外文翻譯--新型直動式壓電電液伺服閥復(fù)合控制方法

1、<p><b>　　中文3450字</b></p><p><b>　　附二: 外文翻譯</b></p><p>　　High Precise Control Method for a New Type of</p><p>　　Piezoelectric Electro—hydraulic Servo Val

2、ve</p><p>　　Abstract：A new type of piezoelectric electro-hydraulic servo valve system was proposed． And then multilayer piezoelectric actuator based on new piezoelectric ceramic material was used as the elec

3、tricity-machine converter of the proposed piezoelectric electro-hydraulic servo valve. The proposed piezoelectric electro -hydraulic servo valve has ascendant performance compared with conventional ones.But the system is

4、 of high nonlinearity and uncertainty, it cannot achieve favorable control performanc</p><p>　　Key words：piezoelectric electro—hydraulic servo valve；hysteresis nonlinearity；Preisach model；fuzzy control</p

5、><p>　　1 Introduction</p><p>　　Electro—hydraulic servo system is widely applied in industrial domain nowadays．for example．robot drive，machine building, architectural engineering．The electro-hydraul

6、ic servo valve is the kernel of the electro-hydraulic servo system,and its performance has decisive effect Of the whole system．The conventional drive mode of electro．hydraulic servo valve has lower resolution and narrowe

7、r work band width，which restricts the applications of the electro-hydraulic servo valve．The proposed piezoelectric</p><p>　　At present，with the research and the development of new-type actuator based on new

8、type materials, it is possible to make the new electricity-machine converter with high frequency. New materials include piezoelectric ceramic materials, magnetostrjctive materials, shape memory alloys．Thereinto, multila

9、yer piezoelectric actuators based on new piezoelectric ceramic materials have many merits such as small cubage，high resolution，high frequency and large drive force．Hence，they are widely used in the</p><p>　　

10、2 Work principle and characteristic of new-type of piezoelectric electro-hydraulic Valve</p><p>　　Because the pulling force capacity of multilayer piezoelectric actuator is very poor, it cannot make the slid

11、e valve of the electro, hydraulic servo valve bidirectionallv move. Two multilayer piezoelectric actuators were adopted to solve this problem [7-8]. The shortcoming of this method is high cost and system is difficult to

12、contro1. Utilizing the restoring force of a leaf spring，one multilayer piezoelectric actuator can realize bidirectional movement of the slide valve in this paper. W hen th</p><p>　　The structure of new type

13、of piezoelectric electro—hydraulic servo valve is shown in Fig．1．</p><p>　　The input-output characteristic of the new type of piezoelectric electro-hydraulic servo valve system indicates that it has hysteres

14、is nonlinearity with nonloca1 memory(see Fig．2). At any reachable point L (Ua ，Ya)in input-output diagram，the number of alternative curve that describes the future path of hysteresis nonlinearity with nonloca1 memory is

15、infinite. Namely, the future output of the system depends not only on the current output Ya and future input，but also on the past history of input v</p><p>　　In the system，there exist other nonlinearities su

16、ch as force of friction and work dead zone of valve, furthermore，damping coefficient and oil temperature are also changed with time．The nonlinearity and uncertainty have seriously effects on the position precision. To im

17、prove the performance of the new type of piezoelectric electro-hydraulic servo valve system, a valid control method is needed</p><p>　　3 Control algorithm</p><p>　　At present, conventional PID c

18、ontroller is widely applied in industrial control domain because of its simple control structure, easy design and inexpensive cost．However, conventional PID controller is difficult to achieve good control performance in

19、the new type of piezoelectric electro, hydraulic servo valve system because the control object has high nonlinearity and uncertainty．Fuzzy controller shows good results in the case of controlling high nonlinear systems.

