中英文翻譯---常規(guī)pid和模糊pid算法的分析比較

1、<p>　　畢業(yè)設(shè)計(jì)(論文) 中英文資料</p><p>　　信 電 系 工業(yè)電氣自動化 專業(yè) 03 級 1 班</p><p>　　課題名稱：基于單片機(jī)的模糊PID溫度控制系統(tǒng)設(shè)計(jì)</p><p>　　畢業(yè)設(shè)計(jì)(論文)起止時間：</p><p>　　2006　年 2月15日～6月8日(共17周)</p>

2、<p>　　學(xué)生姓名： 學(xué)號： </p><p><b>　　指導(dǎo)教師： </b></p><p>　　報告日期： 2006年6月8日 </p><p>　　常規(guī)PID和模糊PID算法的分析比較</p><p>　　摘要：模糊PID控制器實(shí)際上跟傳統(tǒng)的PID控制器有很大聯(lián)系。

3、區(qū)別在于傳統(tǒng)的控制器的控制前提必須是熟悉控制對象的模型結(jié)構(gòu)，而模糊控制器因?yàn)樗姆蔷€性特性，所以控制性能優(yōu)于傳統(tǒng)PID控制器。對于時變系統(tǒng)，如果能夠很好地采用模糊控制器進(jìn)行調(diào)節(jié)，其控制結(jié)果的穩(wěn)定性和活力性都會有改善。但是，如果調(diào)節(jié)效果不好，執(zhí)行器會因?yàn)橹芷谡袷幱绊懯褂脡勖?，特別是調(diào)節(jié)器是閥門的場合，就必須考慮這個問題。為了解決這個問題，出現(xiàn)了很多模糊控制的分析方法。本文提出的方法采用一個固定的初始域，這樣相當(dāng)程度上簡化了模糊控制的設(shè)定問

4、題以及實(shí)現(xiàn)。文中分析了振蕩的原因并分析如何抑制這種振蕩的各種方法，最后，還給出一種方案，通過減少隸屬函數(shù)的數(shù)量以及改善解模糊化的方法縮短控制信號計(jì)算時間，有效的改善了控制的實(shí)時性。</p><p><b>　　1 引言</b></p><p>　　模糊控制器的一個主要缺陷就是調(diào)整的參數(shù)太多。特別是參數(shù)設(shè)定的時候，因?yàn)闆]有相關(guān)的書參考，所以它的給定非常困難。眾所周知，優(yōu)

5、化方法的收斂性跟它的初始化設(shè)定有很大關(guān)聯(lián)，如果模糊控制器的初始域是固定的，那么它的控制就明顯的簡化了。而且我們要控制的參數(shù)大多有其實(shí)際的物理意義，所以模糊控制器完全可以利用PID算法的控制規(guī)律進(jìn)行近似的調(diào)整。也就是說最簡單的模糊PID控制器就是同時采用幾種基本模糊控制算法（P+I+D或者PI+D），控制過程中它會根據(jù)控制要求，做出適當(dāng)?shù)倪x擇，保證在處理跟蹤以抗階躍干擾問題上，其控制性能接近于任何一種PID控制。假設(shè)模糊集的初始域是對稱的

6、，兩個調(diào)節(jié)器的參數(shù)采用Ziegler-Nichols方法。</p><p>　　為了改善上述設(shè)計(jì)的模糊控制器，我們有必要考模糊控制器的參數(shù)問題，有兩種方法可以采納，一種采用手動的方法改變，另一種就是采用一些相關(guān)的優(yōu)化算法。其中遺傳算法就是一種?？刂破鞑捎玫膮?shù)不同，其收斂的優(yōu)化值也會不一樣。這些參數(shù)包括模糊集的分布，模糊集的個數(shù)，映射規(guī)則，基本模糊控制器的參數(shù)和不同的算法組合等。要注意的是在優(yōu)化前必須選定模糊推理

7、及解模糊的方法。很明顯，優(yōu)化過程很耗時，更有甚者，有些優(yōu)化方法要已知系統(tǒng)的精確模型，但是實(shí)際過程中難以得到系統(tǒng)的精確模型，所以在大多數(shù)情況下，這些優(yōu)化算法不能直接應(yīng)用在實(shí)際過程。也就是說模型不精確直接影響優(yōu)化成敗。模糊控制的主要思想就是針對那些傳遞函數(shù)未知的或者結(jié)構(gòu)難以辨識的系統(tǒng)進(jìn)行控制，這也是模糊控制的性能為什么優(yōu)于傳統(tǒng)方法的原因。同時，把模糊控制和傳統(tǒng)的PID控制算法結(jié)合起來，更能體現(xiàn)這種算法的優(yōu)點(diǎn)，因?yàn)樗蟠蠛喕瘜?shí)際過程的調(diào)整。&

