From Linear to Nonlinear Control Means: a Practical Progression
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Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors Wei-Ping Huang University of Vermont
University of Vermont ScholarWorks @ UVM Graduate College Dissertations and Theses Dissertations and Theses 2018 Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors Wei-Ping Huang University of Vermont Follow this and additional works at: https://scholarworks.uvm.edu/graddis Part of the Electrical and Electronics Commons Recommended Citation Huang, Wei-Ping, "Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors" (2018). Graduate College Dissertations and Theses. 967. https://scholarworks.uvm.edu/graddis/967 This Thesis is brought to you for free and open access by the Dissertations and Theses at ScholarWorks @ UVM. It has been accepted for inclusion in Graduate College Dissertations and Theses by an authorized administrator of ScholarWorks @ UVM. For more information, please contact [email protected]. Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors A Thesis Presented by Wei-Ping Huang to The Faculty of the Graduate College of The University of Vermont In Partial Fulfillment of the Requirements for the Degree of Master of Science Specializing in Electrical Engineering October, 2018 Defense Date: July 25th, 2018 Thesis Examination Committee: Hamid R. Ossareh, Ph.D., Advisor Eric M. Hernandez, Ph.D., Chairperson Jeff Frolik, Ph.D. Cynthia J. Forehand, Ph.D., Dean of Graduate College Abstract This thesis investigates Quasilinear Control (QLC) of time-delay systems with non- linear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. -
Applying Classical Control Theory to an Airplane Flap Model on Real Physical Hardware
Applying Classical Control Theory to an Airplane Flap Model on Real Physical Hardware Edgar Collado Alvarez, BSIE, EIT, Janice Valentin, Jonathan Holguino ME.ME in Design and Controls Polytechnic University of Puerto Rico, [email protected],, [email protected], [email protected] Mentor: Prof. Bernardo Restrepo, Ph.D, PE in Aerospace and Controls Polytechnic University of Puerto Rico Hato Rey Campus, [email protected] Abstract — For the trimester of Winter -14 at Polytechnic University of Puerto Rico, the course Applied Control Systems was offered to students interested in further development and integration in the area of Control Engineering. Students were required to develop a control system utilizing a microprocessor as the controlling hardware. An Arduino Mega board was chosen as the microprocessor for the job. Integration of different mechanical, electrical, and electromechanical parts such as potentiometers, sensors, servo motors, etc., with the microprocessor were the main focus in developing the physical model to be controlled. This paper details the development of one of these control system projects applied to an airplane flap. After physically constructing and integrating additional parts, control was programmed in Simulink environment and further downloads to the microprocessor. MATLAB’s System Identification Tool was used to model the physical system’s transfer function based on input and output data from the physical plant. Tested control types utilized for system performance improvement were proportional (P) and proportional-integrative (PI) control. Key Words — embedded control systems, proportional integrative (PI) control, MATLAB, Simulink, Arduino. I. INTRODUCTION II. FIRST PHASE - POTENTIOMETER AND SERVO MOTOR CONTROL During the master’s course of Mechanical and Aerospace Control System, students were interested in The team started in the development of a potentiometer and developing real-world models with physical components servo motor control circuit. -
Control System Design Methods
Christiansen-Sec.19.qxd 06:08:2004 6:43 PM Page 19.1 The Electronics Engineers' Handbook, 5th Edition McGraw-Hill, Section 19, pp. 19.1-19.30, 2005. SECTION 19 CONTROL SYSTEMS Control is used to modify the behavior of a system so it behaves in a specific desirable way over time. For example, we may want the speed of a car on the highway to remain as close as possible to 60 miles per hour in spite of possible hills or adverse wind; or we may want an aircraft to follow a desired altitude, heading, and velocity profile independent of wind gusts; or we may want the temperature and pressure in a reactor vessel in a chemical process plant to be maintained at desired levels. All these are being accomplished today by control methods and the above are examples of what automatic control systems are designed to do, without human intervention. Control is used whenever quantities such as speed, altitude, temperature, or voltage must be made to behave in some desirable way over time. This section provides an introduction to control system design methods. P.A., Z.G. In This Section: CHAPTER 19.1 CONTROL SYSTEM DESIGN 19.3 INTRODUCTION 19.3 Proportional-Integral-Derivative Control 19.3 The Role of Control Theory 19.4 MATHEMATICAL DESCRIPTIONS 19.4 Linear Differential Equations 19.4 State Variable Descriptions 19.5 Transfer Functions 19.7 Frequency Response 19.9 ANALYSIS OF DYNAMICAL BEHAVIOR 19.10 System Response, Modes and Stability 19.10 Response of First and Second Order Systems 19.11 Transient Response Performance Specifications for a Second Order -
