A Motor Feedback Demonstration Model for a Control Systems Class

Andrew L. Wallner, Student Member, AES, Student Member, IEEE

 A. Open vs. Closed Loop Systems Abstract—In the educational context of control systems study, If, in an open-loop system, a device is expected to produce it is useful to provide tangible models of discussed concepts. One a particular output given a certain input, the system can of the most typical applications of feedback control system theory is that of tachometer-feedback motor speed control. A small perform in an unsatisfactory way if an internal or external scale model can be implemented within a moderate budget using force interrupts the device’s operation unbeknownst to the readily available analog components. The design, construction, controller. A closed loop system does a better job of operation, and performance of one such system are discussed achieving the expected operation. It does so by informing the here. controller of the device’s actual operation, and therefore allows it to perform appropriate controlling actions to I. INTRODUCTION maintain the expected performance. HE intent of this project is to investigate an application of Tcontrol system theory and to describe its implementation INSTRUCTION CONTROLLER OPERATION in a small scale motor speed control system. The implemented system is to be used as a model for individual experimentation (a) or classroom demonstration. The design of the system is open-ended to allow further study of control system theory ADJUSTABLE OPERATION and development of the presented model design. Investigation CONTROLLER into the operation of the model design can provide a practical INSTRUCTION example of electronic control circuitry and gives exposure to VERIFICATION OF PERFORMANCE factors involved in the realization of the abstracted system concepts. (b)

Fig. 1. Block diagrams of control systems: (a) open-loop, (b) closed-loop.