8、lt;/p><p>　　圖1 隸屬函數(shù)圖 圖2映射規(guī)則圖</p><p>　　參數(shù)集的啟發(fā)式優(yōu)化法也適用于模糊PI控制器，它采用固定的定義域，其參數(shù)的選取和傳統(tǒng)的PI控制器都一樣。我們采用的控制方法是結(jié)合模糊PI算法和PD算法并利用啟發(fā)式優(yōu)化法處理參數(shù)集，特別要注意這里的調(diào)節(jié)器出現(xiàn)了兩個比例環(huán)節(jié)，所以它的控制可能不同于傳統(tǒng)的PID算法。但是我們

9、調(diào)整的參數(shù)它們本身具有實(shí)際的物理意義，值得一提的是前面所提到的控制可以通過改變采樣時間而不改變定義域的范圍實(shí)現(xiàn)調(diào)整。</p><p>　　2模糊PI控制器設(shè)計(jì)</p><p>　　控制信號由模糊控制器得到（參考文獻(xiàn)[2]）：</p><p>　　模糊PI控制器的一種實(shí)現(xiàn)過程如圖3所示：</p><p>　　圖3 模糊PI控制器結(jié)構(gòu)（區(qū)域單位化

10、）</p><p>　　現(xiàn)在我們假設(shè)控制對象的傳遞函數(shù)如下描述，然后通過仿真圖比較模糊PI控制器和傳統(tǒng)PI控制器的控制性能：</p><p>　　采用[6]中所用的調(diào)節(jié)方法，我們可得參數(shù)，其響應(yīng)如圖4和圖5所示。干擾作用于系統(tǒng)的輸入，模糊控制器如圖3 所示，映射規(guī)則如圖2 所示，隸屬函數(shù)如圖1所示。</p><p>　　圖4 傳統(tǒng)PI控制圖

11、 圖5 模糊PI控制圖</p><p>　　同理取相同的參數(shù)集合，但是采用不用的模糊推理和解模糊化方法進(jìn)行優(yōu)化，我們把最大值設(shè)為10，即，采用周期，則，輸出響應(yīng)如圖5所示，下面的集合已經(jīng)在[3]中測試過了，模糊推理方法采用Min-Max 和Prod-Max，解模糊部分采用COG方法，隸屬函數(shù)采用三角形分布或單值分布，把定義域單位化，然后從七個模糊集中任取三個，進(jìn)行仿真，如果隸屬函數(shù)是單

12、值分布，也一樣。</p><p>　　把傳統(tǒng)的PI控制算法和模糊PI控制算法的結(jié)果進(jìn)行比較并討論。我們發(fā)現(xiàn)采用模糊控制的系統(tǒng)輸出超調(diào)量雖然很小，但是抗干擾能力并不比傳統(tǒng)的PI控制器好。</p><p>　　圖6 有7個隸屬函數(shù)的模糊控制 圖7有3個隸屬函數(shù)的模糊PI</p><p>　　控制器采用最小-最大模糊推理 </p>

13、<p>　　參考文獻(xiàn)[6]，看圖5，發(fā)現(xiàn)給系統(tǒng)的輸入端加上幅度為0.05的階躍干擾，系統(tǒng)輸出響應(yīng)趨向振蕩地很厲害。假設(shè)這里所有響應(yīng)采用的集合都是一樣的，我們看圖6，它的響應(yīng)曲線沒有明顯的振蕩。但是，我們還不能分析[6]所提供導(dǎo)致振蕩的可能原因，因?yàn)檫@里沒有文[6]提供的模糊控制的所需的實(shí)驗(yàn)數(shù)據(jù)集。</p><p>　　我們發(fā)現(xiàn)，即使采用遺傳優(yōu)化算法，其控制結(jié)果也沒有遠(yuǎn)遠(yuǎn)勝過模糊PI控制的近似調(diào)整結(jié)果

14、。但是我們可以通過減少隸屬函數(shù)的個數(shù)達(dá)到縮短計(jì)算控制量所需時間?？墒?，減少隸屬函數(shù)個數(shù)的同時，也會伴隨著動態(tài)性能的降低，但是這種品質(zhì)的降低完全可以通過適當(dāng)調(diào)節(jié)參數(shù)來彌補(bǔ)。從仿真結(jié)果來看，文獻(xiàn)[6]中的結(jié)論沒有理論證明。</p><p>　　3．模糊PD+PI控制器的設(shè)計(jì)</p><p>　　讓我們先給出一個模糊控制器，它是由模糊PI和模糊PD控制器并聯(lián)在一起組合而成。</p>