20、However, conventional fuzzy co</p><p>　　The control system is composed of a feedforward loop based on Preisach model and a feedback loop of high precise fuzzy controller．Ul( is the output of feedforward loop

21、 based on Preisach mode1．As a linear term, it is selected from a Preisach function table based on the given position value．U2( is the output of the high precise fuzzy controller．The sum U(t) of feedforward control voltag

22、e f and feedback control voltage U2(t) ，as ultimate control voltage，is acted on new type piezoelectric electro-hy</p><p>　　3．1 Feedforward loop based on Preisach model</p><p>　　The open loop res

23、ponse of the new type piezoelectric electro-hydraulic servo valve system under an arbitrary and non-cyclic input signal is shown in Fig．2．This phenomenon appears as hysteresis nonlinearity with nonlocal memory, which can

24、 be predicted by Preisachmode1．The numerical form of Preisach model can be</p><p>　　written as foliows： </p><p><b>　　(1)</b></p><p>　　Eqn.(1) can be used to c

25、alculate the response of the new type of piezoelectric electro-hydraulic servo valve subject to a known arbitrary input voltage sequence．A series of first order functions of the new type of piezoelectric electro-hydraul

26、ic servo valve are experimentally determined． The procedure is as follows．</p><p>　　The space between zero and saturation voltage Us is divided into n equipartitions, and the voltage of every equantpoint is

27、kUs／n，where k=-0，1，2， ? n．</p><p>　　Voltage is applied from zero to every equant point kUs／n，and then decreased to zero．In this process，the position output values of the new type of piezoelectric electro-hyd

28、raulic servo valve are recorded at every equant point between zero and saturation voltage Us，therewith， and the Preisach function table are obtained(see Fig．4)，</p><p><b>　　（2）</b></p><

29、;p>　　Based on the driver voltage range of the new type of piezoelectric electro．hydraulic servo valve， the coordinate space is selected as 0≤≤ l 50 V and 0≤< 1 50 V From Fig．4，the limit triangle is divided into sev

30、eral squares and triangles．Decreasing the size of the squares and triangles is expected to increase the accuracy of the mode1, however, it will spend massive computational time．Based on the experiments, n is selected as

31、5，namely, the size of each of sides of the squares and triangles is sel</p><p>　　Based on the given position value and the numerical form of the Preisach model， or can be obtained．Thereby, based on Preisac

32、h function table，the control voltage Ul(t) is obtained when lies on the vertical line or lies on the horizontal line．For the inexistence voltage in the Preisach function table．it can be obtained by the linear interpolati

33、on．</p><p>　　In comparison to a conventional feedback controller, the main advantage of this mode1-based feedforward controller is that it can compensate the hysteresis nonlinearity of the system and achieve

34、 highly dynamic operation at the same time, and no additional sensor is needed．This leads to a very simple and inexpensive control system ．The main drawback of the feedforward</p><p>　　controller is sensitiv

35、e to unmodel data and unconsidered external disturbances such as temperature drift．For a new type of piezoelectric electro—hydraulic servo valve system that needs high control precision．mode1．based feedforward controller

36、 cannot obtain good control effect．Then a compound control method with feedforward and feedback control project was proposed in this pape. In the feedback control loop，a high—precise fuzzy control algorithm was adopted．T

37、he method can obtain good performance．</p><p>　　3．2 High precise fuzzy control</p><p>　　Conventional fuzzy controller has two input variables，e and Δe，and one output variable （U），they are error,

38、 change of error and output control of fuzzy controller． In the new type of piezoelectric electro-hydraulic servo valve system，the physical range of the slide valve position error( and change of error (△e) are [-x，x] and

39、 [-Δx ，Δ x]，respectively．The corresponding discrete universes of discourse of e，△e and u are E，EC and U respectively．E, EC and U are designed as normalized form ：</p><p>　　{-n，-(n一1)，?，0，?，n一1，n}(i=1，2，3)

40、 (3)</p><p>　　The scale factors are ， and ，respectively. Then</p><p>　　, , (4)</p><p>　　Based on control rule of conventional fuzzy controll

