ISSN: 2277 943 Volume 2, Issue, November 23 Self Tuning Mechanism using Input Scaling Factors of PI like Fuzzy Controller for Improved Performance Neha K. Patil, Bhagsen J. Parvat Abstract Design of fuzzy controller includes mainly selection of rule base, membership functions election and scaling factors. In some applications fixed value of scaling factors generates oscillations in process response. In this paper, an algorithm for tuning of scaling factors of fuzzy PI (proportional-integral) controller based on rule base is proposed. The input scaling factors are tuned by updating factors whose values are obtained using rule base with the error and change in error as inputs. The rules are designed for tuning the scaling factors based on the performance measures such as peak overshoot (OV), Rise time (RT) and Integral of square error (ISE). The performance comparison of conventional with self tuned fuzzy controller has been done in terms of several performance measures such as peak overshoot, settling time, rise time and integral square error (ISE). In addition to the responses due to step set-point change, a disturbance is also added in some systems. Simulation results show the effectiveness and robustness of the proposed self tuning mechanism. A simulation analysis of a wide range of processes with and without delay time is carried out and comparison of results shows improvement due to self tuning of fuzzy controller. Index Terms Fuzzy, Proportional Integral, Scaling Factors, Self Tuning,, Membership Functions, ISE. I. INTRODUCTION Now a day s Fuzzy logic controllers (s) are applied to wide range of systems with uncertainty and nonlinearity. Although controlling a plant a skilled human machinist manipulates the output of the controller based on error and change in error with an aim to diminish the error in shortest feasible time. This increased popularity can be attributed to the fact that fuzzy logic provides a powerful vehicle that allows engineers to incorporate human reasoning in the control algorithm. In most of the process control applications, classical PI/PID controllers have been used. However, the performances depend heavily on the process parameters [], [2]. Thus, it is desirable to have a robust controller for the Manuscript received November, 23. Neha K. Patil, Instrumentation Engineering, PREC College, Loni, India, 994389974. Bhagsen J. Parvat, Instrumentation Engineering, PREC College, Loni, India, 975882979. drive system to reduce parameter sensitivity [3], [4]. Adaptive control is an efficient technique for dealing with large parameter variations. The control input is designed to drive the controlled plant to track the response produced by the reference model [5] [7]. Various control algorithms developed require the system states, thus they are not easy to implement [8]. The two types of structure of have been studied so far: one is position-type fuzzy controller which generates control input (u) from error (e) and change in error, and the other is velocity-type fuzzy controller which generates incremental control input (Δu) from error and change in error. The previous is called PD type and the second is called PI type according to the characteristics of information that they process. In the perspective that the is based on the knowledge of human experts, and generally s applied to unknown or partially known systems, PI type is known to be more practical than PD type. Other comparisons also can be seen in the facts that human, generally, are not so sensitive to absolute values of data in their sensing and actuation, and besides sometimes it is not possible to remove out steady state error with PD type controllers for large class of systems [9]. A lot of researchers are working in this area of automated controller tuning using fuzzy logic [] [7]. But most of them reported their work on the tuning of output SF only or for conventional PID controllers. There is a need to put little efforts on the tuning of input scaling factors for s as they affect directly on performance measure and controller part [8], [9]. Designing an auto tuning method using input scaling factor is not an easy task because both the parameters has opposite effect on the performance. Other reason for this is that changing the input SFs changes the normalized universes of discourse, the domains of the membership functions of input/output variable of. The input scaling factors affect the performance measure and the controller part while the output scaling factor affects only the output of the controller. Increasing the input scaling factors makes the performance measures more sensitive around the set-point and less sensitive during rise time. Decreasing or increasing the two parameters has the opposite effect. Both parameters should be defined on low limits below which the amount on tolerance on rise time, steady state error and oscillations around the set point become undesirable. So the input scaling factors should be determined very carefully for the successful implementation of a. All Rights Reserved 23 IJARCSEE 729
