模糊PID控制器的魯棒性研究外文文獻翻

1、 畢 業(yè) 設(shè) 計（論 文）外 文 文 獻 譯 文 及 原 文基于內(nèi)?？刂频哪：齪id參數(shù)的整定xiao-gang duan, han-xiong li,and hua dengschool 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摘要

2、:在本文中將利用內(nèi)?？刂频恼ǚ椒▽崿F(xiàn)模糊pid控制。此種控制方式首次應(yīng)用于模糊pid控制器，它包括一個線性pid控制器和非線性補償部分。非線性補償部分可視為一個干擾過程，模糊pid控制器的參數(shù)可在分析的基礎(chǔ)上確定內(nèi)模結(jié)構(gòu)。模糊pid控制系統(tǒng)利用李亞譜諾夫穩(wěn)定性理論進行穩(wěn)定性分析。仿真結(jié)果表明利用內(nèi)?？刂普：齪id控制參數(shù)是有效的。1 引言一般而言，傳統(tǒng)的pid控制器對于十分復(fù)雜的被控對象控制效果不太理想, 如高階時滯系統(tǒng)。在這種復(fù)雜的環(huán)境下, 眾所周知,模糊控制器由于其固有的魯棒性可以有更好的表現(xiàn)，因此，在過去30年中，模糊控制器，特別是,模糊pid控制器因其對于線性系統(tǒng)和非線性系統(tǒng)都能

3、進行簡單和有效的控制，已被廣泛用于工業(yè)生產(chǎn)過程1-4。 模糊pid控制器有多種形式5,如單輸入模糊pid控制器,雙輸入模糊pid控制器和三個輸入的模糊pid控制器。一般情況下，沒有統(tǒng)一的標準。單輸入可能會丟失派生信息, 三輸入模糊pid控制器會產(chǎn)生按指數(shù)增長的規(guī)則。在本文中所采用的雙輸入模糊pid控制器有一個適當(dāng)?shù)慕Y(jié)構(gòu)并且實用性強，因此在各種研究和應(yīng)用中,是最流行的模糊pid 類型。盡管業(yè)界對于應(yīng)用模糊pid有越來越大的興趣，但從控制工程的主流社會的角度來看,它仍然是一個極具爭議的話題。原因之一是模糊pid參數(shù)整定的基本理論分析方法至今仍不明確。因此，模糊 pid控制器不得不進行兩個級別的整定

4、。在較低層次上， 該整定是由調(diào)整增益獲得線性控制性能。在更高層次上的調(diào)整，是由改變知識庫參數(shù)以提高控制性能, 然而調(diào)整知識庫參數(shù)很難,此外，很難通過改變參數(shù)特性改善瞬態(tài)響應(yīng)。根據(jù)知識庫傳達一般控制規(guī)則傾向于保持成員函數(shù)不變，通過離線設(shè)計和調(diào)試工作擴大增益，然而，由于由模糊pid控制器生成非線性控制表面的復(fù)雜性，調(diào)整機制的衡量因素和穩(wěn)定性分析仍然是艱巨的任務(wù)。如果非線性能得到適當(dāng)?shù)睦?，模糊pid控制器可能得到比傳統(tǒng)pid控制器更好的系統(tǒng)性能。一些非常規(guī)的調(diào)整方法已進行了介紹9-12。雖然非線性被認為是在增益裕度和相位裕度基礎(chǔ)上獲得的，但是由于非線性因素，模糊pid控制器可能會產(chǎn)生比常規(guī)pid控

5、制器較高的增益。而高增益可能使控制系統(tǒng)的穩(wěn)定性變差。常規(guī)pid控制器很容易實現(xiàn)，大量的整定規(guī)則可以涵蓋廣泛的進程規(guī)格。在常規(guī)pid控制器的整定方法中，內(nèi)?？刂苹A(chǔ)整定是在商業(yè)pid控制軟件包中流行的方法之一，因為只需調(diào)整一個參數(shù)，便可以生產(chǎn)更好的設(shè)置點響應(yīng)15。本文提出了一種基于內(nèi)?？刂频膒id控制器的整定分析方法，模糊pid 控制器可分解為線性pid控制器加上非線性補償部分的控制器。把非線性補償部分近似看作一個過程干擾，模糊pid參數(shù)就可以分析設(shè)計使用內(nèi)?？刂?。模糊pid控制器的穩(wěn)定性分析是根據(jù)李亞譜諾夫穩(wěn)定性理論。最后，通過仿真來證明此種調(diào)整方法是有效的。2 問題的提出2.1 常規(guī)pid控