41、er, when < 0．5 and < 0．5，the conventional fuzzy controller considers the inputs e and as zero and the output u is also zero．However, the inputs e and △e are not certainly equal to zero. Hence conventional fuzzy c

42、ontroller has control dead zone. Control dead zone of conventional fuzzy controller is the main reason why the steady state precision of look-up table algorithm is poor. The key to improving the controlling precision of

43、fuzzy control </p><p>　　To resolve this problem, an improved fuzzy controller is adopted. When E or EC is not equal to 0, the look-up table is adapted to calculating the control output U; when E or EC are eq

44、ual to 0,</p><p>　　Interpolation algorithm is adopted to calculating the control output U’ instead of quantization.</p><p>　　The method of interpolation calculation is shown in Fig.5. The U(I,j)

45、,U(i+1,j),and U(i+1,j+1) are four point in the look-up table ,and the value of U’ can be calculated based on them. </p><p>　　4. Experimental research</p><p>　　The position precision of the new

46、type of piezoelectric electro-hydraulic servo valve system is significantly reduced due to the effect of nonlinearity and uncertainty．In this paper，the high-precise fuzzy control method with Preisach hysteresis nonlinear

47、 model in feedforward loop was developed to solve this problem. To demonstrate the effectiveness of this proposed control</p><p>　　method，a series of experiments were performed on the new type of piezoelectr

48、ic electro-hydraulic servo valve system under various conditions．</p><p>　　The experimental setup was built. which consisted of industrial control computer, hydraulic pressure experimental bench，pumping st

49、ation，PES arbitrary waveform generator(Model AG1200，Yokogawa Co．) and multi-purpose FFT analyzer (Model CF-5220，</p><p>　　Onosokki Co．)．The experiments were conducted under a hydraulic pressure of 7 MPa. Hyd

50、raulic pressure experimental bench was used to provide the operational environment for the PESV .</p><p>　　Pumping station was used to provide the liquid pressure for hydraulic pressure experimental bench．Wa

51、veform generator was used to provide the waveform．Fourier analyzer was used to analyze the experimental result． Industrial control computer was used to receive the position feedback signals and provide control voltage ba

52、sed on the proposed control method． The industrial control computer still includes a 12 bit AD／DA card (Model PC一63 l1，Zhongtai Co．)，a power amplifier and program of the proposed c</p><p>　　computer accepts

53、the given signal from waveform generator and position feedback signal through A／D conversion interface， soon afterwards， calculates the control voltage signal based on the proposed the control method and sends it through

54、 D／A conversion interface to a power amplifier．In the power amplifier, the control method was amplified with l 0 times gains to drive the piezoelectric actuator of the PESV The position feedback signal was also sent to t

55、he Fourier analyser for analyzing the exper</p><p>　　Firstly, the experiments were done under open loop control， PID control， and high—precise fuzzy control method with Preisach hysteresis nonlinear model in

56、 feedforward loop． The hysteresis loop curves were plotted．</p><p>　　Fig．6(a) shows the hysteresis loop output curve of the system under open loop contro1．It was calculated that hysteresis loop is about 13．0

57、8％ and the maximum output hysteresis is about 6.64μm．Fig．6(b) shows the hysteresis loop output curve of the system under PID</p><p>　　control method．It was calculated that the hysteresis loop is about 4.22％

58、and the maximum output hysteresis is about 2.11μm．This control method can restrain the nonlinear effects of the system．Fig．6(c) shows the hysteresis loop output curve of the system under the high-precise fuzzy control me

59、thod with Preisach hysteresis nonlinear model in feedforward loop．It was</p><p>　　calculated that the hysteresis loop is about 0.74％ and the maximum output hysteresis is less than 0.37μm．This control method

60、can virtually eliminate the nonlinear effects of the system．</p><p>　　The control results show that the proposed control method gives the minimum output hysteresis and the highest precision compared with ope

61、n loop control and</p><p>　　PID contro1．</p><p>　　Secondly, the comparative experiments of the tracking result for a sine wave reference signal under PID control method and the proposed control