15、<p>　　其中，圖9是傳統(tǒng)的I-PD控制器的輸出，它采用Ziegler-Nichols方法（</p><p><b>　?。?。</b></p><p>　　而模糊PI-PD控制的設(shè)定參考文獻(xiàn)[2] （，，，，，模糊推理采用最小-最大法，解模糊采用COG方法，有7個隸屬函數(shù)）。其中PI和PD的隸屬函數(shù)的分布以及采用的模糊規(guī)則分別如圖1、圖2所示。唯一的區(qū)別

16、在于控制增量的變化，如圖11所示，圖10是仿真結(jié)果，而圖12給出了采用不同的三個集合的系統(tǒng)輸出，實(shí)線表示采用前面文章所用的調(diào)整方法，但模糊推理方法采用Prod-Max。虛線表示采用3個隸屬函數(shù)，最小最大模糊推理、解模糊采用COG（隸屬函數(shù)為三角形分布）的仿真的結(jié)果，點(diǎn)劃線表示采用3個隸屬函數(shù)，最小最大模糊推理、解模糊采用COG（隸屬函數(shù)為單值分布）的仿真的結(jié)果。</p><p>　　圖13表示系統(tǒng)輸入加入0.05

17、的階躍干擾后對系統(tǒng)的輸出影響。</p><p>　　采用模糊控制的系統(tǒng)輸出或多或少都會有振蕩，其原因不僅僅受參數(shù)的調(diào)節(jié)的影響，還有所用的最小最大模糊推理的影響。但是如果采用Prod-Max的模糊推理，解模糊時采用單值法，這種振蕩可以大大的抑制。但是造成振蕩的另一個可能原因就是推理機(jī)構(gòu)的錯誤動作。</p><p>　　從圖14我們發(fā)現(xiàn)，如果兩個相鄰的隸屬函數(shù)的最值的距離只有0.01（所用的區(qū)

18、域已經(jīng)單位化,如圖15所示），在沒有其他干預(yù)的情況下，就會出現(xiàn)等幅振蕩。眾所周知，PD控制會有初始誤差，PI控制會有振蕩。但是如果采用單值隸屬函數(shù)而不是三角形分布的隸屬函數(shù)，上述的振蕩現(xiàn)象就可以抑制。從圖14中可以看出，采用單值隸屬函數(shù)，在剛開始，系統(tǒng)輸出振蕩最厲害的時候采用單值隸屬函數(shù)，等到等幅數(shù)振蕩輸出之后就不采用單值隸屬函數(shù)（虛線表示），之后采用三角形隸屬函數(shù)和COG解模糊方法。（兩種情況都沒有穩(wěn)定誤差）。所以我們可以下結(jié)論：即使

19、采用相同的解模糊方法（COG），如果隸屬函數(shù)不一樣，控制結(jié)果也會不同的。</p><p>　　COMPARATIVE ANALYSIS OF CLASSICAL AND FUZZY PID</p><p>　　CONTROL ALGORITHMS</p><p>　　Abstract: A fuzzy PID controllers are physically r

20、elated to classical PID controller. The settings of classical controllers are based on deep common physical background. Fuzzy controller can embody better behavior comparing with classical linear PID controller because o

21、f its non linear characteristics. Well tuned fuzzy controller can be also more stable and more robust for the time varying systems. On the other hand, when the fuzzy controller is tuned badly it can exhibit limit cycle w

22、hich can d</p><p>　　1. INTRODUCTION</p><p>　　One of the main drawbacks of fuzzy controllers is big amount of parameters to be tuned. It is especially difficult to make initial approximate adjust

23、ment because there is no cookery book how to do it. Also it is very well known that good convergence of optimum method is strongly dependent on initial settings. The adjustment of fuzzy controllers is considerably simpli

24、fied when fuzzy controller with a unified universe is used. The parameters to be tune then have their physical meaning and fuzzy co</p><p>　　To improve behavior of such designed fuzzy controller it is necess

25、ary either to manually change the quantities of fuzzy controller or to use some optimum methods which do this operation. One which can be implied are genetic algorithms. Different quantities can be changed to reach the o

26、ptimum values. These quantities are fuzzy set layout, number of fuzzy sets, rule base mapping, the parameters of basic fuzzy controllers and their various combinations. Note that all the optimum must be always perf</p

27、><p>　　The heuristic optimum of parameters settings is also suitable for fuzzy PI controller with unified universe where the parameters are the same as the ones of classical PI controller. The parallel combinat