Graphical Control Tools to Design Control Systems
Advances in Engineering Research, volume 141 5th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering (ICMMCCE 2017) Graphical Control Tools to Design Control Systems Huanan Liu1,a, , Shujian Zhao1,b, and Dongmin Yu 1,c,* 1 Department of Electrical Engineering, Northeast Electric Power University, Jilin 132012, China a [email protected], b [email protected], c [email protected], *corresponding author: Dongmin Yu email:[email protected] Keywords: Root Locus; Frequency Tools; Bode Diagram; Nyquist Diagram Abstract: Engineers are sometimes asked to analyze the feasibility of existing control systems or design a new system. The conventional analysis and design methods heavily depend on mathematical calculation. In order to minimize calculation, graphical control is proposed. This paper aims to introduce three different graphical control tools (Root Locus, Bode diagram and Nyquist diagram) and then use these tools to analyze and design the control system. Finally, some realistic case studies are used to compare the advantages and disadvantages of graphical tools. The innovation of this paper is adding hand-drawn graphical control to greatly reduce the calculation complexity 1. List of Symbols -1 Ts-settling time (s) ߞ-damping ratio ߱n-natural frequency (rad.s ) %OS-percentage of overshoot Ess-steady state error K-gain of the system Z1, Z2-zeros of the system P1, P2-poles of the system Tp-peak time (s) M-magnitude of the phasor Φ-phase angle of phasor (degrees) Θ-angle of asymptote Z-the number of closed loop poles P-the number of open- loop poles N- the number of counter clockwise rotation PM-phase margin (degrees) GM-gain margin h1, h2- feedback coefficient 2. -
Classical Control of the Neutral Point in 4-Wire 3-Phase DC-AC Converters
Electrical Power Quality and Utilisation, Journal Vol. XI, No. 2, 2005 Classical Control of the Neutral Point in 4-wire 3-phase DC-AC Converters Q.-C. ZHONG 1), L. HOBSON 2), M.G. JAYNE 2) 1) The University of Liverpool, UK; 2) University of Glamorgan, UK Summary: In this paper, the classical control techniques are applied to the neutral point in a Key words: 3-phase 4-wire DC-AC power converter. The converter is intended to be connected to 3-phase DC/AC power converter, 4-wire loads and/or the power grid. The neutral point can be steadily regulated by a simple neutral leg, controller, involving in voltage and current feedback, even when the three-phase converter 3-phase 4-wire systems, system (mostly, the load) is extremely unbalanced. The achievable performance is analyzed split DC link quantitatively and the parameters of the neutral leg are determined. Simulations show that the proposed theory is very effective. 1. INTRODUCTION vector modulation control [7] for this topology is available. Comparing this topology to the split DC link, the neutral point is more stable and the output voltage is about 15% For various reasons, there is today a proliferation of small higher (using the same DC link voltage). However, the power generating units which are connected to the power additional neutral leg cannot be independently controlled to grid at the low-voltage end. Some of these units use maintain the neutral point and, hence, the corresponding synchronous generators, but most use DC or variable control design (including the PWM waveform generating frequency generators coupled with electronic power converters. -
A Review of Transient and Steady State Response of DC Motor Position Control
International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 06, June-2015 A Review of Transient and Steady State Response of DC Motor Position Control Khushboo Sao Dr. Dharmendra Kumar Singh M. Tech Scholer HOD Department of Electrical & Electronics Engineering Dr. C. V. Raman University Department of Electrical & Electronics Engineering Bilaspur, India Dr. C. V. Raman University Bilaspur, India Abstract— The goal of this project is to design an filter and at times both. The ultimate end goal is to meet a electric drive with a dc motor, with the required angular requirement set typically provided in the time-domain called position controlled in two regimes in the given desired reference the Step response, or at times in the frequency domain called command signal . In our practical world we have to use a lot of the Open-Loop response. controlling process in industry or any engineering section. So, it The step response characteristics applied in a does vary initiative attempt to design a control drive in corresponding to our practical field. Modern manufacturing specification are typically percent overshoot, settling time, systems are automated machines that perform the required etc. The open-loop response characteristics applied in a tasks. The electric motors are perhaps the most widely used specification are typically Gain and Phase margin and energy converters in the modern machine-tools and robots. bandwidth. These characteristics may be evaluated through These motors require automatic control of their main simulation including a dynamic model of the system under parameters (position, speed, acceleration, currents). In this case control coupled with the compensation model [3]. -