62、method were done．Fig．7 shows the tracking result of PID control method for sine wave reference signa1．The maximum tracking error is about 5.02％．For the position precise requirement, this tracking result cannot be accepte

63、d．The main reason for this result is the hysteresis nonlinearity of the new type of piezoelectric Electro-hydraulic servo valve system．F</p><p>　　The tracking results show that the proposed control scheme gi

64、ves faster and more accurate responses compared with those Of PID contro1, and they can satisfy the high precision demand of the new type of piezoelectric electro-hydraulic servo valve system．</p><p>　　5. Co

65、nclusions</p><p>　　1) A new type of piezoelectric electro-hydraulic servo valve system is proposed．Multilayer piezoelectric actuator based on new piezoelectric ceramic materials is used as the electricity-ma

66、chine converter of the proposed piezoelectric electro-hydraulic servo valve．</p><p>　　2) Because of high nonlinearity and uncertainty of the proposed piezoelectric electro—hydraulic servo valve system， the p

67、recision requirements for position are</p><p>　　influenced seriously．Hence．a(chǎn) high—precise fuzzy control method with Preisach hysteresis nonlinear model in feedforward loop was proposed．The proposed control m

68、ethod can availably eliminate the influence of the nonlinearity and uncertainty, and improve the performance of the new type of piezoelectric electro—hydraulic servo valve system．</p><p>　　References</p&g

69、t;<p>　　[1] K1M J D，NAM S R．Development of a micro-depth c0ntrol system</p><p>　　for an ultra-precision lathe using a piezo-electric actuator[J]．Intemationa1 Jouma1 of Machine Too1s& Manufacture，I

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78、p>　　[9] GE MUSE J Modeling hysteresis in piezoceramic actuators[J]． Precision Engineering，1995，17(3)：21 l一221·</p><p>　　[10] L1U Shao-jun，HUANG Zhong-hua，CHEN Yi-zhang. Automobile</p><p>

79、;　　active supension on system with fuzzy control[J]. Journal of Cental South University ofTechnology,2004，11(2)：206-209</p><p>　　新型直動式壓電電液伺服閥復(fù)合控制方法</p><p>　　摘 要：設(shè)計了一種新型直動式壓電電液伺服閥。該閥采用壓電疊堆執(zhí)行器作為電一

80、機(jī)械轉(zhuǎn)換器，提高了電液伺服閥的性能。并針對壓電疊堆執(zhí)行器固有的遲滯和蠕變非線性使得壓電型電液伺服系統(tǒng)的輸出精度降低，傳統(tǒng)的控制方法難以得到很好的控制效果的問題。提出了基于動態(tài)Preisach模型的前饋控制和PID反饋控制的一種復(fù)合控制方法。實驗結(jié)果表明，該方法能有效改善新型直動式壓電電液伺服閥的輸出精度。</p><p>　　關(guān)鍵詞：自動控制技術(shù)；壓電電液伺服閥；復(fù)合控制；動態(tài)Preisach模型；非線性<

81、/p><p>　　1 新型直動式壓電電液伺服閥結(jié)構(gòu)</p><p>　　新型直動式壓電電液伺服閥主要由位移傳感器1、彈性回復(fù)板2、左端延長桿3、滑閥4、右端延長桿5、壓電疊堆執(zhí)行器6和閥體等部分組成，見圖1。</p><p>　　當(dāng)輸入電壓增加時，壓電疊堆執(zhí)行器伸長推動滑閥向左運(yùn)動；當(dāng)輸入電壓減小時，壓電疊堆執(zhí)行器縮短，由彈性回復(fù)板的回復(fù)作用力使滑閥向右運(yùn)動。通過滑閥的

