模糊PID控制器的魯棒性研究外文文獻(xiàn)翻

1、 畢 業(yè) 設(shè) 計(jì)（論 文）外 文 文 獻(xiàn) 譯 文 及 原 文基于內(nèi)模控制的模糊pid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)模控制的整定方法實(shí)現(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(gè)線性pid控制器和非線性補(bǔ)償部分。非線性補(bǔ)償部分可視為一個(gè)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(jìn)行穩(wěn)定性分析。仿真結(jié)果表明利用內(nèi)模控制整定模糊pid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(duì)于十分復(fù)雜的被控對(duì)象控制效果不太理想, 如高階時(shí)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(duì)于線性系統(tǒng)和非線性系統(tǒng)都能

3、進(jìn)行簡(jiǎn)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(gè)輸入的模糊pid控制器。一般情況下，沒有統(tǒng)一的標(biāo)準(zhǔn)。單輸入可能會(huì)丟失派生信息, 三輸入模糊pid控制器會(huì)產(chǎn)生按指數(shù)增長(zhǎng)的規(guī)則。在本文中所采用的雙輸入模糊pid控制器有一個(gè)適當(dāng)?shù)慕Y(jié)構(gòu)并且實(shí)用性強(qiáng)，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(duì)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(huì)的角度來看,它仍然是一個(gè)極具爭(zhēng)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(jìn)行兩個(gè)級(jí)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(shí)庫(kù)參數(shù)以提高控制性能, 然而調(diào)整知識(shí)庫(kù)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(shí)庫(kù)傳達(dá)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(jì)和調(diào)試工作擴(kuò)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(jī)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(jìn)行了介紹9-12。雖然非線性被認(rèn)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(huì)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(shí)現(xiàn)，大量的整定規(guī)則可以涵蓋廣泛的進(jìn)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?yàn)橹恍枵{(diào)整一個(gè)參數(shù)，便可以生產(chǎn)更好的設(shè)置點(diǎn)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(bǔ)償部分的控制器。把非線性補(bǔ)償部分近似看作一個(gè)過程干擾，模糊pid參數(shù)就可以分析設(shè)計(jì)使用內(nèi)模控制。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(shí)間常數(shù)和微分時(shí)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(gè)零點(diǎn)和,一個(gè)極點(diǎn)是原點(diǎn)。條件是兩個(gè)零點(diǎn)滿足大于4。cp+udey+_yr 圖1 內(nèi)?？刂婆渲脠D(a) +yedurp_圖2 內(nèi)模控制配置圖(b)2.2 內(nèi)?？刂圃瓌t基本的內(nèi)?？刂圃瓌t如圖1所示，其中p是被控對(duì)象，p是名義上的模型對(duì)象，c是控制器，r和d是設(shè)置點(diǎn)和干擾，y 和 yk分別是被控

7、對(duì)象的輸出和模型對(duì)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(shí)間延遲和右零點(diǎn)，f(s)是一個(gè)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(shí)間常數(shù)n是一個(gè)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(shí)間變量參數(shù)(), a和b分別是每個(gè)輸入和輸出的成員函數(shù)一半的外延。模糊pid控制實(shí)際上有兩個(gè)層次的增益。擴(kuò)大增益(ke, kd, k0, 和k1)處于較低的水平

8、。擴(kuò)大增益的調(diào)整將會(huì)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(dòng)仍然沒有非常清楚，這使得實(shí)際設(shè)計(jì)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)模控制方法，通過分析模糊pid控制模型得到第一個(gè)簡(jiǎn)單推導(dǎo)。然后，參數(shù)模糊pid 控制器可在內(nèi)模控制的基礎(chǔ)上確定參數(shù)。假設(shè)一個(gè)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(shí)間常數(shù)，和延遲時(shí)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(shí)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(gè)非線性項(xiàng)，沒有明確的分析表達(dá)。顯然，模糊pid控制可視為常規(guī)pid的非線性補(bǔ)償。常規(guī)pid控制部分是upid(s)， 非線性補(bǔ)償部分是un(s)?；趦?nèi)?？刂频哪：齪id整定。如果我們考慮非線性補(bǔ)償un(s)作為一個(gè)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(jiǎn)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(shí)間，的值應(yīng)該小，所以，兩個(gè)參數(shù)和可得到確定。備注：模糊pid控制實(shí)際上是一個(gè)傳統(tǒng)pid控制器upid加上滑動(dòng)控制。由于滑?？刂剖且环N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(jìn)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(biāo)準(zhǔn)，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)模控制方法決定的，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(gè)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(shí)間意味著弱非線

