外文翻譯-對采用進(jìn)化策略優(yōu)化電液伺服系統(tǒng)的控制器增益的實驗性研究

1、外文翻譯學(xué)生姓名學(xué)院名稱機(jī)電工程學(xué)院專業(yè)名稱機(jī)械設(shè)計制造及其自動化指導(dǎo)教師An experimental study on the optimization of controller gains for an electro-hydraulic servo system using evolution strategiesAbstract This paper deals with an experimental optimization problem of the controller gains for an electro-hydraulic position control sys

2、tem through evolution strategies (ESs)-based method. The optimal controller gains for the control system are obtained by maximizing tness function designed specially to evaluate the system performance. In this paper, for an electro-hydraulic position control system which would represent a hydraulic

3、mill stand for the roll-gap control in plate hot-rollings, the time delay controller (TDC) is designed, and three control parameters of this controller are directly optimized through a series of experiments using this method. It is shown that the near-optimal value of the controller gains is obtaine

4、d in about 5th generation, which corresponds to approximately 150 experiments. The optimal controller gains are experimentally conrmed by inspecting the tness function topologies that represent system performance in the gain spaces. It is found that there are some local optimums on a tness function

5、topology so that the optimization of the three control parameters of a TDC by manual tuning could be a task of great difculty. The optimized results via the ES coincide with the maximum peak point in opologies. It is also shown that the proposed method is an efcient scheme giving economy of time and

6、 labor in optimizing the controller gains of uid power systems experimentally.Keywords: Controller gain optimization; Evolution strategies; Time delay control; Automatic controller gain search; Electro-hydraulic servo system1. IntroductionRecently, the research on the optimization and adaptation of

7、controller gains or parameters for improving the system performance in hydraulic and pneumatic servo systems has been a eld of increasing interest (Fleming & Purshouse, 2002; Klein, 1992; Jeon, Lee, & Hong, 1998; Hyun & Lee, 1998; Choi, Lee, &Cho, 2000). In general, when control engineers design con

8、troller for hydraulic or pneumatic servo systems, it is very difcult to determine theoretically its control gains to exhibit the best performance of the systems, because the accurate modeling for these systems is hard due to highly nonlinear characteristics of the uid power systems. To be more speci

9、c, the hydraulic and pneumatic servo systems already have a relatively higher degree of nonlinearity than other mechatronic systems like DC or AC servo systems. It results from various factors (Merrit, 1976; Watton, 1989): the pressure-ow characteristics of valve, the saturation of valve and cylinde

10、r, the leakage ow characteristics of valve and cylinder with variation of supply pressure, the friction characteristic in cylinder, the variation of viscosity and compressibility of working uid with the temperature, the ow characteristic due to the shape of pipeline, and most importantly, the variat

11、ion of the system gains with the supply pressure and the load pressure. Therefore, when these uid power systems are controlled, the controller gains are adjusted on the foundation of experts intuitive knowledge about the system and the tuning experience of the controller gains in general. It needs v

12、ery excessive experiments through trial and error. But though some controller gains are obtained, it is hard to say that the results are the best gain set at a given situation. For the automatic adjustment of the controller gains in uid power systems, the research to application of a fuzzy gain adap

13、ter (FGA) has been performed (Jeon, 1997; Klein, 1992). In this case, the knowledge base is needed for transplantation of the expert knowledge to the systems, and some general rules to variation of the system response due to variation of the controller gains are demanded for the construction of this

14、 knowledge base. Therefore, much experts experiences and many experiments are necessary for the implementation of this algorithm.In this study, evolution strategies (ESs) is proposed as a method of the automatic optimization of the controller gains in a electro-hydraulic system. ES is one of the evo

15、lutionary algorithms based on the natural genetics and the survival of the ttest (Rechenberg, 1973; Schwefel, 1981; Back & Schwefel, 1994, 1996). When an appropriate tness function representing potential solutions is given as survivability of candidates, the tuning problem of controller gains can be

16、 considered as an optimization problem, so that an optimal controller gain set is searched in the region of gain spaces specied by operator. A major advantage is that much experience on the gain-tuning for the control system is not required, and the least information for the system is just required.

