Digital Control of MS-150 Modular Position Servo System

Transcription

1 IEEE NECEC Nov. 8, 2007 St. John's NL 1 Digital Control of MS-150 Modular Position Servo System Farid Arvani, Syeda N. Ferdaus, M. Tariq Iqbal Faculty of Engineering, Memorial University of Newfoundland farvani@engr.mun.ca Abstract The MS150 Modular Position Servo System is a popular system used for study of the theory and practice of automatic control systems. It can be controlled using an analog PID type controller or a digital controller. In this paper we describe control of a MS-150 servo system using LabVIEW 8.2 and PC based digital controller. A number of control algorithms are implemented in LabVIEW. It includes PID control, cascade control, optimal state control and a fuzzy logic control. System identification, addition of integral action to the optimal state controller and an estimator are also discussed in the paper. Experimental as well as Matlab/Simulink based simulation results are presented in the paper. The PD type fuzzy logic controller shows the best overall control performance. Index Terms Control systems, Digital control, Fuzzy logic control, Comparison of controllers I. INTRODUCTION Proper implementation of control systems requires the sound understanding of behavior of the underlying system. In this work the procedure to conduct system identification and test control algorithms are discussed. To avoid the problems of the open-loop controller, control theory introduces feedback. A closed-loop controller uses feedback to control states or outputs of a dynamical system. MS150 Modular Position Servo System is used as the test stand, which is a unique medium for study of the theory and practice of automatic control systems. A block diagram of the system is depicted in figure 1. A desired position should be reached in this series of tests under some control design constraints. LabVIEW is employed as rapid prototyping software. LabVIEW is a platform and development environment for a visual programming language G. LabVIEW is commonly used for data acquisition, instrument control, and industrial automation on a variety of platforms [5]. In section II, a brief explanation of system identification is presented. Then in Section III, a number of control algorithms are discussed and their corresponding control diagram is depicted. A brief discussion and conclusion is finally given. A. Initial Identification II. SYSTEM IDENTIFICATION In order to simulate the system in Matlab/Simulink and design controllers, a plant model has to be developed. Step response method is used to determine the system transfer function [1]. In this basic method, second order dynamics are used to estimate the system parameters. In order to obtain the calibration equation, different values of voltage and the corresponding position from the scale on the output potentiometer are used. The following equation is found and employed in controllers. Figure 2. shows the calibration graph. Position = voltage There is no calibration equation for speed and it has been LabVIEW DAQ ±10V Position Feedback ±15V Tacho Feedback 0-10V Fig. 1. Block Diagram of Control System Servo System Fig. 2. Calibration Graph used as such wherever used as a feedback or state and the speed has been measured in volts not in RPM. Simulation of identified system is shown below. This is much similar to the

2 IEEE NECEC Nov. 8, 2007 St. John's NL 2 actual system response and this confirms system identification. system identification toolbox. Several data collections were performed using different excitation signals [3]. LabVIEW VI used to collect the data sets is depicted in figure 3. Various identification algorithms including IDGREY, IDSS, IDARX, IDPROC and IDPOLY are assessed. Using general polynomial method in the frequency domain gave the best results and after appropriate filtering and detrending, system identification was performed. The results were appropriate but were high-order model. The frequency range used was 0 to 60 rad/s. A model with two poles, one integrator and one zero is fitted into the data sets. The initial value for gain of the plant model was taken from the results of the initial test. Model adequacy was tested at all models for variance and noise. Finally IDPOLY model was used for design of the controller. As the identified system is a continuous-time model, it should be converted to a discrete time model. Continuous-time IDPOLY model is B(s) y(t) = u(t) + e(t) F(s) where B(s) = e004 s e004 F(s) = s s s Fig. 2. Comparison of the simulation and actual responses of the identified system B. High-order system Identification In some experiments all of the three states of the system was exploited in the controller design. A black-box state-space representation [2] of the system was identified using Matlab Fig. 4. System Identification: comparison of the identified and the actual system III. CONTROLLER DESIGN AND SIMULATION Fig. 3. Data set collection VI DC Modular Servo system (MS 150) is used to investigate the feedback control systems. MS 150 system has facilitated us to investigate different kind of control techniques and implement simple PID controller to advanced digital fuzzy logic controller with aid of LabVIEW [4] which have been performed by controlling the states of the system, which might be speed and position, current. The objective of this series of experiments is to control the position of the rotor of motor using different kind of controllers. A simple PID controller is so designed and implemented with position feedback that system matches optimum criteria of interest. Design of a cascade controller (PID-PI) is

