MODIFIED FUZZY GAIN SCHEDULING OF PID CONTROLLERS B.HEMAKUMAR

OBJECTIVES To obtain responses for various SISO processes using fuzzy gain scheduling of PID controller and to compare this with conventional PID controller response. To implement fuzzy gain scheduled controller for four tank MIMO process. To perform real time implementation on SISO process using fuzzy gain scheduled PID controller and to compare it with conventional PID controller.

DESIGN OF FUZZY GAIN SCHEDULING OF PID CONTROLLERS This scheme utilities fuzzy rules and reasoning to determine the controller parameters for PID controller to generate the control signals. WORKING RANGE FOR Kp AND Kd Kc,min = 0.4Ku; Kc,max = 0.55Ku Kd,min = 0.09KuTu; Kd,max = 0.16KuTu NORMALISATION:

Ti = α Td For fuzzy set small, μsmall (x) = - ¼ ln(x) or xsmall (μ) = e-4µ For fuzzy set big, μbig (x) = - ¼ ln(1 - x) or xbig (μ) = 1 - e-4µ

Fuzzy Tuning Rules for Kc’ e(k) e(k) NB NM NS ZE PS PM PB S B

Fuzzy Tuning Rules for Kd’ e(k) e(k) NB NM NS ZE PS PM PB S B

Fuzzy Tuning Rules for α e(k) e(k) NB NM NS ZE PS PM PB 5 2 4 3

µi = µAI [e(k)] µBI [ e(k)] Based on µi, the values of Kc’ and Kd’ for each rule are determined from their corresponding membership functions.

CONCLUSION The proposed gain scheduling scheme uses fuzzy rules and reasoning to determine the PID controller parameters. The scheme had been tested on various SISO processes and MIMO process in simulation using C language and Matlab Software and satisfactory results were obtained. The responses obtained revealed that the proposed scheme i.e. the fuzzy gain scheduling yields reduced overshoot, settling time, rise time, delay time and peak time in comparison with the conventional PID controller. The real time implementation of a third order SISO process has been carried out and satisfactory response is obtained for fuzzy gain scheduled PID controller.

REFERENCES George Stephnopoulos, “Chemical Process Control”, Prentice Hall of India Pvt. Ltd.,New Delhi, 2001. Zhao Zy, Tomizuka M. and Isaka S, “Fuzzy Gain Scheduling of PID Controllers”, in Proceedings of the first IEEE Conference on control applications,1992, pp.693-703. N.Jaya, R.Bharathkailash and C.Deepak, “Fuzzy Gain Scheduling of PID Controllers”, Department of Instrumentation Engineering, Annamalai University, 2001. Dimiter Driankov,Hans Hellendoorn and Michael Reinfrank, “An Introduction to Fuzzy Control”, Narosa Publishing House, New Delhi, 1997. Edward Gatzke, Edward S. Meadows, Chung Wang and Francis J. Doyle, “ Model Based Control of a Four Tank System”, University of Delaware,Newark,1999. Timothy J. Ross, “Fuzzy logic with Engineering applications”, McGraw Hill Inc.,New Delhi, 1995. Stamatios V. Kartalopoulos, “Understanding Neural Networks And Fuzzy Logic”, AT&T Bell Laboratories, 2000. Pradeep B. Deshpande and Raymond H. Ash, “Computer Process Control With Advanced Control Applications”, Instrument Society of America, U.S.A., 1987.