In closed-loop systems, the process of performance measurement and subsequent controller adjustment is itself an adjustable process. This sub-process determines how the controller responds to deviation reported by the fed-back measurement, the performance verification signal. Usually, the characteristics of this response are built or programmed into the system before operation. B. Feedback Modes Feedback can be positive or negative. Positive feedback is, generally, unstable. It increases the effects of measured Fig. 1. a small motor/ flywheel assembly with an optical tachometer. deviation in a compounding way; as an operation deviates, positive feedback will cause it to deviate more. This is what happens when a microphone is turned up too far. The sound II. CONTROL THEORY of a lecturer’s voice is amplified so much that the sound Even at the risk of being simplistic, it is important to emanating from the public address system is picked up by the mention the overall goal of a control system. Figure 1 microphone again and again, until the system reaches its contains diagrams of open and closed-loop control systems. loudest possible volume. This happens at the first deviating The purpose of a closed loop system, such as a tachometer- frequency, and then usually at harmonics of that tone, feedback motor control, is to maintain an expected resulting in the ringing sound that is for many people the performance from an operating device. definition of feedback. Negative feedback promotes stability. As an operating process deviates, the feedback is used to A. L. Wallner is an engineering student at Calvin College in Grand Rapids, MI 49546 USA (e-mail: [email protected]). decrease the extent of the deviation. A good control system 2 employing negative feedback should be able to maintain an proportional negative feedback is implemented. The practical instructed operation even when the operating process is design has inherent elements of integral and derivative gain to affected by some form of disturbance. provide system stability, but does not have any user-adjustable Feedback characteristics comprise the majority of control ID parameters. However, the system is designed to system design [1]. The most basic form of feedback is linear. accommodate the future addition of ID circuitry. Both fuzzy Linear feedback applies a percentage of the system output, and neural controls require computer processors, so inverted, to attenuate a portion of the system input and implementation of such devices would distractingly increase compensate for the detected deviation. This arrangement the model’s complexity. works well, but reduces the magnitude of the process output since it is always held in check by the compensating signal. III. SYSTEM CONCEPT Greater amounts of feedback yield more control, but at the The basic design for the system was shown on a schematic cost of reduced output. presented for analytical evaluation as an in-class example of a C. P.I.D. Control linear-feedback control system. It consists of four major functional blocks, the variable power supply, the motor and More sophisticated topologies apply a feedback signal that load, the velocity measurement, and the regulation circuitry. is not just merely a proportion of the output. Such feedback signals are generated based on the absolute magnitude, A. Operation of Example System (integrated) output, and also from the rate of change (the The system presented was a design that used a linear power derivative) of the output. By using combinations of these amplifier for power adjustment and a generator connected to signals, a system can be designed that recovers from the motor output to produce a feedback signal. disturbances in almost any desired way. Using a combination power disturbance of proportional, integral, and derivative (PID) signals, it is reference output possible to control the three possible response errors: 1.) + MOTOR LOAD overshoot, the over-correction in response to the detected T3 T1/T2 error, 2.) settling time, how quickly the output returns to the - (power adjustment) expected value, 3.) steady state error, the difference between POTENTIOMETER GENERATOR the desired value and the actual, stabilized output. This also allows the use of feedback without a reduction in output Fig. 1. Block diagram of a generator feedback motor speed control system. magnitude. It is important to note two things: 1.) corrections to the three error modes are not directly related to the three The schematic also included a power rectification circuit to PID parameters, and 2.) PID control can also be used to allow the low voltage dc system to operate from a standard regulate open loop systems, though without the benefit of 240v ac mains. The power amplifier was a cascaded power disturbance correction. transistor pair controlled by a regulating signal transistor. The D. Advanced Control Methods signal transistor was in a common-emitter configuration and, in response to the current produced by the generator, would It is the interdependence of the amount of each PID sink the power transistors’ reference current to ground, thus parameter on system response that has given the task of tuning implementing negative feedback. PID controls the reputation of being more of an art than science. For these reasons, automated means of adjusting PID B. Conceptual Motivation loops have become very popular. An extension of this It was desirable to assemble a similar circuit. Apparently, convenience has been the development of fuzzy logic controls such a demonstration system is available for purchase, but at a and neural-net controls. Both of these approaches seek to prohibitive expense. The simplicity of the design suggested optimize controller operation through examination of long- that it should be easily reproduced in a moderately-equipped term trends. Fuzzy logic implements a guess-and-check electronics lab. When components were searched for, it system for specific parameter controls with is defining proved to be less convenient to identically reproduce the characteristic being the consideration of a parameter’s degree presented system. There were three factors that motivated the of accuracy [2]. It keeps track of trends, and makes new decision to seek a different design: 1.) a suitably matched guesses if the trends are approaching an undesirable condition. motor / generator pair was not found, 2.) appropriate bi-polar Neural nets are an extension of this idea. They differ in their power transistors were not available in-house, and 3.) it was “learning” capability. Rather than merely iterating desirable to demonstrate a system topology that better depicts parameters, neural nets can create new combinations of current trends in circuit design. parameters to evaluate [3]. For both of these technologies, It was decided to design a system that uses pulse-width system commissioning is greatly simplified when compared to modulation (PWM) to adjust the power delivered to the motor PID loops, as it requires only “teaching” rather than precise and a non-contact tachometer to measure the rotational speed measurement and manual adjustment. Both of these can of the motor output. These decisions directly addressed the respond to the situation and take action based on expected motivating design factors in the following ways: 