電氣類外文翻譯----基于記憶的在線非線性系統(tǒng)pid控制器整定

1、<p><b>　　附錄二:翻譯</b></p><p>　　Memory-Based On-Line Tuning of PID Controllers for Nonlinear Systems</p><p>　　Abstract—Since most processes have nonlinearities, controller design s

2、chemes to deal with such systems are required.On the other hand, PID controllers have been widely used for process systems. Therefore, in this paper, a new design scheme of PID controllers based on a memory-based(MB) mod

3、eling is proposed for nonlinear systems. According to the MB modeling method, some local models are automatically generated based on input/output data pairs of the controlled object stored in the data-base. The</p>

4、<p>　　I. INTRODUCTION</p><p>　　In recent years, many complicated control algorithms such as adaptive control theory or robust control theory have been proposed and implemented. However, in industrial

5、processes, PID controllers[1], [2], [3] have been widely employed for about 80% or more of control loops. The reasons are summarized as follows. (1) the control structure is quitsimple; (2) the physical meaning of contro

6、l parameters is clear; and (3) the operators’ know-how can be easily utilized in designing controllers. Therefo</p><p>　　In this paper, a design scheme of PID controllers based onthe MB modeling method is di

7、scussed. A few PID controllers have been already proposed based on the JIT method[10] and the MoD method[11] which belong to the MB modeling methods. According to the former method, the JIT method is used as the purpose

8、of supplementing the feedback controller with a PID structure. However, the tracking property is not guaranteed enough due to the nonlinearities in the case where reference signals are changed, </p><p>　　II.

9、 PID CONTROLLER DESIGN BASED ON MEMORY-BASED MODELING METHOD</p><p>　　A. MB modeling method</p><p>　　First, the following discrete-time nonlinear system is considered:</p><p>　　,

10、 （1）</p><p>　　where y(t) denotes the system output and f(·) denotes the nonlinear function. Moreover, _(t?1) is called ’information vector’, which is defie

11、d by the following equation:</p><p>　　, （2）</p><p>　　where u(t) denotes the system input. Also, ny and nure spectively denote the orders of the system output and the syst

12、em input, respectively. According to the MB modeling method, the data is stored in the form of the information vector _ expressed in Eq.(2). Moreover, _(t) is required in calculating the estimate of the output y(t+1) cal

13、led ’query’.That is, after some similar neighbors to the query are selected from the data-base, the predictive value of the system can beobtained using these neigh</p><p>　　B. Controller design based on MB m

14、odeling method</p><p>　　In this paper, the following control law with a PID structure is considered:</p><p><b>　　（3）</b></p><p><b>　?。?）</b></p><p

15、>　　where e(t) denotes the control error signal defined by</p><p>　　e(t) := r(t) ? y(t). （5）</p><p>　　r(t) denotes the reference signal. Also

16、, kc, TI and TD respectively denote the proportional gain, the reset time and the derivative time, and Ts denotes the sampling interval. Here, KP , KI and KD included in Eq.(4) are derived by therelations =，=/和=/。denotes

17、 the differencing operator defined by. .</p><p>　　Here, it is quite difficult to obtain a good control performance due to nonlinearities, if PID parameters(KP, KI , KD) in Eq.(4) are fixed. Therefore, a new

18、control scheme is proposed, which can adjust PID parameters in an on-line manner corresponding to characteristics of the system. Thus, instead of Eq.(4), the following PID control law with variable PID parameters is empl

19、oyed:</p><p><b>　?。?）</b></p><p>　　Now, Eq.(6) can be rewritten as the following relations:</p><p><b>　　（7）</b></p><p><b>　?。?）</b>&

20、lt;/p><p><b>　　（9）</b></p><p>　　where g(·) denotes a linear function. By substituting Eq.(7)and Eq.(8) into Eq.(1) and Eq.(2), the following equation canbe derived:</p><

21、p><b>　　（10）</b></p><p><b>　?。?1）</b></p><p>　　where ny _ 3, nu _ 2, and h(·) denotes a nonlinear function.Therefore, K(t) is given by the following equations:<

