模糊PID控制器的鲁棒性研究外文文献翻译

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1、word 毕 业 设 计论 文外 文 文 献 译 文 与 原 文基于模控制的模糊PID参数的整定Xiao-Gang Duan, Han-Xiong Li,and Hua DengSchool of Mechanical and Electrical Engineering, Central South UniVersity, Changsha 410083, China, andDepartment of Manufacturing Engineering and Engineering Management, City UniVersity of Hong Kong, Hong Kong摘要

2、:在本文中将利用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局部。非线性补偿局部可视为一个干扰过程，模糊PID控制器的参数可在分析的根底上确定模结构。模糊PID控制系统利用亚谱诺夫稳定性理论进展稳定性分析。仿真结果明确利用模控制整定模糊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展简单

3、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如此。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参数整定的根本理论分析方法至今仍不明确。因此，模糊 PID控制器不得不进展两个级别的整定。在较

4、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如此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外表的复杂性，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展了介绍9-12。虽然非线性被认为是在增益裕度和相位裕度根底上获得的，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

5、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，大量的整定规如此可以涵盖广泛的进程规格。在常规PID控制器的整定方法中，模控制根底整定是在商业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局部的控制器。把非线性补偿局部近似看作一个过程干扰，模糊PID参数就可以分析设计使用模控制。模糊PID控制器的稳定性分析是根据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。2 问题的提出2.1 常规PID控制器常规PI

6、D 控制器通常被描述为如下方程8-10：=1其中E是跟踪误差，kp 是比例增益，ki是积分增益，kd是微分增益，Ti和TD分别是积分时间常数和微分时间常数，这些控制参数的关系是KI =KP/Ti 和KD =KPTd。PID控制器的传递函数可以表示如下：2在根轨迹中，PID控制器有两个零点和,一个极点是原点。条件是两个零点满足大于4。CP+udey+_yr图1 模控制配置图(a)+yedurP_图2 模控制配置图(b)2.2 模控制原如此根本的模控制原如此如图1所示，其中P是被控对象，P是名义上的模型对象，C是控制器，r和d是设置点和干扰，y 和 yk分别是被控对象的输出和模型对象的输出。模控制

7、结构相当于古典单闭环反响控制器如图1b所示，如果单闭环控制器如下：3与 4其中(s)是被控模型的最小相位局部，包含任何时间延迟和右零点，f(s)是一个低通滤波器，一般形式是：5调整参数tc是理想闭环时间常数n是一个待定的正整数。KiKdRuleBasesERu图3 模糊PID控制器结构2.3 模糊PID控制器模型模糊PID控制器如图2所示，形式为：与6是一种非线性的时间变量参数(), A和B分别是每个输入和输出的成员函数一半的外延。模糊PID控制实际上有两个层次的增益。扩大增益(Ke, Kd, K0, 和K1)处于较低的水平。扩大增益的调整将会影响模糊PID控制器效果，造成控制参数的不断变化。

8、作为控制行为的模糊耦合控制， Ke, Kd, K0, 和 K1以何种不同的控制行动仍然没有非常清楚，这使得实际设计和调试过程相当困难。3 基于模控制的模糊PID整定在模糊PID控制器整定的根底上的模控制方法，通过分析模糊PID控制模型得到第一个简单推导。然后，参数模糊PID 控制器可在模控制的根底上确定参数。假设一个工业过程可以模仿成一阶加上延迟 FOPDT 环节，传递函数如下：(7)其中K、T和 L分别是稳态增益，时间常数，和延迟时间，这些参数通过阶跃响应法，频率响应，和闭环继电反响等方法来描述的，FOPDT是一种最常见最实用的模型，尤其是在过程控制中18。通过式6可以得到：8910是一个非

9、线性项，没有明确的分析表达。显然，模糊PID控制可视为常规PID的非线性补偿。常规PID控制局部是UPID(s)， 非线性补偿局部是UN(s)。基于模控制的模糊PID整定。如果我们考虑非线性补偿UN(s)作为一个过程的干扰，并设置为Gf(s)如图3，基于模控制的模糊PID控制器可简化如下：(11)因此，为 可以分解为=，其中(12)从而得到 13模糊PID在第k水平上的带宽可以通过适合的来控制。带宽和快速的反响，的值越小可得到较大的带宽和较快的响应速度，否如此带宽变小 ，响应缓慢，因此，为了提高上升时间，的值应该小，所以，两个参数和可得到确定。备注：模糊PID控制实际上是一个传统PID控制器u

10、PID加上滑动控制。由于滑模控制是一种鲁棒控制所以模糊PID控制是力的比传统的PID控制有更好的鲁棒性。4 控制仿真在这一节中，通过上述方法进展模糊PID整定的控制性能与常规PID的比拟，选择IEA和ITAE作为标准，数值越小意味着控制性能越好。14 在所有控制仿真中常规PID控制参数是由模控制方法决定的，模糊PID控制参数是由上述整定方法确定的。例1考虑一个工业过程，所描述的一阶延迟环节，模型函数如下：15线性局部在过程中占主导地位。小延迟时间意味着弱非线性特性。由图5可以看出，由于延迟时间小，常规PID控制和模糊PID控制差异不大。然而，当延迟时间增加至L=，如图6 ，模糊PID控制实现了