ISSN: 2277 943 Volume 2, Issue, November 23 Thus, it will compel us to design a simple and effective tuning method for fuzzy logic controllers. In this method, the input scaling factors are tuned using updating factors whose value are determined by rule base with the error and change in error as inputs according to the required controlled process. It should be noted that this tuning method does not train the rule base of while it assumes a working set of rules and is used to tune the controller for a desirable response. The self tuning method is applied to PI type for simulation experiments with various types of processes including well known example of a dc motor. A number of performance indices such as peak overshoot (% ov), settling time (ts), rise time (tr) and integral of square error (ISE) are computed for a detailed performance comparison of the self tuned with conventional. The main idea of this paper is given in literature of Chopra et al. in which they have discussed auto-tuning algorithm for level control of coupled tank [2]. The paper is organized as follows. In section 2, fuzzy controller structure has been discussed. In section 3, self tuning mechanism for fuzzy controller is presented. Simulation results are presented in section 4. Paper is concluded in section 5. II. STRUCTURE OF FUZZY CONTROLLER Block schematic control system using fuzzy controller is illustrated in fig.. r( - Z - - e( ce( GE GCE E( CE( u( GU U( Z - U( PROCESS Figure. Control System using Fuzzy Controller The is two input one output system. It is represented by e( r( y p ( () ce( e( e(k- ) The inputs and output of fuzzy controller are mapped to fuzzy variables by using the gain blocks known as scaling factors G E, G CE and G U. The variables of fuzzy controller are then given by E( G E e( CE( G CE ce( U( U(k ) ΔU( ΔU( G U Δu( Universe of discourse for input is decomposed into seven fuzzy variables for input as NB (negative big), NM (negative y p ( (2) medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium) and PB (positive big). For output it is decomposed into seven fuzzy sets as NB (negative big), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium) and PB (positive big). The range of fuzzy plane is [-, ]. NB NM NS ZE f (E, CE) - -.66 -.33.33.66 NB NM NS ZE - -.66 -.33.33.66 PS f ( u ) PS PM PM PB PB E, CE Figure 2. Membership Functions for E, CE and U In the second stage of the, the fuzzy variables E and CE are processed by an inference engine that executes a set of control rules contained in (7 7) rule bases. Table for Fuzzy Logic Controller CE E NB NM NS ZE PS PM PB NB NB NB NB NB NM NS ZE NM NB NB NB NM NS ZE PS NS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PS PM PB PB PB PB ZE PS PM PB PB PB PB III. SELF TUNING MECHANISM FOR FUZZY CONTROLLER In fuzzy adaptive controllers the fuzzy controller parameters are continuously tuned. There are two types of adaptation are possible. One method is to tune the rule base of the fuzzy controller. The other method is to tune the scaling factors. Now there are three scaling factors two input and one output. In this paper we can consider input scaling factor adaptation i.e. G E and G CE. The researchers have done lot of work on tuning of scaling factors but no exact methodology is available for selection of scaling factors. The method available is based on trial and error. In this paper, the input scaling factors are continuously tuned as per requirement of the fuzzy controller for improved process performance. Fig. 3 shows self tuning mechanism based structure of fuzzy logic controller. The design of the self tuning mechanism includes scaling factor tuning using rule base for α and β which is discussed in next paragraph. U All Rights Reserved 23 IJARCSEE 73
ISSN: 2277 943 Volume 2, Issue, November 23 A. Scaling Factors As per the above discussion is proposed for the tuning of input scaling factors by developing the adjustment rules defined in terms of e and ce for updating the scaling factors, in dependence on the performance of the closed loop system. Auto tuning mechanism simply means that the self-tuning of input gains based on error and change in error. Based on this mechanism, the incremental change in e and ce is obtained by following equations. E( GE e( CE( (3) GCE ce( where and are the updating factors for incremental change in e and ce, which are computed online based on fuzzy logic reasoning using the error and change in error at each sampling time. Thus, the input scaling factors of does not remain fixed while the controller is in operating condition, in fact, it is updating at each sample by updating factors and. increases and G CE decreases. Similarly, if the overshoot or amplitude of oscillation is higher, then decrease the effect of error and increase the effect of derivative of error on the controller. If e is NB and CE is ZE then is S and is VB. Thus the input-scaling factor G CE is increased in this case..5.5 S -.5 -.25.25.5.75.25.5 S M B VB B CE r ( e( GE GCE for E( CE( Fuzzy u( U( U( GU z - ce( z - for Figure 3 Self Tuning Fuzzy Controller B. Membership Functions y p ( All membership functions (MFs) for controller inputs (i.e., e and ce) and incremental change in controller output (i.e., cu) are defined on the common normalized domain [-,]. The membership functions are shown in Figure 8. The MFs for are defined on the range [-.5,.5] but with two fuzzy sets small and big and the MFs of corresponding to the singleton fuzzy sets and varies from [, 5] as shown in Fig. 4. It is assumed that is in the prescribed range and the appropriate range is determined by simulations. C. The rule base used for control output u is same as for the conventional fuzzy controller. In this method of updating factors and, we derive the rules experimentally based on the step response of the process. The evaluation performances measures are peak overshoot (OV), Rise time (RT) and settling time (ST) and ISE. For example, if the system response is slower than desired, i.e. RT is positive, and then it really needs to increase the effect of error on the system and decrease the effect of derivative error. If e is ve (PB, PM or PS) and ce is ve (NB, NM or NS) then is B and is S. Then input scaling factors G E 2 3 4 5 (a) Membership Function for α (b) for β Figure 4 Scaling Factors Membership Function CE The other rules could be explained similarly. The effectiveness of tuning based on scaling factors is sometimes bounded by the contradictory requirements in these factors resulting from different performance measures. For example if change in OV and RT are both negative, then rules say that input scaling factor G CE () should be PB or NB. Such type of conflicts can be resolved by effective a correction based on the relative firing strengths of the conflicting rules. The rule base for and is shown in Table 2 and Table 3. Table 2. for α CE E NB NM NS ZE PS PM PB NB B B B B B B B NM S B B B B B S NS S S B B B S S ZE S S S B S S S PS S S B B B S S PM S B B B B B S PB B B B B B B B Table 3. for β CE NB NM NS ZE PS PM PB E NB S S S S S S S NM M M S S S M M NS B M M S M M B ZE VB B M M M B VB PS B M M S M M B PM M M S S S M M PB S S S S S S S All Rights Reserved 23 IJARCSEE 73
Output yp Output yp Output yp ISSN: 2277 943 Volume 2, Issue, November 23 IV. SIMULATION RESULTS In order to demonstrate the significance of the self tuning mechanism, we test time responses for the control of the variety of processes. For comparison between the conventional and self tuning fuzzy controller, several performance measures such as peak overshoot, rise time, settling time and integral square error (ISE) are used. The values of different performance indices are provided in tabular form in Table 4. In case of auto tuned system, Fuzzy PI type controller is denoted by ATFC and system without tuning (conventional ) is denoted by. The processes are described as follows. A. First Order Plus Delay Time (FOPDT) The transfer function is given by G ( s) e s.s The proposed fuzzy logic controller is applied on a well known example of first order delayed process. This form of transfer function is typically used to approximate process control systems, while computing Ziegler Nichol parameters for a PI controller. The process plant is taken as first order system with time delay. Initially the scaling factors are GE; =, GCE= and GU=. Response characteristics for the system with auto-tuning and without tuning are shown in Fig. 5..2.8.6.4.2 2 4 6 8 2 4 6 8 2 Figure 6 Step Response for marginally stable SOPDT process for given setpoint using and C. DC Motor The term speed control stand for intentional speed variation carried out manually or automatically DC motors are most suitable for wide range speed control and are there for many adjustable speed drives. We have tested the self tuning mechanism on dc motor process given by second order transfer function which is tested using conventional fuzzy controller in [2]..5 G ( 3 s) 2.2s.5s.625 Initially the scaling factors are chosen as GE =, GCE= and GU=.25. Performance curves for the system with auto-tuning and without tuning are shown in Fig 7..2.2.8.8.6.6.4.4.2.2 2 4 6 8 2 4 6 8 2 Figure 5 Step Response for FOPDT process for given setpoint using and B. Marginally Stable Second Order Plus Delay Time This is a marginally stable system because one of its poles is at the origin [] and presence of dead time makes the system further difficult to control. G2 ( s) e s( s ) Ls Initially the scaling factors are chosen as GE =, GCE= and GU=. Performance curves for the system with auto-tuning and without tuning with L=. are shown in Fig 6. 2 4 6 8 2 4 6 8 2 Figure 7 Step Response for DC Motor process for given setpoint using and The comparative results of and are summarized in tabular form in table 4. Table 4. Comparison of controller performance Rise Settling Over Controlle time time shoot r RT(s) ST(s) OV(%) ISE FOPDT.8 2.9.2 2.25e-2.83.46.5 6.97e-3 SOPDT.99 7.88 33.3 8.29e-9.6 7.7 7. 6.68e-9 DC Motor.72 2.43.97 9.92e-6.73 4.3 2.58 3.93e-6 All Rights Reserved 23 IJARCSEE V. CONCLUSIONS Fuzzy logic controllers are robust to the system disturbances. The performance of can be further improved by making 732