1.) a non- results. contact tachometer eliminates the need for a generator, 2.) In the demonstration project presented here, only 3 available power MOSFET transistors can be used, and 3.) will be operated in a laboratory setting connected to a PWM is one of the most common methods of power protected and regulated power source. The motor drive circuit adjustment used in recent designs. This design approach also is robust and can withstand continuous operation. reflects current trends in system development; specifically, the C. Power Adjustment Circuit growth in system complexity. The availability of inexpensive modules permits systems of greater complexity, and offers The current amplifier stage of the original circuit is greater design flexibility and control. replaced by a voltage-controlled PWM driver connected to a MOSFET switch. The pulse width modulation varies the duty IV. SYSTEM DESIGN cycle of a carrier signal to the MOSFET switch. The switch delivers full-voltage power to the motor for a period of time After consideration of the important characteristics of the determined by the modulated carrier signal. original example system, it was determined that any proposed 1) Pulse-Width Modulation design must contain the following: 1.) a motor driven by a In a PWM system, if a carrier signal modulated to have a variable power supply, 2.) a motor speed sensor, and 3.) a 100% duty cycle will trigger a MOSFET to connect the motor (reference) – (feedback) controller input. The design must to the supply voltage constantly. If the carrier is modulated to also be able to be used in a classroom or laboratory setting 50%, the switch will be closed for only half of the carrier with commonly available test equipment. Based on these signal period and, as power is time dependant (power in Watts requirements and the other motivating factors, the system = Joules / second), the motor will receive half as much power. presented here was developed. It follows, that the carrier frequency has no apparent effect on A. Overview the long-term power delivered to the motor, but is important in Figure 2 depicts the functional blocks of the system. These speed regulation. correlate directly to the functions of the original example Consider a small dc motor with a low-inertia load that takes system, with the exception of the reference adjustment, which 1 second to reach full speed; it is connected to a PWM supply. is an additional feature of the new design. As will be The carrier frequency is .01 Hz and the duty cycle is 50%. discussed later, this new system is voltage controlled—a The motor will run for 50 seconds, and be stationary for another 50 seconds. It is true that the power delivered to the subtle difference from the original current-controlled circuit. motor is half of what it could have received in the 100 second power disturbance cycle, but the speed of the motor in operation was not reference output voltage + (speed) affected. Consider the same arrangement, but with a carrier PWM MOTOR LOAD frequency of 100 Hz. In 0.05 sec. (half the carrier period), the adjustment - motor is nowhere near full operating speed. In the next 0.05 feedback OPTICAL sec. (the “off” portion of the duty cycle), the motor slows TACHOMETER somewhat, but has enough inertia to keep turning. In the next adjustment cycle, another pulse of power is delivered, but not enough for the motor to reach full speed. Within a few cycles, the speed Fig. 2. Block diagram of an optical tachometer-feedback motor speed control will center about a certain value. If the frequency of the system with pulse-width modulator (PWM) power adjustment. carrier is high enough, its inverse, the period of consecutive The functionality of each of these blocks is realized largely pulses will be short enough that the irregular power delivered through the use of integrated circuits. This increase in system to the motor will not result in irregular motion. Because the complexity is the most noticeable compromise in comparison increments of power from one pulse to the next are small, they to the original design. It is possible that the increased do not overcome the inertia maintaining the motor’s speed. complexity can detract from the transparency of the design, For successful PWM speed regulation, the carrier that is, it may be less obvious how the system operates, but if frequency should be as high a possible. Limitations on the the system is examined as an assembly, it is obviously similar upper limit of carrier frequency include signal generation and to the original. conveyance, but the most common limitation is inability of a motor coil to pass a high frequency signal. When applied to a B. Power Supply motor, high frequency components that cannot make a While the schematic of the original design had provision complete circuit constructively interfere within the coils and for connection to ac line power, this design calls for produce high voltage transients that can damage insulation. connection to a regulated dc supply. The control circuit is This is called reflected-wave phenomenon and is of concern to presently configured for connection to +/- 15 volts and the designers of variable-frequency motor drives, a technology motor supply can be from the same source, or a separate dc that employs a similar modulated switching technique. supply with a shared ground. With minimal modification, the The design presented here uses a carrier frequency of motor drive circuit could be isolated from the control circuitry, 1000Hz. if it was to be used with a different motor-supply combination. 2) PWM implementation No over-current, over-voltage, or polarity protection devices For this system, a PWM controller is realized with three are incorporated in the design. It is expected that this system main devices: 1.) the carrier frequency generator, 2.) the 4 voltage-to-duty-cycle modulator, and 3.) the power switching unit. The carrier generator is simply a multivibrator created with a 555 timer IC. It produces a steady 1000Hz square wave. The device used was a Texas Instruments NE555. A schematic from the corresponding data sheet [5] is shown, modified, in the left half of Fig. 3. The frequency and duty cycle are a function of resistor and capacitor values; they are calculated below in (1) and (2), respectively. 