3 IEEE NECEC Nov. 8, 2007 St. John's NL 3 commenced. Fig. 6. Simulink block and simulation result Fig. 5. LabVIEW VI for PID controller discussed where it uses the Tacho (speed) feedback in the inner loop. This sort of controller is used in order to filter internal disturbances. State space analysis of the system is discussed. An optimum states controller is designed considering all state of the system. Then the transfer function of system is 3rd order and an estimator for the current (one of states in the system) is implemented in LabVIEW. Design of an optimum state controller with an integral action and an estimator is presented. An estimator, for all states is implemented in LabVIEW since none of the states is measured. PD type fuzzy logic controller is designed and implemented. In this experiment, first, the range of error, rate of error and manipulated input to the system are approximated using PID controller. Two input, single output FIS is selected with Sugeno defuzzification methods. The sampling time for whole experiment is 10ms unless otherwise specified. A. PID controller A PID controller for the system (without any Tacho feedback) with the design constraints of 10% overshoot was designed using Z-N closed loop method to determine the critical gain and period. LabVIEW VI is shown in figure 5. While Integral and derivative gains were kept zero, the proportional gain was increased gradually until oscillations Fig. 7. LabVIEW VI for PID-PI controller: first configuration (A) Inner Loop, (B) Outer Loop

4 IEEE NECEC Nov. 8, 2007 St. John's NL 4 In simulation (figure. 6), the identified system was used and the controller was optimized using response optimization. (A) (A) (B) Fig. 10. Simulink Diagram and simulation results for inner loop (left) and outer loop (right) (B) Fig. 8. LabVIEW VI for PID-PI controller: first configuration (A) Inner Loop, (B) Outer Loop The simulated response and the actual response are due to non-modeled non-linearity different from each other. The optimized parameters did not give the expected results in the system and made the system unstable. B. PID-PI cascade controller The inner loop uses the speed feedback to filter internal disturbances. Inner loop was tuned using pole cancellation method however the outer loop was tuned using Z-N methods. In both cases fine-tuning is performed. A PID noise filter is global variables are used to transfer position data and the PID output the inner loop. Also note that the inner loop is running one hundred times faster due to the updating cycles of LabVIEW and is so chosen to compensate for updating the graphs, allocation of resources to other applications, etc. As it can be seen from the diagrams there is no speed calibration equation and it has been used as such in volts. Figure 9 shows the performance of the controller in front panel. Simulation results are depicted below. Response of the Inner loop and outer loop are shown respectively in figure 10. The difference between the responses above and the actual plant is because of the model differences. Fig. 9. Front Panel of LabVIEW VI for PID-PI controller implemented in the inner loop to filter the noise in the speed input. Figure 7 and 8 show corresponding VIs for two different configurations of the control system. It is noteworthy that the latter configuration is more appropriate than the former one. Loops cannot be wired to each other and therefore two Fig. 11. LabVIEW VI for Optimal States controller C. Optimal States Controller In this design all states of the system were considered. Highorder system identification results were used. First, the system