22、/p><p><b>　?。?2）</b></p><p><b>　　（13）</b></p><p>　　where F(·) denotes a nonlinear function. Since the future output y(t + 1) included in Eq.(13) cannot be

23、obtained at t, y(t+1) is replaced by r(t+1). Because the control system</p><p>　　so that can realize y(t + 1) ! r(t + 1), is designed in this paper. Therefore, ¯_(t) included in Eq.(13) is newly rewritt

24、en as follows:</p><p><b>　　（14）</b></p><p>　　After the above preparation, a new PID control scheme is designed based on the MB modeling method. The controller design algorithm is sum

25、marized as follows.[STEP 1] Generate initial data-base</p><p>　　The MB modeling method cannot work if the past data is not saved at all. Therefore, PID parameters are firstly calculated using Zieglar & N

26、ichols method[2] or Chien, Hrones & Reswick(CHR) method[3] based on historical data of the controlled object in order to generate the initial database. That is, _(j) indicated in the following equation isgenerated as

27、 the initial data-base:</p><p><b>　?。?5）</b></p><p>　　where and are given by Eq.(14) and Eq.(9).</p><p>　　Moreover, N(0) denotes the number of information vectorsstored

28、 in the initial data-base. Note that all PID parametersincluded in the initial information vectors are equal, that is,</p><p>　　K(1) = K(2) = · · · = K(N(0)) in the initial stage.</p>&

29、lt;p>　　[STEP 2] Calculate distance and select neighbors</p><p>　　Distances between the query and the informationvectors are calculated using the following L1-norm with some weights:</p><p>

30、<b>　?。?6）</b></p><p>　　where N(t) denotes the number of information vectors storedin the data-base when the query is given. Furthermore, denotes the l-th element of the j-th information vector.

31、Similarly, denotes the l-th element of the query at t. Moreover, denotes the maximum element among the l-th element of all information vectors stored in the data-base. Similarly, denotes the minimum element. Here, k pie

32、ces with the smallest distances are chosen from all information vectors.</p><p>　　[STEP 3] Construct local model</p><p>　　Next, using k neighbors selected in STEP 2, the localmodel is constructe

33、d based on the following LinearlyWeighted Average(LWA)[12]:</p><p><b>　?。?7）</b></p><p>　　where wi denotes the weight corresponding to the i-th information vector in the selected ne

34、ighbors, and is calculated by:</p><p><b>　　（18）</b></p><p>　　[STEP 4] Data adjustment</p><p>　　In the case where information corresponding to the current state of the co

35、ntrolled object is not effectively saved in the data-base, a suitable set of PID parameters cannot be effectively calculated. That is, it is necessary to adjust PID parameters so that the control error decreases. Therefo

36、re, PID parameters obtained in STEP 3 are updated corresponding to the control error, and these new PID parameters are stored in the data-base. The following steepest descent method is utilized in order to </p>&l

37、t;p><b>　?。?9）</b></p><p><b>　?。?0）</b></p><p>　　where _ denotes the learning rate, and 饎he following J(t+1)denotes the error criterion:</p><p><b>　　

38、（21）</b></p><p><b>　　（22）</b></p><p>　　yr(t) denotes the output of the reference model which isgiven by:</p><p><b>　　(23)</b></p><p><b

39、>　　(24)</b></p><p>　　Here, T (z?1) is designed based on the reference</p><p>　　literature[13]. Moreover, each partial differential of Eq.(19)</p><p>　　is developed as follo

40、ws:</p><p>　　. （25）</p><p>　　Note that a priori information with respect to the systemJacobian is required in order to calculateEq.(25). Here, using the relation x = |x|sign(x), the syst

41、emJacobian can be obtained by the following equation:</p><p><b>　　（26）</b></p><p>　　where sign(x) = 1(x > 0), ?1(x < 0). Now, if the sign of the system Jacobian is known in adv

42、ance, by including in , the usage of the system Jacobian can make easy[14]. Therefore, it is assumed that the sign of the system Jacobian is known in this paper.</p><p>　　[STEP 5] Remove redundant data</

43、p><p>　　In implementing to real systems, the newly proposed scheme has a constraint that the calculation from STEP 2 to STEP 4 must be finished within the sampling time. Here,storing the redundant data in the d

