【正文】 onal PID (dotted line) .Example 2. Assume that an industrial process is described by (16)where a=1, Suppose that there is no modeling error in the process . On the basis of step response and Nyquist curves of the industrial process , the approximation model can be obtained as follows: (17)As shown in Figure 7, little difference isobserved between the conventional PID control and fuzzy PIDcontrol because the model is , suppose that there is modeling error and the practical value of the parameter a is .. As shown in Figure 8, fuzzy PID control achieves better control performance than conventional PID control. Morever, the gain of the fuzzy PID controller is lower than that of the conventional PID controller, which is shown in Figure 8. Figure 6. Control performance of fuzzy PID Figure 7. Control performance of fuzzy PID and PIDand PID for a ) 1. Fuzzy PID (solid line) and for process a = PID conventional PID (dotted line). (solid line) and conventional PID (dotted line)5 ConclusionAn effective tuning method for fuzzy PID controllers based on IMC is presented in this paper. An analytical model is first developed for the tuning of fuzzy PID controllers. The analytical model includes a linear PID control and a nonlinear pensation item. On the basis of the IMC method, the parameters of fuzzy PID controller can be analytically determined by regarding the pensation item as a process disturbance. Although the scaling gains and are coupled, a procedure is used to decouple them on the basis of the sliding mode control. The stability analysis shows that the control system is globally asymptotically stable. Fuzzy PID controllers tuned by the proposed method are more robust than the conventional PID controller. The simulation results show that fuzzy PID controllers tuned by the proposed method achieve better control performance in both the transient and steady states and are more robust than conventional PID controllers.Literature Cited(1) Sugeno. M. Industrial Applications of Fuzzy Control。 Elsevier: Amsterdam, The Netherlands, 1985.(2) Manel, A.。 Albert, A.。 Jordi, A.。 Manel, P. Wastewater NeutralizationControl Based on Fuzzy Logic: Experimental Results. Ind. Eng. Chem. Res. 1999, 38, 2709–2719.(3) Zhang, J. A Nonlinear Gain Scheduling Control Strategy Based on Neurofuzzy Networks. Ind. Eng. Chem. Res. 2001, 40, 3164–3170.(4) Hojjati, H.。 Sheikhzadeh, M.。 Rohani, S. Control of Supersaturation in a Semibatch Antisolvent Crystallization Process Using a Fuzzy Logic Controller. Ind. Eng. Chem. Res. 2007, 46, 1232–1240.(5) George, K. I. M.。 Hu, B. G.。 Raymond, G. G. Analysis of Direct Action Fuzzy PID Controller Structures. IEEE Trans. Syst., Man, Cybernetics, Part B 1999, 29 (3), 371–388.(6) Li, H. X.。 Gatland, H. Conventional Fuzzy Logic Control and Its Enhancement. IEEE Trans. Syst., Man, Cybernetics 1996, 26 (10), 791–797.(7) George, K. I. M.。 Hu, B. G.。 Raymond, G. G. TwoLevel Tuning of Fuzzy PID Cotrollers. IEEE Trans. Syst., Man, Cybernetics, Part B 2001, 31 (2), 263–269.(8) Woo, Z. W.。 Chung, H. Y.。 Lin, J. J. A PID Type Fuzzy Controller with SelfTuning Scaling Factors. Fuzzy Sets Syst. 2000, 115, 321–326.(9) Vega, P.。 Prada, C.。 Aleixander, V. SelfTuning Predictive PID Controller. IEE Pro. D 1991, 138 (3), 303–311.(10) Rajani, K. M.。 Nikhil, R. P. A Robust SelfTuning Scheme for PIand PDtype Fuzzy Controllers. IEEE Ttrans. Fuzzy Syst. 1999, 7 (1), 2–16.(11) Rajani, K. M.。 Nikhil, R. P. A SelfTuning Fuzzy PI Controller. Fuzzy Sets Syst. 2000, 115, 327–338.(12) Yesil, E.。 Guzelkaya, M.。 Eksin, I. Self Tuning Fuzzy PID Type Load and Frequency Controller. Energy ConVers. Manage. 2004, 45, 377–390.(13) Xu, J. X.。 Pok, Y. M.。 Liu, C.。 Hang, C. C. Tuning and Analysis of a Fuzzy PI Controller Based on Gain and Phase Margins. IEEE Trans. Syst., Man, Cybernetics, Part A 1998, 28 (5), 685–691.(14) Xu, J. X.。 Hang, C. C.。 Liu, C. Parallel Structure and Tuning of a Fuzzy PID Controller. Automatica 2000, 36, 673–684.(15) Kaya, I. Obtaining Controller Parameters for a New PIPD Smith Predictor Using Autotuning. J. Process Control 2000, 13, 465–472.(16) Li, Y.。 Kiam, H. A.。 Gregory, C. Y. Patents, Software, and Hardware for PID Control. IEEE Control Syst. Mag. 2006, 42–54.(17) Cha, S. Y.。 Chun, D. W.。 Lee, . TwoStep IMCPID Method for Multiloop Control System Design. Ind. Eng. Chem. Res. 2002, 41, 3037–3041.(18) Li, H. X.。 Gatland, H. B.。 Green, A. W. Fuzzy Variable Structure Control. IEEE Trans. Syst., Man, Cybernetics, Part B 1997, 27 (2), 306–312.