11、性特性。由圖5可以看出，由于延遲時(shí)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(shí)間增加至l= 0.6，如圖6 ，模糊pid控制實(shí)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(shí)線）和常規(guī) 圖5 延遲時(shí)間增加至l= 0.6，模糊pid控pid控制（虛線）性能比較 制（實(shí)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?yàn)樵撃Ｐ褪钦_的。但

12、是，假設(shè)有建模誤差和參數(shù)a的實(shí)際值是0.95 。如圖8，模糊pid控制比常規(guī)pid控制實(shí)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(shí)，模糊pid控制（實(shí)線）和常規(guī) 圖7 a=0.95時(shí)，模糊pid控制（實(shí)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(gè)線性pid控制及非線性補(bǔ)償部分。在內(nèi)?？刂品椒ɑA(chǔ)上， 模糊pid控制器的參數(shù)可由過程干擾的補(bǔ)償部分來分析確定。雖然擴(kuò)大收益 和是耦合的，這一程序是

13、在解耦基礎(chǔ)上的滑動(dòng)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(qiáng)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(dòng)態(tài)和靜態(tài)上都實(shí)現(xiàn)更好的控制性能和更好的魯棒性。參考文獻(xiàn)(1) sugeno. m. industrial applications of fuzzy control; elsevier: amsterdam, the netherlands, 1985.(2) manel, a.; albert, a.; jordi, a.; manel, p. wastewater neut

14、ralization.control based on fuzzy logic: experimental results. ind. eng. chem. res. 1999, 38, 27092719.(3) zhang, j. a nonlinear gain scheduling control strategy based on neuro-fuzzy networks. ind. eng. chem. res. 2001, 40, 31643170.(4) hojjati, h.; sheikhzadeh, m.; rohani, s. control of supersatura

15、tion in a semibatch antisolvent crystallization process using a fuzzy logic controller. ind. eng. chem. res. 2007, 46, 12321240.(5) george, k. i. m.; hu, b. g.; raymond, g. g. analysis of direct action fuzzy pid controller structures. ieee trans. syst., man, cybernetics, part b 1999, 29 (3), 371388.

16、(6) li, h. x.; gatland, h. conventional fuzzy logic control and its enhancement. ieee trans. syst., man, cybernetics 1996, 26 (10), 791797.(7) george, k. i. m.; hu, b. g.; raymond, g. g. two-level tuning of fuzzy pid cotrollers. ieee trans. syst., man, cybernetics, part b 2001, 31 (2), 263269.(8) wo

17、o, z. w.; chung, h. y.; lin, j. j. a pid type fuzzy controller with self-tuning scaling factors. fuzzy sets syst. 2000, 115, 321326.(9) vega, p.; prada, c.; aleixander, v. self-tuning predictive pid controller. iee pro. d 1991, 138 (3), 303311.(10) rajani, k. m.; nikhil, r. p. a robust self-tuning s

18、cheme for piand pd-type fuzzy controllers. ieee ttrans. fuzzy syst. 1999, 7 (1), 216.(11) rajani, k. m.; nikhil, r. p. a self-tuning fuzzy pi controller. fuzzy sets syst. 2000, 115, 327338.(12) yesil, e.; guzelkaya, m.; eksin, i. self tuning fuzzy pid type load and frequency controller. energy conve

19、rs. manage. 2004, 45, 377390.(13) xu, j. x.; pok, y. m.; liu, c.; hang, c. c. tuning and analysis of a fuzzy pi controller based on 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 a fuzzy p

20、id controller. automatica 2000, 36, 673684.(15) kaya, i. obtaining controller parameters for a new pi-pd smith predictor using autotuning. j. process control 2000, 13, 465472.(16) li, y.; kiam, h. a.; gregory, c. y. patents, software, and hardware for pid control. ieee control syst. mag. 2006, 4254.

21、(17) cha, s. y.; chun, d. w.; lee, j.t. two-step imc-pid method for multiloop control system design. ind. eng. chem. res. 2002, 41, 30373041.(18) li, h. x.; gatland, h. b.; green, a. w. fuzzy variable structure control. ieee trans. syst., man, cybernetics, part b 1997, 27 (2), 306312.effective tunin

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