5 IEEE NECEC Nov. 8, 2007 St. John's NL 5 Fig. 12. Front Panel LabVIEW VI for Optimal States controller is simulated using Simulink and the maximum values of states are observed in order to identify weighting matrix Q. With the weighting matrices Q (states) and R (Input), optimum state controller (gain of controller) is designed using DLQR command in Matlab. An estimator for the current (one of states in the system) is implemented in LabVIEW since it is not measured. The interaction between states and the control effort is also considered in the design [7]. Using plant model, the following equation was derived to estimate the current (one of the three states): Ts RaTs Ts I a ( k) = I a ( k 1) + Vin ( k 1) I a ( k 1) K1ω( k) L L L Figure 11 and 12 demonstrate the LabVIEW VI and the performance of the controller. The results of the simulated system is better than the actual controller due to unknown initial values of the states and due to noise that was presented by Matrix K in identification process. This is concluded from the settling times and sustained oscillations in the system. It is clear that the valuable data has been put aside as error and noise. So there is no wonder that the model is not a good presenter of the actual plant. Simulink block diagram and the graphs are shown in figure 13. D. Optimal State Controller with an Integral Action Similar to the procedure discussed in previous section an estimator is designed so that it would be faster than controller [6]. This estimator estimates all the states of the system since none of states (except for position) is measured. The system is simulated with optimum state controller with integral action. The model was tested for different values but the model was not proper system and it seems that it is mainly due to excitation procedure. However the identified system matches the standard state space model and the provided system parameters. The other important issue is the selection of Q and R, where it was relied on the max values of the states to derive the matrices as it guaranties the stability of the designed controller in this case. Fig. 13. Simulink Diagram and simulation Fig. 14. Front Panel LabVIEW VI for Optimal States controller with an Integral Action

6 IEEE NECEC Nov. 8, 2007 St. John's NL 6 E. Fuzzy Logic Controller Design of PD type fuzzy logic controller is presented. First, the range of error, derivative error and manipulated input to the system are approximated using PID controller. Two input, single output FIS is selected with Sugeno defuzzification methods. Three triangular membership functions are used for each input and tested for response. The response was satisfactory and two membership functions were added to enhance the response of the controller and system. The membership function fuzzification system for e& is shown in figure 15 and the rule set is shown in figure 16. LabVIEW diagram and front panel are shown in figure 17. Simulation performed in Simulink verifies the sound performance of the controller. Fig. 15. Sample Membership Functions for e& Fig. 16. Rule set IV. CONCLUSION In this brief, different kind of controllers for the MS 150 servo system has been investigated. The cascade control technique, PID-PI can achieve substantial improvement over the other techniques and shows better performance in both overshoot and settling time. An advantage of the cascade control schemes is that it does not require any estimator and is relatively easy to implement and robust to disturbances in the inner loop, which should be faster than outer loop. This may be a possible drawback of this scheme compared to the conventional PID control. State space design of controllers shows poor performance since it uses estimation of states and initial values and the performance of the system depends entirely upon the estimator. It becomes even worse when the estimator estimates all the system states. When it estimates only one state (current) of the system it shows reasonable performance although it uses more sensors. It is concluded that the design of these controllers are heavily dependent on the Fig. 17. LabVIEW diagram and its front panel proper identified plant model, which is the greatest pitfall compared to fuzzy controllers. The PD type fuzzy logic controller shows the best overall performance. This type of controller does not pose a problem selecting sampling time as it appear in the case of cascade controller (in inner loop) and the state space estimator. Highspeed sampling should occur in later cases. Moreover, FLC is very easy to implement and most of the time it is robust and it is designed base on the input and output of the plant and does not require a mathematical model of the plant. However existence of the model can help better design and the proof of the stability of this nonlinear controller is hard to perform not at least for this system. REFERENCES [1] K. Ogata, Modern Control Engineering, 3rd ed., Prentice Hall 1997 [2] Ljung, L., System Identification: Theory for the User, Prentice Hall, 1986 [3] System Identification Toolbox User's Guide, Mathworks, September 2006 [4] LabVIEW PID Control User Manual, National Instruments, November 2001 [5] LabVIEW User Manual, National Instruments, January 2006 [6] K. Ogata, Designing Linear Control Systems with Matlab, Prentice Hall, 1994 [7] A. Tewari, Modern Control design, John Wily & Sons, 2002