44、ata-base needs excessive computational time. Therefore, an algorithm to avoid the excessive increase of the stored data, is further discussed. The procedure is carried out in the following two steps. First, the informati

45、on vectors which satisfy the following first condition, are extracted from the</p><p>　　[First condition]</p><p><b>　?。?7）</b></p><p>　　whereis defined by</p><

46、;p><b>　?。?8）</b></p><p>　　Moreover, the information vectors which satisfy the following second condition, are further chosen from the extracted:</p><p><b>　　（29）</b>&

47、lt;/p><p>　　where is defined by</p><p><b>　　（30）</b></p><p>　　If there exist plural, the information vector with the smallest value in the second condition among all, is

48、only removed. By the above procedure, the redundant datacan be removed from the data-base. Here, a block diagram summarized mentioned above algorithms are shown in Fig.</p><p>　　III. SIMULATION EXAMPLE</p

49、><p>　　In order to evaluate the effectiveness of the newly proposed</p><p>　　scheme, a simulation example for a nonlinear system is considered.</p><p>　　As the nonlinear system, the fo

50、llowing Hammerstein</p><p>　　model[15] is discussed:</p><p>　　[System 1]</p><p><b>　?。?1）</b></p><p>　　[System 2]</p><p><b>　?。?2）</b&

51、gt;</p><p>　　where denotes the white Gaussian noise with zero mean and variance. Static properties of System 1 and System 2 are shown in Fig.2. </p><p><b>　　Fig.2 </b></p>&

52、lt;p>　　From Fig.2, it is clear that gains of System 2 are larger than ones of System 1 at. Here, the reference signal r(t) is given by:</p><p><b>　?。?3）</b></p><p>　　The informati

53、on vector ¯_ is defined as follows:</p><p><b>　?。?4）</b></p><p>　　The desired characteristic polynomial included in the reference model was designed as follows:</p><p

54、><b>　?。?5）</b></p><p>　　where T (z?1) was designed based on the reference literature[13]. Furthermore, the user-specified parameters included in the proposed method are determined as shown inT

55、able I.</p><p>　　TABLE I USER-SPECIFIED PARAMETERS INCLUDED IN THE PROPOSED METHOD (HAMMERSTEIN MODEL).</p><p>　　For the purpose of comparison, the fixed PID control scheme which has widely used

56、 in industrial processes was first employed, whose PID parameters were tuned by CHR method[3]. Then, PID parameters were calculated as</p><p><b>　　（36）</b></p><p>　　Moreover, the PID

57、 controller using the NN, called NN-PID controller, was applied for the purpose of the comparison, where the NN was utilized in order to supplement the fixed PID controller.</p><p>　　The control results for

58、System 1 are summarized in Fig.3, where the solid line and dashed line denote the control results of the proposed method and the fixed PID controller, respectively. </p><p>　　Furthermore, trajectories of PID

59、 parameters using the proposed method are shown in Fig.4. From Fig.3, owing to nonlinearities of the controlled object, the control result by the fixed PID controller is not good. On the other hand, from Fig.3 and Fig.4,

60、 the good control result can be obtained using the proposed method, because PID parameters are adequately adjusted. Moreover, the number of data stored in the database was 49. Using the algorithm to remove needless data,

61、 the number of data stored i</p><p><b>　　（37）</b></p><p>　　where N denotes the number of steps per 1[epoc]. Furthermore, the number of iteration was set as 1, because PID parameters

62、can be adjusted in an on-line manner by the proposed method. Moreover, the NN-PID controller was applied to System 1. Error behaviors of _ expressed in Eq.(37) are shown in Fig.5, and control results are shown in Fig.6.

