rd level

Nonlinear Hydraulic and Thermal System Model M-file

% This m-file simulates the Hydraulic and Thermal Model clear all clc T_ref = 130; Te_o = 70; Tr_o = 70; %%% final time %%% tf = 1350; %%%%%%%%%%%%%%%%%%%%%%%%%% Valve %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% xv_max = 0.11811; % max valve displacement (in) or 3 mm stepv = 0.8*xv_max; % equivalent of 8 VDC step input

%%%%%%%%%%%%%%%%%% Constant Parameters (fan) %%%%%%%%%%%%%%%%%%%%%%%%%% P_s_f = 1000; % Supply Pressure (psi) Dm_f = 0.711/(2*pi); % Motor Displacement (in^3/rad) TL = 0; % Load Torque (in*lb) Cd = 0.63; % Discharge Coefficient (-) w = 3.35*0.425; % Area Gradient (in^2/in) rho = 0.03251; % fluid density (lbm/in^3) Cim =1/9506.97; % (1/Ri) Internal motor leakage coefficient (in^5/(lb*s)); beta_f = 100000; %Bulk Modulus (psi) Vt_f = 2250; % Total Compressed Volume (in^3) Jm_f =.001; % Fan Inertia (lb*in*s^2) Bm_f = 0.47; % Fan Damping(lb*s/in)

%%%%%%%%%%%%%%%%%% Constant Parameters (pump) %%%%%%%%%%%%%%%%%%%%%%%%% P_s_p = 500; % Supply Pressure (psi) Dm_p = 0.388/(2*pi); %.388/(2*pi); % Motor Displacement (in^3/rad) TL = 0; % Load Torque (in*lb) Cd = 0.63; % Discharge Coefficient (-) w = 3.35*0.425; % Area Gradient (in^2/in) rho = 0.03251; % fluid density (lbm/in^3) Cim =1/9506.97; % (1/Ri) Internal motor leakage coefficient (in^5/(lb*s)); beta_p = 100000; % Bulk Modulus (psi) Vt_p = 7300; % Total Compressed Volume (in^3) Jm_p = 0.0008;% Pump Inertia (lb*in*s^2) Bm_p = 0.084; % Pump Damping (lb*s/in)

%%%%%%%%%%%%%%%%%%%%%%%% Thermal Parameters %%%%%%%%%%%%%%%%%%%%%%%%%%% C_r = 18; %53; % Thermal Capacity of Radiator(BTU/F) C_e = 51; %428; % Thermal Capacity of Engine (BTU/F) Qo = 1; % Heat lost due to random air flow (BTU/s) Qin = 10.7; %11.38; % Heat input from heaters (BTU/s) rho_a = 0.06243; % Density of Air (lbm/ft^3) rho_w = 62.43; % Density of Water (lbm/ft^3) cp_a = 0.25; % Specific Heat of Air (BTU/(lbm*F)) cp_w = 1; % Specific Heat of Water (BTU/(lbm*F))

Tinf = 78; % Ambient Air Temperature (F)

%%%%%%%%%%%%%%%%%%%%%%%%% Radiator Parameters %%%%%%%%%%%%%%%%%%%%%%%%% A_r = 4.1; % frontal area of radiator (ft^2) e = 0.69; % radiator efficiency (-)

%%%%%%%%%%%%%%%%% Simulate Nonlinear model using ode45 %%%%%%%%%%%%%%%% sim('controlsimulation',tf); Te = simout(:,1); Tr = simout(:,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Plotting %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% load temp_step_2 y1 = temp_step_2.Y(3).Data; y2 = temp_step_2.Y(4).Data; x = temp_step_2.X.Data; x = x - 200; % shift data back 200 seconds tout = tout - 200; % shift results back 200 seconds y1 = (y1 + 459.67)./1.8; y2 = (y2 + 459.67)./1.8; Te = (Te + 459.67)./1.8; Tr = (Tr + 459.67)./1.8;

figure plot(x,y1,x,y2,'--',tout,Te,'-.',tout,Tr,':') grid on xlim([0 1150]) xlabel('Time [sec]') ylabel('Temperature [K]') legend('Measured Engine Temp., T_e','Measured Radiator Temp., T_r',... 'Simulated Engine Temp., T_e','Simulated Radiator Temp., T_r')

Appendix D

Matlab/SimulinkTM Control Algorithms

Servo-Solenoid Valve Control

RTI Data

T_erorr Fan Sig

Bosch Valve Control

RPM acquire fan

Fan Sig

Hydraulic pump Valves

Pressure Reading

Error Temperature Sensing/Flowrate 120

Set Point

RPM acquire pump Sine Wave Tref

Figure D.1: Servo-solenoid valve control, 1st level

0.025 1 fan s 0.4 1/10 Bad Link K_I Integrator Saturation1 DS1104DAC_C5 Kf DS Gain

1 0.65 1 T_erorr Fan Sig K_p

Fan Signal

0.6 pump 1.1 du/dt 0.4 1/10 Bad Link 0.6s+0.6 Transfer Fcn4 Saturation DS1104DAC_C6 K_d Kp DS Gain1

