【正文】 如圖 7所示， 常規(guī) PID控制和模糊 PID控制 差異不大。 因為該模型是正確的。但是，假設(shè)有建模誤差和參數(shù) a的實際值是 。 如 圖 8，模糊 PID控制比常規(guī) PID控制實現(xiàn)更好的控制性能。 此外 ， 由圖 5 8可以看 出 模糊 PID 控制器增益低于常規(guī) PID控制器 。 圖 6 a=1時， 模糊 PID控制 （實線） 和常規(guī) 圖 7 a=， 模糊 PID控制 （實線） 和常規(guī) PID控制 （虛線）性能比較 PID控制 （虛線）性能比較 5 結(jié)論 本文 介紹 了 一種基于內(nèi)?？刂频?模糊 PID控制器的 整定分析方法 。 解析模型是第一 次應(yīng)用于 模糊PID控制器 的 整 定。 分析模型包括一個線性 PID控制及非線性補償 部分 。在 內(nèi)?？刂?方法 基礎(chǔ)上 ， 模糊 PID 控制器 的 參數(shù) 可由過 程干擾 的補 償 部分來 分析 確定。雖然擴大收益 ? 和 ? 是 耦合 的 ，這一程序是 在 解耦 基礎(chǔ)上的滑 動 模 型 控制。穩(wěn)定性分析表明，該控制系統(tǒng)是全局漸近穩(wěn)定 的 。 模糊 PID控制器 采用此種整定方法 比傳統(tǒng)的 PID控制器 有更的魯棒性 強大 。仿真結(jié)果表明，模糊PID 控制器 通過此種 整 定方法，與 傳統(tǒng)的 PID 控制器 相比在動態(tài)和靜態(tài)上都 實現(xiàn)更好的控制性能 和更好的魯棒性。 參考文獻 (1) Sugeno. M. Industrial Applications of Fuzzy Control。 Elsevier: Amsterdam, The Netherlands, 1985. (2) Manel, A.。 Albert, A.。 Jordi, A.。 Manel, P. Wastewater Neutralization. Control Based on Fuzzy Logic: Experimental Results. Ind. Eng. Chem. Res. 1999, 38, 2709–2719. (3) Zhang, J. 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(17) Cha, S. Y.。 Chun, D. W.。 Lee, . TwoStep IMCPID Method for Multiloop Control System Design. Ind. Eng. Chem. Res. 2020, 41, 3037–3041. (18) Li, H. X.。 Gatland, H. B.。 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, and Hua Deng School of Mechanical and Electrical Engineering, Central South UniVersity, Changsha 410083, China, and Department of Manufacturing Engineering and Engineering Management, City UniVersity of Hong Kong, Hong Kong An internal model control (IMC) based tuning method is proposed to auto tune the fuzzy proportional integral derivative (PID) controller in this paper. An analytical model of the fuzzy PID controller is first derived, which consists of a linear PID controller and a nonlinear pensation item. The nonlinear pensation item can be considered as a process disturbance, and then parameters of the fuzzy PID controller can be analytically determined on the basis of the IMC structure. The stability of the fuzzy PID control system is analyzed using the Lyapunov stability theory. The simulation results demonstrate the effectiveness of the proposed tuning method. 1. Introduction Generally speaking, conventional proportional integral derivative (PID) controllers may not perform well for the plex process, such as the highorder and time delay systems. Under this plex environment, it is wellknown that the fuzzy controller can have a better performance due to its inherent robustness. Thus, over the past three decades, fuzzy controllers, especially, fuzzy PID controllers have been widely used for industrial processes due to their heuristic natures associated with simplicity and effectiveness for both linear and nonlinear There are too many variations of fuzzy PID controllers,such as, oneinput, twoinput, and threeinput PID type fuzzy controllers. In general, there is no standard benchmark. The oneinput may miss more information on the derivative action, and the threeinput fuzzy PID controllers may cause exponential growth of rules. The twoinput fuzzy PID, as we used in the paper, has a proper structure and the most practical use, and thus is the most popular type of fuzzy PID used in various research and application. Despite the fact that industry shows greater and greater interest in the applications of fuzzy PID, it is still a highly controversial topic from the point of view of the mainstream control engineering munity. One reason is that the fundamental theory for the analytical tuning methods of fuzzy PID is still missing. Therefore, fuzzy PID controllers had to be tuned qualitatively by twolevel tuning. At a lower level, the tuning is performed by adjusting the scaling gains to obtain overall li