63、</p><p><b>　　Fig.5</b></p><p><b>　　Fig.6</b></p><p>　　From Fig.5, the necessary number for learning iterations was 86[epoc] until the control result using th

64、e NN-PID controller could be obtained the same control performances as the proposed method, that is, until was satisfied. Therefore, the effectiveness of the proposed method is also verified in comparison with the NN-PI

65、D controller for nonlinear systems.Next, the case where the system has time-variant parametersis considered. That is, the system changes from Eq.(31)</p><p>　　Fig. 5. Error behaviors using the controller fus

66、ed the fixed PID with the NN-PID for Hammerstein model.Fig. 6. Control result using the controller fused the fixed PID with the NN-PID for Hammerstein model. to Eq.(32) at t = 70. First, the control result with the fixed

67、 PID controller, is shown in Fig.7, </p><p>　　where PID parameters are set as the same parameters as shown in Eq.(36). Since the gain of the controlled object becomes high gain around r(t) = 2.0, the fixed P

68、ID controller does not work well. On the other hand, the proposed control scheme was employed in this case. The control result and trajectories of PID parameters are shown in Fig.8 and Fig.9. </p><p><b&g

69、t;　　Fig.8</b></p><p>　　From these figures, a good control performance can be also obtained because PID parameters are adequately adjusted using the proposed method. The usefulness for the nonlinear sys

70、tem with time-variant parameters is suggested in this example.</p><p>　　IV. CONCLUSIONS</p><p>　　In this paper, a new design scheme of PID controllers using the MB modeling method has been propo

71、sed. Many PID controller design schemes using NNs and GAs have been proposed for nonlinear systems up to now. In employing these scheme for real systems, however, it is a serious problem that the learning cost becomes co

72、nsiderably large.On the other hand, according to the proposed method, such computational burdens can be effectively reduced using the algorithm for removing the redundant data. In add</p><p>　　基于記憶的在線非線性系統(tǒng)PI

73、D控制器整定</p><p><b>　　摘 要</b></p><p>　　由于大部分控制過程具有非線性，所以設(shè)計(jì)一種能夠處理具有非線性系統(tǒng)的控制器就顯得尤為重要。另一方面，PID控制器也被廣泛應(yīng)用于過程控制系統(tǒng)中。因此，在本文中提出了一種基于記憶的MB模型用來處理非線性PID控制器設(shè)計(jì)方案。通過MB方法，可以自動(dòng)產(chǎn)生基于存儲(chǔ)在數(shù)據(jù)中的控制對(duì)象的輸入/輸出數(shù)據(jù)對(duì)的

74、本地模型。這種設(shè)計(jì)方案，通過存儲(chǔ)在數(shù)據(jù)庫中的輸入/輸出數(shù)據(jù)產(chǎn)生變量。即使系統(tǒng)具有非線性，該設(shè)計(jì)方案。同樣能在線調(diào)整PID變量。最后，我們通過一個(gè)仿真系統(tǒng)的數(shù)據(jù)演化過程來證明該方案的有效性。</p><p><b>　?、?引言</b></p><p>　　近年來，像自適應(yīng)控制理論，魯棒控制理論等一些復(fù)雜的控制算法被提出和應(yīng)用。但是，在工業(yè)過程中PID控制器依然占80%

75、甚至更多的比例，其原因如下所述：（1）控制結(jié)構(gòu)簡單；（2）控制參數(shù)物理意義清晰；（3）能夠很好地滿足客戶要求。因此，PID控制器的設(shè)計(jì)自然具有強(qiáng)大的吸引力。但是由于大部分控制系統(tǒng)具有非線性，簡單地應(yīng)用固定PID參數(shù)很難得到交好的控制效果。所以到現(xiàn)在為止已經(jīng)提出了神經(jīng)網(wǎng)絡(luò)（NN）和遺傳算法（GA）等PID參數(shù)整定方法。使用這些方法的學(xué)習(xí)代價(jià)是很大的，而且PID參數(shù)由于系統(tǒng)的非線性特征不能得到充分的調(diào)整。因而通過這些方便的方法不能得到很好的

76、控制效果。</p><p>　　不過，計(jì)算機(jī)的發(fā)展讓我們能夠記憶，快速檢索以及讀取大量數(shù)據(jù)?；谶@些優(yōu)點(diǎn)我們提出了以下方案：無論何時(shí)獲得的新數(shù)據(jù)都被保存下來。被稱為“詢問”的信息要求從保存的數(shù)據(jù)中提取出來。這種基于記憶模型（MB）的方法叫做JIT方法。懶散學(xué)習(xí)方法或MOD方法。并且在過去的十年中，這些方法被給予了大量的關(guān)注。</p><p>　　在本文中討論了一種基于MB模型的PID控制器