ISSN: 2277 943 Volume 2, Issue, November 23 it adaptive. A methodology was discussed to modify a PI type fuzzy logic controller using self tuning mechanism. The self tuning controller was tuned online by scaling factor updating factors that tunes input scaling factors of. The updating factors are based on fuzzy inference rules defined on error and change in error. Performances of self tuning were also compared with those of their corresponding conventional with respect to several indexes such as peak overshoot, settling time and integral square error (ISE). By comparing their performance with conventional method, it is seen that self tuned PI type performed better but needs a set of fuzzy inference rules for updating scaling factors. In this paper, the self tuning mechanism is tested on FOPDT, Marginally stable SOPDT and DC motor process. A simulation analysis shows that the proposed methodology gives better performance than existing schemes, fast, robust. The other feature of this scheme is it depends neither on the process being controlled nor on the controller used. REFERENCES [] J. R. Layne and K. M. Passino, : Fuzzy model reference learning control, Journal of Intelligent.Fuzzy Systems., vol. 4, no., pp. 33 47, 996. [2] L. Zhen, L. Xu: Fuzzy learning enhanced speed control of an indirect field oriented control induction machine drive, IEEE Trans. on Control Systems Technology, Vol. 8, No. 2, pp. 27-278, 2. [3] J.L. Silva Neto, H. Le Huy: An improvement fuzzy learning algorithm for motion control applications, Proc. of the IEE, Vol., pp. -5, July 998. [4] M. Kadjoudj, R. Abdessemed, M.E. Benbouzid, C. Ghennai: Current control of PMSM fed by two and three levels VSI, in Proc. of EPE/PEMC, Tuke (Slovakia), Vol. 7, pp. 69-74, 2. [5] D.S. Reay, M.W. Dunniganu: Learning issues in model reference based fuzzy control, Proc. of the IEE Control Theory Application, Vol. 44, No. 6, 997. [6] J.T. Spooner, R. Ordonez and K.M. Passino: Stable direct adaptive control of a class of discrete time non-linear systems, Proc. of the 3th IFAC world congress, San Francisco, pp. 343-348, 996. [7] Ying Shich Koing, and Pin Ging Huang, High performance position controller for permanent magnet synchronous motor drives based on TM532F288 DSP,, Proc. Of the 24 IEEE Int. Conf. on Control applications. Torpei, Taiwan, pp.29-295, 24. [8] Sidney R. Bowes, and Jian Li, New robust adaptive control algorithm for high performance Ac drive, IEEE Trans. Electronics, Vol. 47, No2, pp.325-336, 2. [9] Jihong Lee, On Methods for Improving Performance of PI-Type Fuzzy Logic Controllers, IEEE Transactions On Fuzzy Systems, Vol.. No. 4, November 993. [] R.K.Mudi and N.R.Pal, A robust self-tuning scheme for PI and PD type fuzzy controllers, IEEE trans. Fuzzy System., 7(), 999, 2-6. [] Walter C. Daugherity, Balaji Rathakrishnan and John Yen, Performance Evaluation of a Self-Tuning Fuzzy Controller, in Proc. IEEE Int. Conference Fuzzy systems, San Diego, CA, March 992, pp 389-387. [2] Kuldip S. Rattan and Dale Van Cleave, Design and Implementation of a Reduced Rule Fuzzy Logic PID Controller, URL: email: krattan@cs.wright.edu. [3] Yu Cheng, Fu-Rong Lei, Wen-Li Xu and Yi-Sheng Zhong, Speed Control of Ultrasonic Motors by Auto-Tuning Fuzzy PI Control, Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, China, June -4, 22, PP- 882-886. [4] S. Z. He, S. Tan, F. L. Xu, and P. Z. Wang, Fuzzy self-tuning of PID controller, Fuzzy Sets Syst., vol. 56, pp. 37 46, 993. [5] M. Maeda and S. Murakami, A self-tuning fuzzy controller, Fuzzy Sets Syst., vol. 5, pp. 29 4, 992. [6] T. J. Procyk and E. H. Mamdani, A linguistic self-organizing process controller, Automatica, vol. 5, no., pp. 53 65, 979. [7] Z.Z.Zhao, M. Tomizuka and S. Isaka, Fuzzy gain Scheduling of PID Controllers, IEEE Transactions on Systems, Man, And Cybernetics.,Vol. 23, No. 5. September/October 993. [8] R.R. Yager and D.P. Filev, Essentials of Fuzzy Modeling and Control. Singapore: John-Wiley & Sons, 994. [9] T. J. Procyk and E. H. Mamdani, A linguistic self-organizing process controller, Automatica, vol. 5, no., pp. 53 65, 979. [2] S. Chopra, R. Mitra, V. Kumar, Auto tuning of Fuzzy PI type controller using Fuzzy logic, International Journal of Computational Cognition, vol. 6, no., pp. 2-8, 28. [2] R. Kushwah and S. Wadhwani, Speed Control of Separately Excited DC Motor Using Fuzzy Logic Controller, International Journal of Engineering Trends and Technology, vol.4 no.6, pp. 258-2523, 23. Neha K. Patil has done her B.E. in Instrumentation Engineering from D. N. Patel College of Engineering Shahada. She is doing his M.E. in Instrumentation Engineering from PREC, Loni. Her research interest includes PID Control, Fuzzy Control etc. Bhagsen J. Parvat received his M.Tech. in Instrumentation Engineering from Govt. college of engineering, Pune. Presently he is Associate professor in instrumentation at Pravara rural engineering college, Loni. He had more than fifteen years of experience in academics and industry. Also he is doing Ph.D. from S.G.G.S. Institute of Engineering and Technology, Nanded. His research interests include higher order sliding mode control, process control, intelligent control etc. All Rights Reserved 23 IJARCSEE 733