82、運(yùn)動來控制進(jìn)油口的開口量，進(jìn)而控制液體流量以及壓力的變化。</p><p><b>　　2 系統(tǒng)特性分析</b></p><p>　　壓電疊堆執(zhí)行器雖然具有諸多優(yōu)點，但是其輸出位移存在非線性，主要表現(xiàn)為遲滯非線性和蠕變非線性兩種。遲滯非線性特性是由壓電陶瓷晶體極化的偶極矩偏轉(zhuǎn)引起的，表現(xiàn)為壓電疊堆執(zhí)行器在同一輸入電壓作用下的輸出位移并不相同。蠕變非線性是隨外加電壓變化

83、產(chǎn)生的一種特性，是在恒定電場作用時晶體電疇緩慢排列所表現(xiàn)出來的現(xiàn)象，當(dāng)施加電壓時，壓電疊堆執(zhí)行器的輸出位移會在ms級時間內(nèi)產(chǎn)生變化，之后在很長的一段時間內(nèi)會發(fā)生很微小的位移變化。蠕變的位移變化方向總是與施加電壓變化方向相一致。</p><p>　　由于壓電疊堆執(zhí)行器的輸出通過延長桿直接作用到滑閥上，所以新型直動式壓電電液伺服閥滑閥的輸出位移也具有遲滯和蠕變非線性。研究新型直動式壓電電液伺服閥的特性主要是研究該閥在

84、控制。</p><p>　　電壓作用下的輸出位移以及電壓不變時輸出位移和時間的關(guān)系。圖2為新型直動式壓電電液伺服閥在三角波作用下的位移輸出曲線。圖中虛線代表新型直動式壓電電液伺服閥的標(biāo)稱輸入／輸出線性化關(guān)系。可見，新型直動式壓電電液伺服閥具有較強(qiáng)的遲滯非線性，輸出響應(yīng)與標(biāo)稱輸出相比有很大的偏差。圖3是新型直動式壓電電液伺服閥在9O V 電壓作用下100 S內(nèi)的位移輸出變化曲線，在這段時間內(nèi)的位移輸出的蠕變量約為1

85、．37 m?？梢姡滦椭眲邮綁弘婋娨核欧y的蠕變非線性會對控制精度產(chǎn)生一定的影響。</p><p>　　通過對新型直動式壓電伺服系統(tǒng)的特性分析可知，由于遲滯非線性和蠕變非線性的存在，系統(tǒng)</p><p>　　的輸出精度會受到較大的影響，需要采用適當(dāng)?shù)目刂品椒▉硖岣呦到y(tǒng)的輸出精度。</p><p><b>　　3 控制算法</b></p&g

86、t;<p>　　工業(yè)上普遍采用的PID控制方法具有結(jié)構(gòu)簡單、造價低廉和無需精確建模等優(yōu)點，在精密定位控制系統(tǒng)中被廣泛采用。但是新型直動式壓電電液伺服閥存在遲滯和蠕變非線性，用傳統(tǒng)PID控制算法不能取得很好的控制效果。為了滿足新型直動式壓電電液伺服閥的高精度性能要求，作者提出了基于動態(tài)preisach模型前饋控制和PID反饋控制的復(fù)合控制方法。</p><p>　　3．1 動態(tài)Preisach模型&l

87、t;/p><p>　　古典Preisach模型常被用來對遲滯非線性進(jìn)行描述，它是由最簡單的遲滯算子疊加構(gòu)造而成。對新型直動式壓電電液伺服閥施加電壓 時，輸出位移，而僅發(fā)生在第一象限，其遲滯算子 “的值只能為0或1，因此對古典preisach模型進(jìn)行修正[6]，得到如下數(shù)學(xué)形式</p><p><b>　　(1)</b></p><p>　　Prei

88、sach模型的建立過程如下[7,8 ]：首先建立遲滯環(huán)升壓和降壓曲線的模型，其次建立用來</p><p>　　存儲每個升程和回程中不同電壓處位移值的模型函數(shù)表，然后根據(jù)實際加壓歷程以及上面離線建立的模型函數(shù)表來查找對應(yīng)的輸出位移值。對于不在模型函數(shù)表中的電壓可以通過插值的方法來確定實際電壓作用下的位移值。該模型的特點是具有全局記憶特性，即能夠考慮到電壓施加的全部路徑對其位移值進(jìn)行預(yù)測計算，該模型為一個二重積分，路

