模糊PID控制器的鲁棒性研究外文文献

基于内模控制的模糊PID参数的整定 摘要:在本文中将利用内模控制的整定方法实现模糊PID控制。此种控制方式首次应用于模糊PID控制器，它包括一个线性PID控制器和非线性补偿部分。非线性补偿部分可视为一个干扰过程，模糊PID控制器的参数可在分析的基础上确定内模结构。模糊PID控制系统利用李亚谱诺夫稳定性理论进行稳定性分析。仿真结果表明利用内模控制整定模糊PID控制参数是有效的。

1 引言 一般而言，传统的PID控制器对于十分复杂的被控对象控制效果不太理想, 如高阶时滞系统。在这种复杂的环境下, 众所周知,模糊控制器由于其固有的鲁棒性可以有更好的表现，因此，在过去30年中，模糊控制器，特别是,模糊PID控制器因其对于线性系统和非线性系统都能进行简单和有效的控制，已被广泛用于工业生产过程[1-4]。 模糊PID控制器有多种形式[5],如单输入模糊PID控制器,双输入模糊PID控制器和三个输入的模糊PID控制器。一般情况下，没有统一的标准。单输入可能会丢失派生信息, 三输入模糊PID控制器会产生按指数增长的规则。在本文中所采用的双输入模糊PID控制器有一个适当的结构并且实用性强，因此在各种研究和应用中,是最流行的模糊PID 类型。尽管业界对于应用模糊PID有越来越大的兴趣，但从控制工程的主流社会的角度来看,它仍然是一个极具争议的话题。原因之一是模糊PID参数整定的基本理论分析方法至今仍不明确。因此，模糊 PID控制器不得不进行两个级别的整定。在较低层次上， 该整定是由调整增益获得线性控制性能。在更高层次上的调整，是由改变知识库参数以提高控制性能, 然而调整知识库参数很难,此外，很难通过改变参数特性改善瞬态响应。根据知识库传达一般控制规则倾向于保持成员函数不变，通过离线设计和调试工作扩大增益，然而，由于由模糊PID控制器生成非线性控制表面的复杂性，调整机制的衡量因素和稳定性分析仍然是艰巨的任务。如果非线性能得到适当的利用，模糊PID控制器可能得到比传统PID控制器更好的系统性能。一些非常规的调整方法已进行了介绍[9-12]。虽然非线性被认为是在增益裕度和相位裕度基础上获得的，但是由于非线性因素，模糊PID控制器可能会产生比常规PID控制器较高的增益。而高增益可能使控制系统的稳定性变差[。 常规PID控制器很容易实现，大量的整定规则可以涵盖广泛的进程规格。在常规PID控制器的整定方法中，内模控制基础整定是在商业PID控制软件包中流行的方法之一，因为只需调整一个参数，便可以生产更好的设置点响应[15]。 本文提出了一种基于内模控制的PID控制器的整定分析方法，模糊PID 控制器可分解为线性PID控制器加上非线性补偿部分的控制器。把非线性补偿部分近似看作一个过程干扰，模糊PID参数就可以分析设计使用内模控制。模糊PID控制器的稳定性分析是根据李亚谱诺夫稳定性理论。最后，通过仿真来证明此种调整方法是有效的。 1

Effective Tuning Method for Fuzzy PID with Internal Model Control 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 compensation item. The nonlinear compensation 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 complex process, such as the high-order and time delay systems. Under this complex environment, it is well-known 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 systems.1-4 There are too many variations of fuzzy PID controllers,such as, one-input, two-input, and three-input PID type fuzzy controllers. In general, there is no standard benchmark. The one-input may miss more information on the derivative action, and the three-input fuzzy PID controllers may cause exponential growth of rules. The two-input 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 community. 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 two-level tuning. At a lower level, the tuning is performed by adjusting the scaling gains to obtain overall linear control performance. At a higher level, the tuning is performed by changing the knowledge base parameters to enhance the control performance. However, it is difficult to tune the knowledge base parameters. Moreover, it is hard to improve the transient response by changing the member function.As the knowledge base conveys a general control policy, it is preferred to keep the member function unchanged and to leave the design and tuning exercises to scaling gains. However, the 2

tuning mechanism of scaling factors and the stability analysis are still difficult tasks due to the complexity of the nonlinear control surface that is generated by fuzzy PID controllers. If the nonlinearity can be suitably utilized, fuzzy PID controllers may pose the potential to achieve better system performance than conventional PID controllers. Some nonanalytical tuning methods were introduced.9-12 Although the nonlinearity was considered on the basis of gain margin and phase margin specifications, the fuzzy PID controller may produce higher gains than conventional PID controllers due to the nonlinear factor. A high gain could deteriorate the stability of the control system.15 The conventional PID controller is easy to implement, and lots of tuning rules are available to cover a wide range of process specifications. Among tuning methods of the conventional PID controller, the internal model control (IMC) based tuning is one of the popular methods in commercial PID software packages because only one tuning parameter is required and better set point response can be produced.17 An analytical tuning method based on IMC to tune fuzzy PID controllers is proposed in this paper. The fuzzy PID controller is first decomposed as a linear PID controller plus an onlinear compensation item. When the nonlinear compensation item is approximated as a process disturbance, the fuzzy PID scaling parameters can then be analytically designed using the IMC scheme. The stability analysis of the fuzzy PID controllers is given on the basis of the Lyapunov stability theory. Finally, the effectiveness of the tuning methodology is demonstrated by simulations.