6、制器常規(guī)pid 控制器通常被描述為下列方程8-10：= （1） 其中e是跟蹤誤差，kp 是比例增益，ki是積分增益，kd是微分增益，ti和td分別是積分時間常數(shù)和微分時間常數(shù)，這些控制參數(shù)的關(guān)系是ki =kp/ti 和kd =kptd。pid控制器的傳遞函數(shù)可以表示如下： （2）在根軌跡中，pid控制器有兩個零點和,一個極點是原點。條件是兩個零點滿足大于4。cp+udey+_yr 圖1 內(nèi)?？刂婆渲脠D(a) +yedurp_圖2 內(nèi)?？刂婆渲脠D(b)2.2 內(nèi)模控制原則基本的內(nèi)?？刂圃瓌t如圖1所示，其中p是被控對象，p是名義上的模型對象，c是控制器，r和d是設(shè)置點和干擾，y 和 yk分別是被控

7、對象的輸出和模型對象的輸出。內(nèi)?？刂平Y(jié)構(gòu)相當(dāng)于古典單閉環(huán)反饋控制器如圖1（b）所示，如果單閉環(huán)控制器如下： （3）及 （4）其中(s)是被控模型的最小相位部分， 包含任何時間延遲和右零點，f(s)是一個低通濾波器，一般形式是： （5） 調(diào)整參數(shù)tc是理想閉環(huán)時間常數(shù)n是一個待定的正整數(shù)。kikdrulebaseseru 圖3 模糊pid控制器結(jié)構(gòu)2.3 模糊pid控制器模型模糊pid控制器如圖2所示，形式為：及 （6） 是一種非線性的時間變量參數(shù)(), a和b分別是每個輸入和輸出的成員函數(shù)一半的外延。模糊pid控制實際上有兩個層次的增益。擴大增益(ke, kd, k0, 和k1)處于較低的水平

8、。擴大增益的調(diào)整將會影響模糊pid控制器效果，造成控制參數(shù)的不斷變化。作為控制行為的模糊耦合控制， ke, kd, k0, 和 k1以何種不同的控制行動仍然沒有非常清楚，這使得實際設(shè)計和調(diào)試過程相當(dāng)困難。3 基于內(nèi)?？刂频哪：齪id整定在模糊pid控制器整定的基礎(chǔ)上的內(nèi)?？刂品椒?，通過分析模糊pid控制模型得到第一個簡單推導(dǎo)。然后，參數(shù)模糊pid 控制器可在內(nèi)?？刂频幕A(chǔ)上確定參數(shù)。假設(shè)一個工業(yè)過程可以模仿成一階加上延遲（ fopdt ）環(huán)節(jié)，傳遞函數(shù)如下： (7) 其中k、t和 l分別是穩(wěn)態(tài)增益，時間常數(shù)，和延遲時間，這些參數(shù)通過階躍響應(yīng)法，頻率響應(yīng)，和閉環(huán)繼電反饋等方法來描述的，fopdt

9、是一種最常見最實用的模型，尤其是在過程控制中18。通過式（6）可以得到： （8） （9） （10）是一個非線性項，沒有明確的分析表達。顯然，模糊pid控制可視為常規(guī)pid的非線性補償。常規(guī)pid控制部分是upid(s)， 非線性補償部分是un(s)?；趦?nèi)模控制的模糊pid整定。如果我們考慮非線性補償un(s)作為一個過程的干擾，并設(shè)置為gf(s)如圖3，基于內(nèi)?？刂频哪：齪id控制器可簡化如下： (11)因此，為 可以分解為= ，其中 (12)從而得到 （13）模糊pid在第k水平上的帶寬可以通過適合的來控制。帶寬和快速的反應(yīng)，的值越小可得到較大的帶寬和較快的響應(yīng)速度，否則帶寬變小 ，響應(yīng)緩

10、慢，因此，為了提高上升時間，的值應(yīng)該小，所以，兩個參數(shù)和可得到確定。備注：模糊pid控制實際上是一個傳統(tǒng)pid控制器upid加上滑動控制。由于滑模控制是一種魯棒控制所以模糊pid控制是力的比傳統(tǒng)的pid控制有更好的魯棒性。4 控制仿真在這一節(jié)中， 通過上述方法進行模糊pid整定的控制性能與常規(guī)pid的比較，選擇iea和itae作為標準，數(shù)值越小意味著控制性能越好。 （14） 在所有控制仿真中常規(guī)pid控制參數(shù)是由內(nèi)?？刂品椒Q定的，模糊pid控制參數(shù)是由上述整定方法確定的。范例1 考慮一個工業(yè)過程，所描述的一階延遲環(huán)節(jié)，模型函數(shù)如下： （15）線性部分在過程中占主導(dǎo)地位。小延遲時間意味著弱非線