89、徑對應(yīng)著積分區(qū)域，只要知道電壓的施加過程，就可以算出被控對象的輸出位移值。相反，進(jìn)行逆控制，即已知位移給定值求所加控制電壓大小時，可根據(jù)該位移給定值及加壓歷程來查找Preisach模型函數(shù)表進(jìn)行求逆運(yùn)算，從而得到所需要施加的控制電壓。然而，在針對新型直動式壓電電液伺服閥系統(tǒng)進(jìn)行的實驗中發(fā)現(xiàn)，當(dāng)外加電壓信號的頻率不同時,系統(tǒng)輸出的遲滯環(huán)的斜率是不同的。圖4為在0．1 Hz和1O Hz這兩種頻率的電壓下系統(tǒng)輸出的遲滯環(huán)曲線。這表明新型直動式

90、壓電電液伺服閥的非線性特性是與速率相關(guān)的，而修正Preisach模型僅代表靜態(tài)(與速率無關(guān))的非線性特性，該模型僅僅根據(jù)施加某一頻率電壓時產(chǎn)生的位移值來建立Preisach模型函數(shù)表，而當(dāng)電壓的施加頻率發(fā)生變化時，函數(shù)表的值是變化的。因此單純采用修正Pr</p><p>　　為了解決這個問題，作者參考文獻(xiàn)[9]，在修正Preisach模型中引入一表示速率變化的函數(shù)，得出新型直動式壓電電液伺服閥的動態(tài)Preisac

91、h模型，該模型的數(shù)學(xué)形式為</p><p><b>　?。?）</b></p><p>　　式中： 是輸入變化率的函數(shù)，用于描述輸入變化率和遲滯環(huán)之間的關(guān)系。</p><p>　　針對對函數(shù)進(jìn)行冪級數(shù)展開:</p><p><b>　?。?）</b></p><p>　　取前

92、兩項，可得下面動態(tài)模型:</p><p><b>　?。?）</b></p><p>　　式中：，)為遲滯的靜態(tài)部分，式(4)的第二項代表遲滯的動態(tài)部分。</p><p>　　引入，代表動態(tài)和靜態(tài)輸出的差值，由式(4)可得 （5）</p><p>　　通過數(shù)學(xué)推導(dǎo)可得

93、出其數(shù)字實現(xiàn)形式</p><p><b>　　（6）</b></p><p>　　式中： 為輸入電壓增長到并衰減到時的位移輸出值，見圖5。</p><p>　　輸入變化率函數(shù)在平面中的變化可由實驗結(jié)果決定。圖4的實驗結(jié)果顯示隨著輸入頻率的增加，位移輸出的最大值和遲滯環(huán)的寬度變小。經(jīng)過多個頻率下的遲滯環(huán)曲線測試實驗結(jié)果可知，函數(shù)可由式(7)表示，

94、以描述不同的靜態(tài)和動態(tài)遲滯環(huán)。</p><p><b>　　（7）</b></p><p>　　式中 、 和均為常系數(shù)。</p><p>　　根據(jù)動態(tài)Preisaeh模型的數(shù)字實現(xiàn)形式，可以建立動態(tài)Preisaeh模型，以對系統(tǒng)輸出進(jìn)行控制。</p><p><b>　　3．2 復(fù)合控制</b>&l

95、t;/p><p>　　建立在動態(tài)Preisaeh模型基礎(chǔ)上的前饋控制能有效地克服遲滯非線性的影響，改善控制精度，但難以消除蠕變非線性及外部干擾的影響，其定位精度不是很高，無法滿足新型直動式壓電閥的要求。為了實現(xiàn)高精度定位，作者提出了一種基于動態(tài)Preisaeh模型的前饋控制和PID反饋控制的復(fù)合控制方法。該復(fù)合控制方法在結(jié)構(gòu)上分為動態(tài)Preisaeh模型前饋控制環(huán)節(jié)和PID反饋控制環(huán)節(jié)兩部分。PID反饋控制環(huán)節(jié)的作用