1.44 Fig. 4. Schematic of MOSFET power switch circuit with motor. fc   1005Hz (1) (RA  2  RB ) CC D. Motor Assembly R DC  1 B  50.4% (2) The motor selected is a permanent magnet dc motor. It is a R  2 R A B high-quality rotary actuator that has published performance characteristics. This sophistication is not mandatory for the Where: RA  1.1k, RB  68k,C  10nF design’s operation, but can be useful for comparison of a theoretical analysis with empirical testing. The model chosen is from the Canon Precision FN30S series [6]. The load connected to the motor is a simple flywheel. The wheel is a solid aluminum cylinder measured to have a 25.4cm diameter, a 12.7mm length, and a 4mm, axially concentric hole. It also has a threaded hole that accommodates a #4-40 x ¼” socket- head set-screw in perpendicular orientation to the concentric hole. The end of the wheel that is not directed toward the motor has two finishes. One half of its surface area is a semi- circle of the smooth, bare aluminum. The other half is covered with a non-reflective finish. This gives the optical Fig. 3. Schematic of carrier signal generator (U1), a 555 timer configured for tachometer a target for counting revolutions. astable (clock) operation, and the VC-PWM (U2), a 555 timer configured for duty cycle modulation. E. Optical Tachometer The voltage-to-duty-cycle modulator function is The optical tachometer provides a way of detecting rotation accomplished with a second 555 timer. It varies the duty of the flywheel without damping its mechanical energy. It cycle of its square wave output proportionately to the counts rotations by sensing light reflected off of the wheel’s amplitude of the voltage present at the modulation input. The end. It is comprised of four major components: 1.) the photo- frequency of the cycles is that of the signal applied to the detector, 2.) the pulse shaper, 3.) the frequency-to-voltage clock input from the carrier generator. This circuit, also converter, and 4.) the output buffer. modified from the TI data sheet, is shown in the right half of 1) Photo-detector Fig. 3. The photo-detector is a diffuse light-reflection sensor. For 3) Power Switching its operation, a red LED is used to illuminate the target to be The final stage of the PWM is simply a high-speed switch sensed. Light reflecting off the target is detected by a photo- used to toggle the motor’s connection to the power source. Its diode oriented symmetrically to the incident angle of the LED. major component is a MOSFET transistor. For this The photodiode, which appeared to be a somewhat standard application, an International Rectifier IRF130 was used. (though unmarked), component worked suitably to detect the Many other power MOSFETs would be equally suitable red wavelengths. For maximum sensitivity, the diode is used devices, and possibly less over-qualified. The `130 is rated at in an unbiased “photovoltaic mode” [7]. This arrangement 14A and up to 100V, so no heat-sink was required for this works by sensing the voltage produced by photons “pushing” design. Since all MOSFETS are susceptible to damage caused electrons across the diode’s p-n junction. This highly by reverse-bias voltages, a diode is connected between the sensitive configuration has inherent signal bandwidth drain and source of the transistor to divert transient over- limitations, but the charge-carrier propagation time does not voltages to the power source and parallel buffer capacitor. limit performance in the present application. The circuit is shown in Fig. 4. The voltage produce by the incident red light is on the order of 0.01-0.1mV. This voltage is amplified by an LF366 JFET input operational amplifier. The JFET input preamp presents a high impedance load and a minimally interfering bias current to the delicate signal produced by the photodiode. As diagrammed in Fig. 5., it was determined that using a 10 5 mega ohm feedback resistor produces output voltages near F. Controller 0V when the diode was subjected to ambient light and about The controller delivers the duty cycle instruction signal to 2V when exposed to moderate amounts of red light. the PWM motor drive. It synthesizes this signal from a reference signal and the feedback loop. All three signals are dc voltages and it is required that the feedback signal be subtracted from the reference signal, so this function is realized with a direct-coupled unity-gain difference amplifier. Another LM 301 op-amp is used for this purpose. The reference signal is the voltage that corresponds to the desired motor speed. This voltage is obtained from the positive Fig. 5. Schematic of photo-detector and preamp. voltage supply with a potentiometer voltage divider. The feedback signal is also adjustable with a similar mechanism. 2) Pulse shaper The reference voltage selected with the potentiometer is The output of the photo-detector preamp provides a applied to the non-inverting input of the difference amp and somewhat inconsistent analog waveform. A pulse shaper is the selected feedback signal is applied to the inverting input. used to create square digital pulses. This function is The output to the PWM drive is then the (reference) – accomplished with an LM193 voltage comparator. The (feedback) signal. comparator is set to produce full-voltage pulses when the preamp’s output increases above a threshold slightly higher V. ANALYSIS that the noise floor. A limited amount of hysteresis is incorporated to reduce false triggering. A. Calculations 3) Frequency-to-voltage converter As documented, many calculations were performed in the The frequency of the digital pulses produced by the photo- development of the circuit design for this system. In addition detector and pulse shaper is translated into a voltage by an LM to the critical calculations shown, other component values 331. The voltage/frequency relationship is a function of were determined with quick calculations and estimations. As resistor and capacitor values. This relationship is shown in (3) will be discussed, it is advisable that this entire system be re- and a schematic, modified from the `331 datasheet, is in Fig. analyzed and some component values be reselected for 6. optimal performance. B. Simulations There are three major ways that this design can be simulated. Each examines a different level of abstracted operation. They are the: 1.) detailed electrical, 2.) detailed functional, and 3.) abstract functional. 1) Detailed electrical First, the electrical characteristics can be examined. Depending on whether the motor load is represented dynamically, this simulation approach would have the most parameters and be the most complex. It would likely yield detail about many parameters that are not of interest. This Fig. 6. Schematic of frequency to voltage converter. virtual model would require a powerful simulation tool, such as OrCAD PSpice®. The student evaluation version of the software does not support all the devices used in the design, RL Vout  f in  2.09V   (Rt Ct ) (3) nor does it allow simulation of the quantity of components R S involved. However, the program is mentioned here because 4) Output buffer its companion program Capture® was used as a CAD tool for The output buffer is simply a voltage follower that isolates the schematic layout. the output of the frequency to voltage converter from the input 2) Detailed functional impedance of the device to which it is connected. This is An approach that would yield similar detail regarding the necessary to allow the feedback signal to be attenuated with a operation of the system, would entail creating a detailed model potentiometer. The feedback voltage can be adjusted without of the functional blocks that the circuit components instantiate. altering the relationship presented in (3), above. The voltage This approach was taken using Simulink® for MATLAB® follower is realized with an LM301 op-amp. from The MathWorks, Inc. and is introduced as follows: It is also useful to note that the buffered voltage level can First, a basic open-loop PWM / motor model is created. be used as a stimulus to almost any circuit. It leaves provision This model is tested against known parameters, if available. for the insertion of advanced control circuitry into the Second, a model of the tachometer is created. Third, a feedback loop. feedback loop is connected and examined. 6