Classical Control Theory
Classical Control Theory: A Course in the Linear Mathematics of Systems and Control Efthimios Kappos University of Sheffield, School of Mathematics and Statistics January 16, 2002 2 Contents Preface 7 1 Introduction: Systems and Control 9 1.1 Systems and their control . 9 1.2 The Development of Control Theory . 12 1.3 The Aims of Control . 14 1.4 Exercises . 15 2 Linear Differential Equations and The Laplace Transform 17 2.1 Introduction . 17 2.1.1 First and Second-Order Equations . 17 2.1.2 Higher-Order Equations and Linear System Models . 20 2.2 The Laplace Transform Method . 22 2.2.1 Properties of the Laplace Transform . 24 2.2.2 Solving Linear Differential Equations . 28 2.3 Partial Fractions Expansions . 32 2.3.1 Polynomials and Factorizations . 32 2.3.2 The Partial Fractions Expansion Theorem . 33 2.4 Summary . 38 2.5 Appendix: Table of Laplace Transform Pairs . 39 2.6 Exercises . 40 3 Transfer Functions and Feedback Systems in the Complex s-Domain 43 3.1 Linear Systems as Transfer Functions . 43 3.2 Impulse and Step Responses . 45 3.3 Feedback Control (Closed-Loop) Systems . 47 3.3.1 Constant Feedback . 49 4 CONTENTS 3.3.2 Other Control Configurations . 51 3.4 The Sensitivity Function . 52 3.5 Summary . 57 3.6 Exercises . 58 4 Stability and the Routh-Hurwitz Criterion 59 4.1 Introduction . 59 4.2 The Routh-Hurwitz Table and Stability Criterion . 60 4.3 The General Routh-Hurwitz Criterion . 63 4.3.1 Degenerate or Singular Cases . 64 4.4 Application to the Stability of Feedback Systems . -
Stability Analysis of BLDC Motor Drive Based on Input Shaping
M.Murugan et.al / International Journal of Engineering and Technology (IJET) Stability Analysis of BLDC Motor Drive based on Input Shaping M.Murugan#1, R.Jeyabharath*2 and P.Veena*2 ∗ Assistant Professor, Department of Electrical & Electronics Engineering, K.S.Rangasamy College of Technology,Tiruchengode, TamilNadu, India ; email: {[email protected]} # Professor, Department of Electrical & Electronics Engineering, K.S.R. Institute for Engineering & Technology,Tiruchengode, TamilNadu, India Abstract: The main objective of this work is to analyze the brushless DC (BLDC) motor drive system with input shaping using classical control theory. In this paper, different values of damping ratio are used to understand the generalized drive performance. The transient response of the BLDC motor drive system is analyzed using time response analysis. The dynamic behaviour and steady state performance of the BLDC motor drive system is judged and compared by its steady state error to various standard test signals. The relative stability of this drive system is determined by Bode Plot. These analysis spotlights that it is possible to obtain a finite-time setting response without oscillation in BLDC motor drive by applying input in four steps of different amplitude to the drive system. These analyses are helpful to design a precise speed control system and current control system for BLDC motor drive with fast response. The Matlab/Simulink software is used to perform the simulation. Keywords: BLDC Motor, Input Shaping, Precise Speed Control Nomenclature: r Vqs : q-axis equivalent stator voltage in volts r iqs : q-axis equivalent stator current in amps Ls : Equivalent stator self-inductance in henry Rs : Equivalent stator winding resistance in ohms P : Number of poles of motor TL : Load torque of motor in N-m Bm : Motor viscous friction coefficient in N-m/rad/sec 2 Jm : Rotor inertia of motor in Kg-m ω r : Angular speed of rotor in mechanical rad/ sec Te : Electromechanical Torque in N-m A : Amplitude of Step input I. -
Control Theory
Control theory This article is about control theory in engineering. For 1 Overview control theory in linguistics, see control (linguistics). For control theory in psychology and sociology, see control theory (sociology) and Perceptual control theory. Control theory is an interdisciplinary branch of engi- Smooth nonlinear trajectory planning with linear quadratic Gaussian feedback (LQR) control on a dual pendula system. Control theory is The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is subtracted from the desired value to create the error signal, • a theory that deals with influencing the behavior of which is amplified by the controller. dynamical systems • an interdisciplinary subfield of science, which orig- inated in engineering and mathematics, and evolved neering and mathematics that deals with the behavior of into use by the social sciences, such as economics, dynamical systems with inputs, and how their behavior psychology, sociology, criminology and in the is modified by feedback. The usual objective of con- financial system. trol theory is to control a system, often called the plant, so its output follows a desired control signal, called the Control systems may be thought of as having four func- reference, which may be a fixed or changing value. To do tions: measure, compare, compute and correct. These this a controller is designed, which monitors the output four functions are completed by five elements: detector, and compares it with the reference. The difference be- transducer, transmitter, controller and final control ele- tween actual and desired output, called the error signal, ment. -