77、設(shè)計(jì)方案。一些基于用屬于MB模型方法的JIT方法的PID控制器已經(jīng)被提出。基于以前的方法，用JIT方法的目的是應(yīng)用PID結(jié)構(gòu)的輔助反饋控制器，但是，在相關(guān)信號(hào)改變的情況下的非線性，將會(huì)導(dǎo)致跟蹤特性沒有足夠的保證，因?yàn)樵谡麄€(gè)控制系統(tǒng)中控制器不包含任何的積分行為。另一方面，后一種方法具有一個(gè)PID控制結(jié)構(gòu)。PID參數(shù)不是通過與控制對(duì)象的特征相一致的在線方式整定的。</p><p>　　因此，在本文中我們設(shè)計(jì)提出了一種

78、基于MB模型的方法。通過這種新方法，有MB模型方法得到的PID參數(shù)在比例環(huán)節(jié)中得到了充分的整定，這主要是為了控制誤差。規(guī)劃后的PID參數(shù)被保存在數(shù)據(jù)庫中。因此，回游更多的與空話子對(duì)象特征相一致的適當(dāng)?shù)腜ID參數(shù)被保存。再者，我們進(jìn)一步提出了一種避免存儲(chǔ)數(shù)據(jù)過分增長的算法。這種算法可以減少記憶和計(jì)算機(jī)花費(fèi)。最后，這種新方法的有效度通過一個(gè)仿真模型來檢測。</p><p>　　Ⅱ 基于記憶模型的PID控制器設(shè)計(jì)方法&

79、lt;/p><p><b>　　A MB模型方法</b></p><p>　　第一，我們引入了如下時(shí)間遞減非線性系統(tǒng)</p><p><b>　?。?）</b></p><p>　　其中，表示系統(tǒng)輸出， 表示非線性函數(shù)，被稱為‘信息矢量’通過下式定義：</p><p><

80、b>　?。?）</b></p><p>　　其中， 表示系統(tǒng)輸入，另外，和分別表示系統(tǒng)的輸出和輸入的階數(shù)。在MB模型方法中數(shù)據(jù)一等式（2）中的信息矢量 的形式被存儲(chǔ)。在估計(jì)輸出時(shí)，需要 ，因此被叫做詢問。一些相似相鄰數(shù)被從數(shù)據(jù)庫中選出后，我們可以通過這些相鄰數(shù)而獲得系統(tǒng)的預(yù)測值。</p><p>　　B 基于MB模型方法的控制器設(shè)計(jì)</p><p

81、>　　在本文中我們引用了具有如下PID結(jié)構(gòu)的控制規(guī)律：</p><p><b>　　（3）</b></p><p><b>　?。?）</b></p><p>　　其中表示誤差控制信號(hào)，有如下定義：</p><p><b>　　（5）</b></p><

82、;p>　　其中表示相關(guān)信號(hào)，另外，，和分別表示比例增益，調(diào)節(jié)時(shí)間和微分時(shí)間，表示采樣時(shí)間。在這里等式（4）中的,和有如下聯(lián)系： =，=/和=/。表示操作者的區(qū)別，并被定義為：。在這里由于非線性的存在我們將很難獲得好的控制效果，這是在式（4）中的，，確定不變的假設(shè)下才成立的。因此，一種新的控制方案被提出來，這種方法能夠通過與系統(tǒng)特征保持一致的在線方式調(diào)整PID參數(shù)。因而有了如下取代等式（4）的具有可變PID參數(shù)的PID控制規(guī)律：&l

83、t;/p><p><b>　?。?）</b></p><p>　　現(xiàn)在等式（6）可以重新變成如下形式：</p><p><b>　　（7）</b></p><p><b>　?。?）</b></p><p><b>　　（9）</b>&