In development of this project a PWM / motor model was developed. This transparent approach ignores the individual created and two Simulink models of the Canon FN30S were mechanisms of the functional blocks, such as the PWM implemented. The basic PWM / motor model is shown in Fig. instantiation of the speed controller. If interest lies only in 7. One of the motor models used the format of a known system behavior, there is no need to observe the inner working model from Carnegie Mellon University [9], shown workings of the system. in Fig. 8. The other was developed based on a topology from C. Financial White [10] and is shown in Fig. 9. The two models were used to investigate the role of the motor model parameters in Economic considerations are becoming a vital part of simulation. White’s model uses a motor velocity constant, almost all aspects of engineering design. While financial which, is what is provided with the Canon motor data. The matters ought not interfere with the technical quality of CMU model uses a mechanical damping ratio. This ratio was engineering matters, they are often motivating factors when tentatively calculated for the FN30S using (4). Neither of determining a design’s feasibility or success. Often, after the these models effectively reproduced the data found in the questions, “could it work?” and “is it physically possible?” are published specifications. It appears, however, that the asked, comes the question “what is the cost?” Since one of the discrepancy lies in the numbers, not the structure of the model. motivations of this project was to minimize expense, the cost Further investigation should reveal coherent results. of development is considered here. Since the design procedure is intended for education, time  mech  starting _ torque  mech _ const (4) and effort is not explicitly quantified. It should be noted that this design is developed with the intent that it can be reproduced by undergraduate engineering students within the context of a control systems class. With such consideration, it is believed that subsequent similar projects will pose challenges intellectually, and not necessarily temporally. The design of this system is based on components available in a college electronics lab. All the parts are readily available, Fig. 7. Basic PWM motor simulation. so the cost of materials (already depreciated) is zero. Admittedly, there is a positive list price associated with the developed prototype, but a quick estimate would suggest that, to replicate the design from recently purchased components, would cost less than $20. The itemization of development, component purchase, assembly, and maintenance costs is a task recommended to be done before and during progression of the prototype through its stages of revision.