96、主要是用來消除蠕變非線性及外部干擾產(chǎn)生的誤差，進(jìn)一步提高系統(tǒng)的控制精度。</p><p>　　提出的基于動態(tài)Preisaeh模型的前饋控制和PID反饋控制的復(fù)合控制方法的系統(tǒng)框圖如圖6所示。其中：為動態(tài)Preisaeh模型前饋環(huán)節(jié)輸出控制量，為PID反饋控制器輸出控制量。前饋控制量和反饋控制量二者的電壓和作為最終控制電壓作用到新型直動式壓電電液伺服閥上，則新型直動式壓電伺服閥的控制量方程可寫為：</p>

97、;<p><b>　?。?）</b></p><p>　　式中：T為控制系統(tǒng)的采樣時間；、和代表PID反饋控制器的比例、積分和微分增益；和分別為當(dāng)前采樣時刻和上一次采樣時刻系統(tǒng)的偏差。</p><p><b>　　4 實驗驗證</b></p><p>　　為驗證所提控制方法的控制效果，在新型直動式壓電電液伺服

98、閥系統(tǒng)實驗平臺上進(jìn)行了實驗。實驗時的工作參數(shù)如下：閥芯位移范圍為，位移傳感器反饋信號范圍為-5～+5V，供油壓力為7 MPa，流量為O～4 L／rain。</p><p>　　由于電液伺服閥的輸出流量與滑閥閥芯位移成線性關(guān)系?；y閥芯位移實際輸出值與位移給定輸出值之間關(guān)系可以表征伺服閥的實際輸出流量與給定輸出流量的關(guān)系。本實驗中測試的是滑閥閥芯位移實際輸出值與給定輸出值之間的關(guān)系。</p><

99、p>　　作者分別采用PID 反饋控制方法，基于Preisaeh模型前饋的PID反饋控制方法和所提出的復(fù)合控制方法對某一給定參考曲線進(jìn)行了跟蹤控制研究。圖7和圖8分別為采用PID反饋控制時的跟蹤曲線及誤差曲線，最大跟蹤誤差為1．71um。由于非線性的影響，采用傳統(tǒng)PID反饋控制方法時的跟蹤誤差比較大。不能滿足新型直動式壓電電液伺服閥的高精度控制要求。圖9和圖1O分別為采用基于Preisach模型前饋的PID反饋控制方法時的跟蹤控制曲

100、線及誤差曲線，最大跟蹤誤差為0．96 pm。圖11和圖12分別為采用基于動態(tài)Preisach模型的前饋控制和PID反饋控制的復(fù)合控制方法時的跟蹤控制曲線及誤差曲線，最大跟蹤誤差為0．77 pm。</p><p>　　通過上面的3種控制方法的對比實驗可見，基于動態(tài)Preisach模型前饋控制和PID反饋控制的復(fù)合控制方法能夠取得更高的跟蹤精度，滿足新型直動式電液伺服閥的高精度控制要求。</p><

101、;p><b>　　5 結(jié)束語</b></p><p>　　介紹了新型直動式壓電電液伺服閥的結(jié)構(gòu)并對其特性進(jìn)行了分析。實驗中發(fā)現(xiàn)系統(tǒng)存在遲滯和蠕變非線性，嚴(yán)重地影響了系統(tǒng)的輸出精度。為了消除非線性對系統(tǒng)精度的影響，作者提出一種基于動態(tài)Preisach模型的前饋控制和PID反饋控制的復(fù)合控制方法。為了驗證所提復(fù)合控制方法的控制效果，針對一條參考曲線分別采用PID控制方法、對基于Preisa