Pump Signal

Figure D.2: Bosch valve control, 2nd level

Hz 0

Hz-F

Bad Link double 5 Signal RPM 0

RPM-F DS1104BIT_IN_C15 Data Type Conversion Gain Period 0

Period-F Frequency Couting Fan

Display

Figure D.3: RPM acquire fan and pump, 2nd level

if(u1 < 2.5) u1 1 10 else Signal Gain If else { } if { } In1 A In1 Out1 Subsys 2 Read A 1 In2 1 u Hz Out2 Invert A B 0 In3 Data Store Data Store 60 2 Clock Subsys 1 Memory Memory2 RPM Gain1 3 Period

Figure D.4: Frequency counting fan and pump, 3rd level

if { }

Action Port

1 u1if(u1 > 2.5) In1 If1

if { }

3 In1 Out1 1 In3 Out1

B In2 Out2 2 Out2 Read B Subsys 1a

2 A In2 Write A

Figure D.5: Subsystem 1, 4th level

if { }

Action Port 1 1 In1 Out1 B

Write B 2 2 In2 Out2

Figure D.6: Subsystem 1a, 5th level

fan 1 1/2 boolean Bad Link

Data Type Conversion Gain _DS1104BIT_OUT_C1 1 Fan Sig pump Sign 1 Bad Link

Valve 2 s1 DS1104BIT_OUT_C3

0 Bad Link

Valve 1 s2 DS1104BIT_OUT_C2

0 Bad Link

Valve 2 s2 DS1104BIT_OUT_C4

Figure D.7: Hydraulic pump valves, 2nd level

Fmr

.5 Bad Link 10 400 .5s+.5 DS1104ADC_C5 Transfer Fcn Gain Gain2 Scope_C5

Fms .5 Bad Link 10 400 .5s+.5 DS1104ADC_C6 Transfer Fcn1 Gain1 Gain3 Scope_C6

Pms .5 Bad Link 10 400 .5s+.5 DS1104ADC_C7 Transfer Fcn2 Gain4 Gain6 Scope_C7

Pmr .5 Bad Link 10 400 .5s+.5 DS1104ADC_C8 Transfer Fcn3 Gain5 Gain7 Scope_C8

Figure D.8: Pressure reading, 2nd level

1 Te

(F) Tamb

Tr (F)

(F) Te 32 9/5 Constant3 flowrate F Conversion2

32 9/5 Tamb (C) Tamb Constant Conversion F 32

9/5 3 Constant1

F Conversion1 Constant2 (C) Tr level level

nd DS Gain5 Radiator Temp Radiator 27/10 2 ,

Temperature Ambient Te (C) Temp Engine

100 Conversion

rate /flow 100 g 10

Gain4 DS 80 100

10 Conversion2 DS Gain DS Conversion1

10 10

Gain2 DS Gain1 DS erature sensin p

0.6

0.6s+0.6 Fcn Transfer 0.6

0.6 0.6 0.6s+0.6 0.6s+0.6 0.6s+0.6 Transfer Fcn2 Transfer ure D.9: Tem Transfer Fcn1 Transfer Fcn4 Transfer g Fi

Bad Link Bad DS1104MUX_ADC

Solenoid Poppet Valve Control

RTI Data

T_erorr

Valve Control

RPM acquire fan

Hydraulic pump valves

Pressure Reading

Temperature Sensing/flowrate Error 120

Set Point

RPM acquire pump Tdes Sine Wave

Figure D.10: Solenoid poppet valve control, 1st level

100

clock

Clock 1/10 1/20 Bad Link

1 DS Gain4 amp gain DS1104DAC_C1 f

12 u0 MyPWM y0 emu PWM amp Duty Cycle

1 0.00076 s

K_I Integrator

Saturation 1 0.02 T_erorr K_p DC_signal

0.6 0.04 du/dt pump 0.6s+0.6 12 1/10 Bad Link K_d Derivative Constant LPF DS Gain1 DS1104DAC_C6

Figure D.11: Valve control, 2nd level

fan 1 Bad Link

Valve 1 s1 _DS1104BIT_OUT_C1

0 Bad Link

Valve 1 s2 DS1104BIT_OUT_C2

pump 1 Bad Link

Valve 2 s1 DS1104BIT_OUT_C3

0 Bad Link Valve 2 s2 DS1104BIT_OUT_C4

Figure D.12: Hydraulic pump valves, 2nd level

101

C Code Used in MyPWM S-function

double t, f, amp, dc, n, T, V;

t = u0[0]; f = u0[1]; amp = u0[2]; dc = u0[3]; n = u0[4];

T = 1/f;

if (fmod(t, T) == 0.00) {n = t/T;}

if (t <= (dc * T + n * T)) {V = amp;} else {V = 0;}

y0[0] = V; y0[1] = n;

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Appendix E

Empirical Regressions

14 y = 0.0114x

6 Air Velocity [kph] Air Velocity

0 0 200 400 600 800 1000 1200 1400 Fan Speed [RPM]

Figure E.1: Linear regression for air velocity versus fan speed

14 y = 0.01124x - 1.67494

6 Coolant Flow [GPM]

0 0 200 400 600 800 1000 1200 1400 1600 Pump Speed [RPM]

Figure E.2: Linear regression for coolant flow versus pump speed

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