VI. TESTING A prototype of the system was assembled and tested. It performed very well. The test assembly is shown in Fig. 10. The most significant test performed was the verification of the PWM duty cycle increase in response to decreased tachometer Fig. 8. DC motor model using back-emf. frequency. After setting a less-than-full power speed reference and increasing feedback the amount just until the speed decreased, the duty cycle of the signal delivered to the motor would increase as the tachometer frequency decreased. Thus, if the flywheel was slowed by applied friction, the power to the motor was increased to compensate and maintain the expected speed.

Fig. 9. DC motor model using velocity constant.

3) Abstract functional It is recommended that, for purposes of investigation into feedback control mechanism, the most basic simulation be 7

ACKNOWLEDGMENT The author gratefully acknowledges the contributions of the following persons to this project: B. Bouma, C. Holwerda, M. E. Husson, J. Lester, K. Palmer, P. F. Ribeiro, and D. Ryskamp.

REFERENCES [1] R. C. Dorf, R. H. Bishop, Modern Control Systems, ed. 9. Upper Saddle River, New Jersey: Prentice Hall, 2001, p. 553. [2] Steven D. Kaehler, “Fuzzy Logic – An Introduction” (2004, Dec). [online]. Available: http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part1.html [3] H. T. Nguyen, N. R. Prasad, C. L. Walker, E. A. Walker, A First Course in Fuzzy and Neural Controls, Boca Raton: Chapman & Hall/ CRC, 2003, p.168, 86 [4] P. Avoke, presentation on neural networks, Calvin College ENGR 315. (2004, Dec 8). (unpublished presentation) Fig. 10. Prototype assembly showing system on breadboard, regulated power [5] (Data sheet) NE555 Precision Timers, Publication SLFS022E, Texas supply, and oscilloscopes. Instruments, (2004, March) [online] Available: http://www.ti.com [6] (data sheet) DC motor catalog 2003(English), Canon Precision, Inc., [online] Available: http://www.canon-prec.co.jp/english/e.pdf [7] Designing Photodiode Amplifier Circuits with OPA128, Burr - Brown, Tucson, AZ, Application Bulletin AB-077, Jan. 1994. [online] Available: http://www.ti.com [8] (Datasheet) LM231A/LM231/LM331A/LM331 Precision Voltage-to- VII. CONCLUDING REMARKS Frequency Converters, Publication DS005680, National Semiconductor, (1999, June) [online] Available: http://www.national.com The design, construction, and testing of a small scale motor [9] Control Tutorials for MATLAB® and Simulink®, Addison-Wesley speed control system provides an excellent method of Publishing Company, Inc., 1998 [online] Available: investigating control system theory and its practical http://www.library.cmu.edu/ctms/ctms/index.htm [10] Dr. J. R. White, “Dynamic Model of a Permanent Magnet DC Motor” application. The development of a pulse-width modulated (Spring 1997), UMass-Lowell, [online] Available: switching motor drive presents many power-systems issues for http://www.profjrwhite.com/ the designer to consider. The development of a high- system_dynamics/sdyn/s6/s6fanal/s6fanal.html sensitivity optical detector is a good exercise in analog design and touches on concepts relative to control systems such as Andrew L. Wallner was born in Milwaukee, WI in frequency response, bandwidth, gain and phase margins, and 1981 and has ties to Chattanooga, TN and compensation to promote stability. The testing of the Sheboygan, WI. He studied at the University of assembled system provides undeniable validity to the abstract Wisconsin, Sheboygan and Lakeshore Technical College, in Manitowoc, WI. He is currently a concepts considered. Furthermore, this project is a self- student at Calvin College pursuing a Bachelor of evident study of feasibility, demonstrating the opportunity to Science in Engineering degree with a concentration wisely use available resources. It is also, hopefully, an in electrical engineering in May 2005. impetus for future, similar applications and projects. The His employment experience included work at a tool and equipment company, Quasius Equipment, design presented here, is not complete by any measure, but is a Calvin College Technical Services, and an engineering internship at Red starting point for ongoing development. Arrow Products. His fields of interest include audio processing, and analog electronics.

APPENDIX

A. Comments for further development. There are a few known issues regarding circuit performance. These are being investigated and will be documented later. A schematic of the prototype circuit is available. B. Availability of prototype The prototype will be left available for inspection and testing at Calvin College. 8