11、优于常规PID控制控制性能。此外模糊PID控制器增益低于常规PID控制器。图4 例1中模糊PID控制实线和常规 图5 延迟时间增加至L=，模糊PID控PID控制虚线性能比拟制实线和常规PID控制虚线性能比拟例2假设一工业过成描述如下：16其中a=1，假设不存在建模误差，在阶跃响应和奈奎斯特工业过程曲线根底上可获得逼近模型如下：17如图7所示，常规PID控制和模糊PID控制差异不大。因为该模型是正确的。但是，假设有建模误差和参数a的实际值是0.95 。如图8，模糊PID控制比常规PID控制实现更好的控制性能。此外，由图8可以看出模糊PID 控制器增益低于常规PID控制器。图6 a=1时，模糊PI

12、D控制实线和常规 图7 a=0.95时，模糊PID控制实线和常规PID控制虚线性能比拟PID控制虚线性能比拟5 结论本文介绍了一种基于模控制的模糊PID控制器的整定分析方法。解析模型是第一次应用于模糊PID控制器的整定。分析模型包括一个线性PID控制与非线性补偿局部。在模控制方法根底上，模糊PID控制器的参数可由过程干扰的补偿局部来分析确定。虽然扩大收益和是耦合的，这一程序是在解耦根底上的滑动模型控制。稳定性分析明确，该控制系统是全局渐近稳定的。 模糊PID控制器采用此种整定方法比传统的PID控制器有更的鲁棒性强大。仿真结果明确，模糊PID控制器通过此种整定方法，与传统的PID控制器相比在动态

13、和静态上都实现更好的控制性能和更好的鲁棒性。参考文献(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, 27092719.(3) Zhang,

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19、 Gain and Phase Margins. IEEE Trans.Syst., Man, Cybernetics, Part A 1998, 28 (5), 685691.(14) Xu, J. X.; Hang, C. C.; Liu, C. Parallel Structure and Tuning of aFuzzy PID Controller. Automatica 2000, 36, 673684.(15) Kaya, I. Obtaining Controller Parameters for a New PI-PD SmithPredictor Using Autotun

20、ing. J. Process Control 2000, 13, 465472.(16) Li, Y.; Kiam, H. A.; Gregory, C. Y. Patents, Software, andHardware for PID Control. IEEE Control Syst. Mag. 2006, 4254.(17) Cha, S. Y.; Chun, D. W.; Lee, J.t. Two-Step IMC-PID Method forMultiloop Control System Design. Ind. Eng. Chem. Res. 2002, 41, 3037

21、3041.(18) Li, H. X.; Gatland, H. B.; Green, A. W. Fuzzy Variable StructureControl. IEEE Trans. Syst., Man, Cybernetics, Part B 1997, 27 (2), 306312.Effective Tuning Method for Fuzzy PID with Internal Model ControlXiao-Gang Duan, Han-Xiong Li, and Hua DengSchool of Mechanical and Electrical Engineeri

22、ng, Central South UniVersity, Changsha 410083, China, andDepartment of Manufacturing Engineering and Engineering Management, City UniVersity of Hong Kong, Hong KongAn internal model control (IMC) based tuning method is proposed to autotune the fuzzy proportional integral derivative (PID) controller

23、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. Thenonlinear pensation item can be considered as a process disturbance, and then parameters of the fuzzy PID controller can be analytically determ

24、ined 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. IntroductionGenerally speaking, conventional proportional integral derivative (

25、PID) controllers may not perform well for the plex process, such as the high-order and time delay systems. Under this plex 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, espec

26、ially, 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

27、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 p

28、ractical 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 enginee

29、ring 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 two-leveltuning. At a lower level, the tuning is performed by adjusting the scaling gains to obtain overall linear

30、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 k

31、nowledge 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 tuning mechanism of scalingfactors and the stability analysis are still difficult tasks due to the plexity of the nonlinea

32、r 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 nonline

33、arity 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 e

34、asy 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 oneof the popular methods in mercial PID software packagesbecause only one tuning parame

35、ter is required and better setpoint response can be produced.17An analytical tuning method based on IMC to tune fuzzyPID controllers is proposed in this paper. The fuzzy PIDcontroller is first deposed as a linear PID controller plus anonlinear pensation item. When the nonlinear pensation item is app

36、roximated 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 controllersis given on the basis of the Lyapunov stability theory. Finally, the effectiveness of the tuning methodology is demonstrated

37、 by simulations.2Problem Formulation2.1 Conventional PID ControllerThe conventional PID controller is often described by the following equation:20,21=1where e is the tracking error, KP is the proportional gain, KI is the integral gain, KD is the derivative gain, and Ti and Td are the integral time c

38、onstant and the derivative time constant, respectively. The relationships between these control parameters are KI =KP/Ti and KD=KPTd. The transfer function of the PID controller (1) can be expressed as follows:2On the root-locus plane, the PID controller has two zeros ti and td, and one pole at the