84、lt;/p><p>　　其中表示一個(gè)線性函數(shù)，將式（1）和式（2）帶入式（7）和式（8）中我們可以得到如下等式：</p><p><b>　?。?0）</b></p><p><b>　　（11）</b></p><p>　　其中，ny≥3,nu≥2,h(1)表示一個(gè)非線性函數(shù)，因而通過下面等式給出：&

85、lt;/p><p><b>　?。?2）</b></p><p><b>　　（13）</b></p><p>　　其中，表示非線性函數(shù)，既然下一個(gè)輸出不能在t時(shí)刻得到我們就用來代替。為了使控制系統(tǒng)能夠識(shí)別本文中所定義的 —> ，等式（13）中的可以被重新寫成如下形式：</p><p><b

86、>　　（14）</b></p><p>　　經(jīng)過以上的準(zhǔn)備工作以后，一種基于MB模型方法的PID控制被設(shè)計(jì)出來了。下面對(duì)控制器的設(shè)計(jì)算法作簡單闡述。</p><p>　　第一步：產(chǎn)生初試數(shù)據(jù)庫</p><p>　　如果以前的數(shù)據(jù)沒有被全部保存，MB模型方法將不能工作。因此首先通過Z-N方法或CHR方法計(jì)算出PID參數(shù)。這兩種方法都是在原有歷史記錄的

87、基礎(chǔ)上初始化數(shù)據(jù)庫。在下面等式中存在的被稱為初試數(shù)據(jù)庫。</p><p><b>　　（15）</b></p><p>　　其中，和分別由式（14）和式（9）獲得。表示存儲(chǔ)在初始數(shù)據(jù)庫中的信息矢量的數(shù)量。注意它在初始信息矢量中的PID參數(shù)是相等的，即：。</p><p>　　第二步：計(jì)算距離，選擇相鄰數(shù)</p><p>

88、　　詢問和信息矢量之間的距離通過下述具有一定重復(fù)的—一范數(shù)計(jì)算出</p><p><b>　?。?6）</b></p><p>　　表示當(dāng)詢問給出時(shí)，數(shù)據(jù)庫中存儲(chǔ)的信息矢量數(shù)量表示第個(gè)信息矢量的第個(gè)元素。類似地，表示在t時(shí)刻詢問第個(gè)元素。表示在數(shù)據(jù)庫中所存儲(chǔ)的所有信息矢量的第個(gè)元素的最大值。</p><p>　　類似地，則表示最小元素，在這里具

89、有最小距離的被從所有的信息矢量中選擇出來。</p><p>　　第三步：建立本地模型</p><p>　　接下來，使用第一步中所選擇的，然后基于如下線性平均質(zhì)量建立本地模型：</p><p><b>　　（17）</b></p><p>　　其中，表示和第個(gè)信息矢量相一致的重量。取自于所選擇的鄰居，并且通過下式計(jì)算：&l

90、t;/p><p><b>　　（18）</b></p><p><b>　　第四步：數(shù)據(jù)調(diào)整</b></p><p>　　在和控制對(duì)象相一致的現(xiàn)在狀態(tài)不能有效保存到數(shù)據(jù)庫中的情況下，一個(gè)適當(dāng)?shù)腜ID參數(shù)不可能被有效的計(jì)算出來。為了減少控制誤差，必須調(diào)整PID參數(shù)。因此在步驟3中所得出來的PID參數(shù)將作和控制誤差一致的更新。然后

91、這些新的PID參數(shù)被保存到數(shù)據(jù)庫中。如下懸崖遞減法被用來規(guī)范PID參數(shù)。</p><p><b>　?。?9）</b></p><p><b>　?。?0）</b></p><p>　　其中表示學(xué)習(xí)率。下式所示表示誤差指標(biāo)：</p><p><b>　?。?1）</b><

92、/p><p><b>　?。?2）</b></p><p>　　表示相關(guān)模型的輸出，該模型如下所示：</p><p><b>　　(23)</b></p><p><b>　　(24)</b></p><p>　　在這里，是基于文獻(xiàn)[13]而設(shè)計(jì)的。與等式（