28、ion of fuzzy PI and PD controllers can be used for heuristic optimum of parameters settings but it should be noted that because of the presence of double proportional part in this regulator</p><p>　　the adju

29、sted parameters will differ from the ones of classical PID controller. But important thing is that the adjustment of this parameters is still in the same physical meaning. Note that for all previously mentioned controlle

30、rs it is also possible to employ time transformation (sample time modification) without having to change the scope of universes.</p><p>　　2. FUZZY PI CONTROLLER DESIGN</p><p>　　The control signa

31、l generated by fuzzy PI controller (according to [2]) is</p><p>　　A realization of the fuzzy PI controller is shown in Fig. 3.</p><p>　　Let us assume plant described by following transfer functi

32、on to illustrate and to compare behavior of fuzzy PI controller with classical continuous PI controller:</p><p>　　Using the tuning method from [6] we obtain parameters K=2.14, TI = 5.8 s. The responses of co

33、ntrolled system using this control algorithm are shown in Fig. 4. The disturbance acts on the input of the system. Fuzzy controller was realized according to Fig. 3 with rule base mapping according to Fig. 2. The members

34、hip functions were distributed as shown in Fig.1. </p><p>　　The similar settings of parameters K = 2.14, TI = 5 with respect to optimum for different methods of inference and defuzzification methods was used

35、. The scale was settled to M = 10 and sample period was set to T = 0.1 s. The time responses for different inference and defuzzification methods are shown in Fig. 5. The following settings were tested according to [3]. T

36、he inference method Min-Max and Prod-Max. Defuzzification was done using COG method with singletons or triangles as an output members</p><p>　　Comparing the results obtained using classical PI and fuzzy PI c

37、ontrollers following discussion can take place. The output of the system has very small overshoot when it is controlled with fuzzy regulator. The disturbance rejection using fuzzy controller is comparable with disturbanc

38、e rejection of classical PI controller.</p><p>　　In the reference [6] in Fig. 5 there was shown that the step disturbance in the input of the system with amplitude 0.05 brings the system to the significant o

39、scillations. The same settings as in this article were used to obtain time responses. As it can be seen in Fig. 6, where there are corresponding time responses, there are no any oscillations visible. However, it was not

40、possible to analyze potential causes of oscillations which were obtained in article [6] due to the lack of detailed settin</p><p>　　Significantly better results comparing with approximately adjusted fuzzy PI

41、 controller were not obtained even after the optimum using genetic algorithms. It is possible to shorten time required for computing the command by reducing the number of membership functions to three. Reduction of membe

42、rship functions brings together small degradation of dynamical behavior (Fig. 7). This degradation can be almost eliminated by fine tuning of the parameters. As a result of these simulations we can state t</p><

43、;p>　　3. FUZZY PD+PI CONTROLLER DESIGN</p><p>　　Let us create fuzzy controller as a parallel combination of fuzzy PI and PD controllers. Simulation </p><p>　　results obtained using classical I

44、-PD controller are shown in Fig. 9. This controller was adjusted using Ziegler-Nichols method (K = 7.28, TI = 2.8 s, TD = 0.7 s). </p><p>　　The initial adjustment of fuzzy PI-PD controller is taken up from r

45、eference [2] (KI = KD = 4, TI = 2.2, TD = 2, MI = MD = 10, T = 0.1 s, Min-Max inference method, COG method for defuzzification, 7 membership functions). Membership function layout and rule base for both PI and PD parts a

46、re shown in Fig. 1 and Fig. 2 respectively. The only exception is in increment of command which is realized as shown in Fig. 11. Simulation results can be seen in Fig. 10. Fig. 12 shows the time responses with thr</p&

47、gt;<p>　　The influence of disturbance with small amplitude of 0.05 which acts at the input of the system is shown in Fig. 13.</p><p>　　Fuzzy controller is generally inclinable to oscillation with rela

48、tively small amplitude. The origin of this oscillation is not only incorrect tuning of the parameters but also the inference method Min-Max. The oscillations are considerably eliminated when the Prod-Max inference method

49、 is employed and singletons for defuzzification are used. Another potential source of oscillations is wrong implementation of inference engine.</p><p>　　Shift of the vertex point of middle membership functio

50、n just for 0.01 on the normalized universe (illustrated in Fig. 15) causes the limit cycles to appear (see results in Fig. 14) without any other external intervention. The initial deviation is caused by PD controller and

51、 the oscillations by PI controller. When the singleton membership functions are used instead of triangular ones the described phenomena of oscillations disappear. Following the results in Fig. 14 it can be seen that the