Quantum Control Theory and Applications: a Survey
Quantum control theory and applications: A survey ∗† Daoyi Dong ,‡ Ian R. Petersen§ 9 January, 2011 Abstract: This paper presents a survey on quantum control theory and applica- tions from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several con- trol design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed- loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control. Key words: quantum control, controllability, coherent control, incoherent control, feedback control, robust control. 1 Introduction Quantum control theory is a rapidly evolving research area, which has developed over the last three decades [1]-[9]. Controlling quantum phenomena has been an implicit goal of much quantum physics and chemistry research since the establishment of quan- tum mechanics [5], [6]. One of the main goals in quantum control theory is to establish a firm theoretical footing and develop a series of systematic methods for the active manipulation and control of quantum systems [7]. This goal is nontrivial since mi- croscopic quantum systems have many unique characteristics (e.g., entanglement and arXiv:0910.2350v3 [quant-ph] 10 Jan 2011 coherence) which do not occur in classical mechanical systems and the dynamics of quantum systems must be described by quantum theory. -
Control Theory Tutorial Basic Concepts Illustrated
SPRINGER BRIEFS IN APPLIED SCIENCES AND TECHNOLOGY Steven A. Frank Control Theory Tutorial Basic Concepts Illustrated by Software Examples SpringerBriefs in Applied Sciences and Technology SpringerBriefs present concise summaries of cutting-edge research and practical applications across a wide spectrum of fields. Featuring compact volumes of 50– 125 pages, the series covers a range of content from professional to academic. Typical publications can be: • A timely report of state-of-the art methods • An introduction to or a manual for the application of mathematical or computer techniques • A bridge between new research results, as published in journal articles • A snapshot of a hot or emerging topic • An in-depth case study • A presentation of core concepts that students must understand in order to make independent contributions SpringerBriefs are characterized by fast, global electronic dissemination, standard publishing contracts, standardized manuscript preparation and formatting guidelines, and expedited production schedules. On the one hand, SpringerBriefs in Applied Sciences and Technology are devoted to the publication of fundamentals and applications within the different classical engineering disciplines as well as in interdisciplinary fields that recently emerged between these areas. On the other hand, as the boundary separating fundamental research and applied technology is more and more dissolving, this series is particularly open to trans-disciplinary topics between fundamental science and engineering. Indexed by EI-Compendex, -
Linear Control Theory 2001
References Wonham Linear Multivariable Control – A Geometric Approach, Summer School 3rd edition, Springer Verlag, 1985. on Time Delay Equations and Control Theory Dobbiaco, June 25–29 2001 Basile and Marro Controlled and Conditioned Invariants in Linear Sys- tem Theory, Prentice Hall, 1992 Trentelman, Stoorvogel and Hautus Control Theory for Linear Systems, Springer Verlag, Linear Control Theory 2001 Giovanni MARRO∗, Domenico PRATTICHIZZO‡ Early References Basile and Marro Controlled and Conditioned Invariant Subspaces in Linear System Theory, Journal of Optimization The- ∗DEIS, University of Bologna, Italy ory and Applications, vol. 3, n. 5, 1969. ‡DII, University of Siena, Italy Wonham and Morse Decoupling and Pole Assignment in Linear Multivari- able Systems: a Geometric Approach, SIAM Journal on Control, vol. 8, n. 1, 1970. d Introduction to Control Problems u Σ y Consider the following figure that includes a controlled system (plant) Σ and a controller Σr, with a feedback part Σ and a feedforward part Σ . c f Σr rp e d1 d2 Fig. 1.2. A reduced block diagram. + rp r e u y1 Σf + Σc + Σ _ y2 In the above figure d := {d1,d2}, y := {y1,y2,d1}. Σr All the symbols in the figure denote signals,repre- sentable by real vectors varying in time. The plant Σ is given and the controller Σr is to be Fig. 1.1. A general block diagram for regulation. designed to (possibly) maintain e(·)=0. Both the plant and the controller are assumed to be linear (zero state and superposition property). • rp previewed reference The blocks represent oriented systems (inputs, out- • r reference puts), that are assumed to be causal.