11、性特性。由圖5可以看出，由于延遲時間小，常規(guī)pid控制和模糊pid控制差異不大。然而，當(dāng)延遲時間增加至l= 0.6，如圖6 ，模糊pid控制實現(xiàn)了優(yōu)于常規(guī)pid控制控制性能。此外模糊pid控制器增益低于常規(guī)pid控制器。 圖4 范例1中模糊pid控制（實線）和常規(guī) 圖5 延遲時間增加至l= 0.6，模糊pid控pid控制（虛線）性能比較 制（實線）和常規(guī)pid控制（虛線）性能比較 范例2 假設(shè)一工業(yè)過成描述如下： （16）其中a=1，假設(shè)不存在建模誤差，在階躍響應(yīng)和奈奎斯特工業(yè)過程曲線基礎(chǔ)上可獲得逼近模型如下： （17）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

12、是，假設(shè)有建模誤差和參數(shù)a的實際值是0.95 。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=0.95時，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)?？刂频哪：齪id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)模控制方法基礎(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

13、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 neut

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22、g method for fuzzy pid with internal model controlxiao-gang duan, han-xiong li, and hua dengschool 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 ko

23、ngan 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

24、 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 res

25、ults demonstrate the effectiveness of the proposed tuning method.1. introductiongenerally 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-

26、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 effective

27、ness 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

28、-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 great

29、er 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 c

30、ontrollers 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

31、. 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 ex

32、ercises to scaling gains. however, the 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 p

33、ose 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 tha

34、n 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 c

35、onventional 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.17an analytical tuning method based on imc to tune fuzzy pid control

36、lers 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

37、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.2 problem formulation2.1 conventional pid controllerthe conventional pid controller is often describ

38、ed by the following equation:20,21= （1）where 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 constant and the derivative time constant, respectively. the relationships between these control parameters are k

39、i = kp/ti and kd= kptd. the transfer function of the pid controller (1) can be expressed as follows: （2）on the root-locus plane, the pid controller has two zeros ti and td, and one pole at the origin. the condition to have real zeros is that ti 4td.cp+udey+_yr_figure 1 imc configuration（a）pre_+udyfi

40、gure 2 imc configuration (b)2.2 principle of imc the basic imc principle is 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 and the disturbance, and y and yk are the outputs of the plant and its nominal model, respectively.the

41、 imc structure is equivalent to the classical single-loop feedback controller shown in figure 1b. if the single-loop controller cimc is given by（3）with （4）where p (s)=p -(s)p +(s), p -(s) is the minimum phase part of the plant model, p +(s) contains any time delays and right-half plane zeros, and f(

42、s) is a low-pass filter with a steady-state gain of one, which typically has the form: （5） the tuning parameter tc is the desired closed-loop time constant, and n is a positive integer to be determined.kikdrulebaseserufigure figure 3 fuzzy-pid controller structure2.3 model of fuzzy pid controllerthe

43、 fuzzy pid controller, as shown in figure 2, is described as follows: (6)with is a nonlinear time varying parameter(), a and b are half of the spread of each input and out member function, respectively.the fuzzy pid control actually has two levels of gains.6 the scaling gains (ke, kd, k0, and k1) ar

44、e at the lower level. the tuning of these scaling gains will affect the gains of fuzzy pid the fuzzy pid control 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 pid controllers, resulti

45、ng 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 design and tuning process rather difficult.3 tuning fuzzy pid based on the imcto tune

46、 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 of the imc principle. suppose that an industrial process can be modeled by a first

47、 order 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 using the step response method, frequency response, and closed-loop relay feedba

48、ck, etc., is well-described. the fopdt model is one of the most common and adequate ones used, especially in the process control industries.18one obtains from(6): （8） （9） （10）with (s) being a nonlinear term without an explicit analytical expression. obviously, the fuzzy pid control can be considered

49、 as a conventional pid with a nonlinear compensation. the conventional pid control term is upid(s) and the nonlinear compensation is un(s).tuning of fuzzy pid controller based on imc. if we consider the nonlinear compensation un as a process disturbance and set gf(s) )=cimc(s), which is shown in fig

50、ure 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 achieve （13）the bandwidth of the fuzzy pid at the kth

51、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 can be determined.remark: the fuzzy-pid control (11

52、) 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 control performance of fuzzy pid tuned by the propos

53、ed method is compared 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 are determined by imc-based method and the parameters of fuzzy pid control are determined by th