93、19）的每一部分區(qū)別描述如下：</p><p><b>　?。?5）</b></p><p>　　注意到為了計(jì)算等式（25）要求一個(gè)考慮系統(tǒng)雅可比行列式的優(yōu)先信息。在這里通過關(guān)系式，系統(tǒng)的雅可比行列式可以通過如下等式獲得：</p><p><b>　?。?6）</b></p><p>　　其中?，F(xiàn)在

94、如果系統(tǒng)的雅可比行列式的標(biāo)記提前知道，在里包括，雅可比行列式的使用將會(huì)變的簡單。因而在本文中我們假設(shè)系統(tǒng)雅可比行列式的標(biāo)記是已知的。</p><p>　　第五步：轉(zhuǎn)移多余的數(shù)據(jù)</p><p>　　應(yīng)用到理想系統(tǒng)，新提出的這種方法具有一定的局限性那就是：從步驟2到步驟4需要在一個(gè)采樣周期內(nèi)完成。在這里保存了多余的數(shù)據(jù)于數(shù)據(jù)庫中需要很多的計(jì)算時(shí)間，因而進(jìn)一步提出了一種防止保存數(shù)據(jù)過分增加的算

95、法。這一過程通過以下兩個(gè)步驟實(shí)現(xiàn)：</p><p>　　首先，滿足如下第一種情況的信息矢量被從數(shù)據(jù)庫中抽取出來。</p><p>　　[第一種情況] </p><p><b>　　（27）</b></p><p><b>　　其中被定義為：</b></p><p>&l

96、t;b>　　[第二種情況] </b></p><p><b>　?。?8）</b></p><p>　　其次，滿足如下第二種情況的信息矢量，將會(huì)被進(jìn)一步從已經(jīng)抽出里選取出來。 </p><p><b>　?。?9）</b></p><p><b>　　其中被定義為 &

97、lt;/b></p><p><b>　?。?0）</b></p><p>　　如果存在復(fù)數(shù)，在第二種情況中所有的中具有最小值的信息矢量將會(huì)被從數(shù)據(jù)中轉(zhuǎn)移出去。</p><p>　　在這里，一個(gè)關(guān)于以上所提出的方法的簡要原理圖如圖1所示。</p><p>　　圖1 所提出系統(tǒng)的框圖</p><p

98、><b>　?、?仿真實(shí)例</b></p><p>　　為了評(píng)價(jià)我們新提出的方法的有效度引用了一個(gè)非線性系統(tǒng)進(jìn)行仿真，作為非線性系統(tǒng)，我們討論如下的Hammerstein模型。</p><p><b>　　[系統(tǒng)1] </b></p><p><b>　?。?1）</b></p>

99、;<p><b>　　[系統(tǒng)2] </b></p><p><b>　?。?2）</b></p><p>　　其中，表示具有零定義且變量為的高斯白噪聲信號(hào)。系統(tǒng)1和系統(tǒng)2的靜態(tài)特性如圖2所示，</p><p>　　圖2 系統(tǒng)1和系統(tǒng)2的靜態(tài)特性</p><p>　　從圖2中我們可

100、以清楚地看出在是系統(tǒng)2具有比系統(tǒng)1大的增益。這里相關(guān)信號(hào)有下式給出： </p><p><b>　?。?3）</b></p><p>　　而信息矢量作如下定義： </p><p><b>　?。?4）</b></p><p>　　它包含在相關(guān)模型中的期望多項(xiàng)式特征設(shè)計(jì)如下：</

101、p><p><b>　　（35）</b></p><p>　　其中是基于相關(guān)文獻(xiàn)[13]而設(shè)計(jì)的。另外，該方法中用戶規(guī)格的參數(shù)是有表1所決定的。</p><p>　　表1 包含在設(shè)計(jì)方法（Hammerstein方法）中的用戶指定參數(shù)</p><p>　　為了比較，首先采用在工業(yè)過程中廣泛使用的確定PID參數(shù)控制方法，這種方法

102、的PID參數(shù)的整定通過CHR方法，然后計(jì)算得出參數(shù)如下：</p><p><b>　?。?6）</b></p><p>　　然后，使用NN-PID控制器，使用它的目的是為了作比較，其中NN被用來輔助固定的PID控制器。</p><p>　　圖3 用設(shè)計(jì)的方法（實(shí)線）和固定的PID控制方法（虛線）對(duì)系統(tǒng)1的控制結(jié)果</p><