39、origin. The condition to have real zeros is that Ti 4Td.CP+udey+_yr_Figure 1IMC configurationaPre_+udyFigure 2IMC configuration(b)2.2 Principle of IMCThe basic IMC principleis shown in Figure 1a, where P is the plant, P is a nominal model of the plant, C is a controller; r and d are the set point an

40、d the disturbance, and y and yk are the outputs of the plant and its nominal model, respectively.The IMC structure is equivalent to the classical single-loop feedback controller shown in Figure 1b. If the single-loop controller CIMC is given by3with4where P (s)=P -(s)P +(s), P -(s) is the minimum ph

41、ase part of the plant model,P +(s) contains any time delays and right-halfplane zeros, and f(s) is a low-pass filter with a steady-state gain of one, which typically has the form:5The tuning parameter tc is the desired closed-loop time constant, and n is a positive integer to be determined.KiKdRuleB

42、asesERuFigure Figure3Fuzzy-PID controller structureModel of Fuzzy PID ControllerThe fuzzy PID controller, as shown in Figure 2, is described as follows: (6)with is a nonlinear timevarying parameter(), A and B are half of the spread of each input and out member function, respectively.The fuzzy PID co

43、ntrol actually has two levels of gains.6 The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuning of these scaling gains will affect the gains of fuzzy PIDThe fuzzy PID control actually has two levels of gains.6 The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuni

44、ng of these scaling gains will affect the gains of fuzzy PID controllers, resulting in the changing of the control performance. As the control actions are fuzzily coupled, the contribution of each Ke, Kd, K0, and K1 to different control actions is still not very clear, which makes the practical desi

45、gn and tuning process rather difficult.3 Tuning Fuzzy PID Based on the IMCTo tune the fuzzy PID controller based on the IMC method,an analytical model of the fuzzy PID controller is obtained first by simple derivation. Then, the parameters of the fuzzy PID controller can be determined on the basis o

46、f the IMC principle.Suppose that an industrial process can be modeled by a firstorder plus delay time (FOPDT) structure that has the transfer function as follows:(7)where K, T, and L are the steady-state gain, the time constant,and the time delay, respectively. The estimation of these parameters usi

47、ng the step response method, frequency response,and closed-loop relay feedback, etc., is well-described. The FOPDT model is one of the most mon and adequate ones used, especially in the process control industries.18One obtains from(6):8910with (s) being a nonlinear term without an explicit analytica

48、lexpression. Obviously, the fuzzy PID control can be considered as a conventional PID with a nonlinear pensation. The conventional PID control term is uPID(s) and the nonlinear pensation is uN(s).Tuning of Fuzzy PID Controller Based on IMC. If we consider the nonlinear pensation uN as a process dist

49、urbance and set Gf(s) )=CIMC(s), which is shown in Figure 3, the IMCbased tuning for fuzzy PID controllers can be simplified as follows. By the first-order Pade approximation, the delay time is approximated as follows:(11)Therefore, the P (s) can be factorized as P (s) ) P +(s)P -(s),其中(12)We can ac

50、hieve 13The 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; otherwise, it gives a low bandwidthand sluggish response. To improve the rise time, the value of R should be small. Therefore, the two parameters and c

51、an be determined.Remark: The fuzzy-PID control (11) is actually a conventional PID control uPID plus a pseudo-sliding mode control . Because the sliding mode control is a robust control, the fuzzy PID control is more robust than a conventional PID control.4 Control SimulationsIn this section, the co

52、ntrol performance of fuzzy PID tuned by the proposed method is pared with that of conventional PID control. Quantitative criteria for measuring the performance are chosen as IAE and ITAE. Smaller numbers imply better performance. (14)In all control simulations, parameters of conventional PID control

53、 are determined by IMC-based method and the parameters of fuzzy PID control are determined by the proposed tuning method.Example 1.Consider an industrial process that is approximately described by a first-order rational transfer function model with a delay time as follows:(15)The linear part is the

54、dominant process. The small delay time implies weak nonlinear features. As shown in Figure 5, little difference is observed between the conventional PID control and fuzzy PID control due to the small delay time. However, when the delay time is increased to L=0.6, therewill be large model error cause

55、d by approximating the delay time with a first-order Pade 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.Figure 4 Control

56、 performance of fuzzy PID Figure 5 Performance of fuzzy PID and PIDand PID for example 1, fuzzyPID (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(16)where a=1, Suppo

57、se 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

58、 the model is accurate.However, suppose that there is modeling error and the practical value of the parameter a is 0.95. 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

59、conventional PID controller, which is shown in Figure 8.Figure 6. Control performance of fuzzy PIDFigure 7. Control performance of fuzzy PIDand PIDand PID for a ) 1. FuzzyPID (solid line) andfor process a = 0.95.Fuzzy PID conventional PID (dotted line). (solid line) and conventional PID (dotted line

60、)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

61、, the parameters of fuzzy PID controller can be analytically determined by regarding the pensation item as a process disturbance. Although thescaling gainsand are coupled, a procedure is used to decouple them on the basis of the sliding mode control. The stability analysis shows that the control sys

62、tem 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 stat

63、es 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. In

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