【正文】 Green, A. W. Fuzzy Variable Structure Control. IEEE Trans. Syst., Man, Cyberics, Part B 1997, 27 (2), 306–312. 。 Lee, . TwoStep IMCPID Method for Multiloop Control System Design. Ind. 14 Eng. Chem. Res. 2021, 41, 3037–3041. (18) Li, H. X.。 Gregory, C. Y. Patents, Software, and Hardware for PID Control. IEEE Control Syst. Mag. 2021, 42–54. (17) Cha, S. Y.。 Liu, C. Parallel Structure and Tuning of a Fuzzy PID Controller. Automatica 2021, 36, 673–684. (15) Kaya, I. Obtaining Controller Parameters for a New PIPD Smith Predictor Using Autotuning. J. Process Control 2021, 13, 465–472. (16) Li, Y.。 Hang, C. C. Tuning and Analysis of a Fuzzy PI Controller Based on Gain and Phase Margins. IEEE Trans. Syst., Man, Cyberics, Part A 1998, 28 (5), 685–691. (14) Xu, J. X.。 Pok, Y. M.。 Guzelkaya, 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.。 Prada, C.。 Chung, H. Y.。 Hu, B. G.。 Raymond, G. G. Analysis of Direct Action Fuzzy PID Controller Structures. IEEE Trans. Syst., Man, Cyberics, Part B 1999, 29 (3), 371–388. (6) Li, H. X.。 Rohani, S. Control of Supersaturation in a Semibatch Antisolvent Crystallization Process Using a Fuzzy Logic Controller. Ind. Eng. Chem. Res. 2021, 46, 1232–1240. (5) Gee, K. I. M.。 Manel, P. Wastewater Neutralization Control 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. 2021, 40, 3164–3170. (4) Hojjati, H.。 Albert, A.。 approximation in (15). As shown in Figure 6, fuzzy PID control achieves better control performance than conventional PID control. Morever, the gain of the fuzzy PID controller is lower than that of conventional PID controller. 12 Figure 4 Control performance of fuzzy PID Figure 5 Performance of fuzzy PID and PID and PID for example 1, fuzzy PID (solid line), for delay L= , fuzzy PID (solid line), and conventional PID (dotted line). and conventional PID (dotted line) . Example 2. Assume that an industrial process is described by ? ? ? ?8as 1s ??P (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: ? ? ~ 1s ???P (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 PID and 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 Conclusion An 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 13 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。 approximation, the delay time is approximated as follows: 11 s21s21e s LLL???? (11) Therefore, the P? (s) can be factorized as P? (s) ) P? +(s)P? (s),其中 ? ?? ? ?????? ???? s211ss~LTKP (12) We can achieve ? ? ? ?? ?st1 s211ssc??????? ??? KLTC IM C （ 13） The bandwidth of the fuzzy PID at the kth level can be controlled by adjusting R. A small value of R gives wide bandwidth and fast response。 Green, A. W. Fuzzy Variable Structure Control. IEEE Trans. Syst., Man, Cyberics, Part B 1997, 27 (2), 306–312. 7 Effective Tuning Method for Fuzzy PID with Internal Model Control XiaoGang Duan, HanXiong Li