103、p>　　圖4 與圖3的PID參數(shù)相一致的軌跡</p><p>　　系統(tǒng)的控制結(jié)果如圖3所示，圖中的實(shí)線和虛線分別表示我們所提出的方法和固定PID控制器的控制結(jié)果，使用所提出方法的PID參數(shù)的軌跡如圖4所示。從圖3中得出：由于控制對(duì)象的非線性特征固定控制器的控制結(jié)果不很理想。而從圖3和圖4中可以看出，我們所提出的方法則獲得了很好的控制效果。因?yàn)樵谶@個(gè)過程中PID參數(shù)得到了充分的調(diào)整。數(shù)據(jù)庫中存儲(chǔ)的數(shù)據(jù)數(shù)量為4

104、9。通過使用算法轉(zhuǎn)移沒用的數(shù)據(jù)，存儲(chǔ)的數(shù)據(jù)數(shù)量被有效地從206減少到49。另外，通過我們所提出的方法由下面等式給出的誤差是0.0417。</p><p><b>　?。?7）</b></p><p>　　其中N表示沒1[epoc]步驟的數(shù)量，更進(jìn)一步講就是迭代的次數(shù)被設(shè)為1，通過所提出的方法PID參數(shù)可以在線調(diào)整。然后，NN—PID被應(yīng)用于系統(tǒng)1，通過式（37）所獲得

105、的誤差曲線如圖5所示，控制結(jié)果如圖6所示。</p><p>　　圖5 對(duì)Hammerstein模型使用NN-PID控制器的誤差動(dòng)作</p><p>　　圖6 對(duì)Hammerstein模型用NN-PID控制器的控制結(jié)果</p><p>　　從圖5得出必需的學(xué)習(xí)迭代次數(shù)是86[epoc]，直到NN—PID控制器能夠獲得與我們所提出的方法有同樣的控制效果，即直到滿足，因此

106、對(duì)我們所提出方法的有效度的檢驗(yàn)需要在非線性系統(tǒng)中與NN—PID控制器相比較。</p><p>　　接下來我們引用時(shí)變控制系統(tǒng)，即在=70時(shí)，系統(tǒng)從式（31）變?yōu)槭剑?2）。首先，固定PID控制器的控制結(jié)果如圖7所示。</p><p>　　圖7 在用固定PID控制器的情況下由系統(tǒng)1變?yōu)橄到y(tǒng)2的控制結(jié)果</p><p>　　其中PID參數(shù)具有和式（36）相同的設(shè)定。在時(shí)

107、，控制對(duì)象的增益變大，所以固定PID控制器的運(yùn)行效果不是很理想。另一方面，我們在同樣的情況下應(yīng)用我們所提出的方法?？刂平Y(jié)果和PID參數(shù)變化軌跡如圖8和圖9所示。從圖中我們可以看出，可以獲得一個(gè)較好的控制效果。因?yàn)樵谖覀兯岢龅姆椒ㄖ蠵ID參數(shù)得到了充分的調(diào)整。在此仿真實(shí)例中我們使用了具有時(shí)變控制系統(tǒng)參數(shù)的非線性傳統(tǒng)。</p><p>　　圖8 使用固定的設(shè)計(jì)方法情況下改變系統(tǒng)參數(shù)的控制結(jié)果</p>

108、<p>　　圖9 與圖8的PID控制參數(shù)想一致的軌跡</p><p><b>　?、?結(jié)論</b></p><p>　　在本文中提出了一種應(yīng)用MB模型方法的新型PID控制器設(shè)計(jì)方案。到現(xiàn)在，像NN以及GA等一些PID控制器設(shè)計(jì)方法已經(jīng)提出來了，但是，在理想系統(tǒng)中使用這些方法具有余割嚴(yán)重的問題：付出的學(xué)習(xí)代價(jià)相當(dāng)大，另一方面，通過我們所提出的方法計(jì)算機(jī)的負(fù)擔(dān)