17、 Especially, in cases that a real experimental system is directly used for evaluating candidates, ESs are more suitable than other evolution algorithms due to its own characteristic called self-adaptation.In this study, a time delay controller (TDC) is designed as a controller for position control o

18、f an electro-hydraulic servo system. The controller designed to have 2nd order error dynamics has three controller gains implicitly. By using an ES as optimization algorithms, the optimal controller gain set in the specied gain spaces is determined through online experiments. For the verication of t

19、he obtained results, the tness function topologies in the gain spaces experimentally are made out, and analyzed. Finally, the experimental results searched through ESs are shown to coincide with the optimal peak point that has best tness value on the specied gain spaces. 2. Hydraulic servo system2.1

20、. Electro-hydraulic position control system is the schematic diagram of the electro-hydraulic position control system used in this study. This system is a test rig for the roll-gap control of hydraulic mill stand, which was made for the improvement of thickness control performance in plate hot-rolli

21、ng processes (Gizburg, 1984; Lee, Lim, & Park, 1997). The rig simulates a roll-gap control system composed of a hydraulic mill stand in a number of automatic gauge control systems for hot rolling processes. The system consists of structure spring to represent a modulus of mill stand, material spring

22、 to represent a modulus of rolled strip, roll-gap control cylinder to control a deformation of material spring, and disturbance cylinder to give the control system a disturbance. The force applied to roll-gap cylinder is measured through Load cell, the deformation of structure spring through linear-

23、variable differential transformer (LVDT), and the deformation of material spring through Linear scale. The roll-gap control cylinder is a cylinder of ram type as in real hot rolling process, and the disturbance cylinder is just used to apply a disturbance to the system during roll-gap control. A con

24、trol current signal (i1) of the closed-loop is used to perform the position control of roll-gap is used to perform the position control of roll-gap control cylinder, which is inputted to a servo valve connected to ram cylinder. The other current signal (i2) of the open-loop is used to generate a dis

25、turbance, which is inputted to a servo valve connected to disturbance cylinder. In this article, responses of the system with the xed disturbance cylinder are considered. Table 1 shows some of the technical specications of the experimental setup composed of power unit, roll-gap control cylinder, str

26、ucture spring, material spring, linear scale, servo valve, and interface card.Fig.1.Schematic diagram of the electro-hydraulic position control system.Table1Specifications of the components used in the experiment2.2. A time delay controller (TDC) for the position control systemA selected controller

27、for the position control of this system is the TDC (Youcef-Toumi & Ito, 1990; Hsia & Gao, 1990), which is based on the estimation of unknown effects due to system uncertainties using the time delay technique, that is, sampling technique of the discrete control. The time delayed information (the cont

28、rol input and the derivatives of state variables at the previous sampling time) plays a role to cancel various effects which result from variations of system parameters, unpredictable external disturbances, and un-modeled nonlinear system dynamics. Since the current control input can be obtained by

29、using just the control input and the system responses observed at the previous sampling time, the controller is little affected by a system modeling, so that can be effectively applied whenever there is the large variation of system paramenters and a disturbance. comparing with the Proportional plus

30、 integral plus derivative (PID) controller, the state feed-back controller, or adaptive controller, the structure of this controller is as simple as the PID controller, because it does not require a real-time estimation of state variables or system parameters using observers, nor does it a computati

31、on of inverse system dynamics. Recently, a research has been performed on a uid power system using a TDC by Chin, Lee, and Chang (1994). The application results show easiness of the real implementation of this controller and robustness on various uncertainties of the plant.For the hydraulic system s

32、hown in Fig. 1, a study on For the hydraulic system shown in Fig. 1, a study on (1998). He designed a 2nd order TDC with simplication of the nonlinear system dynamics of 5th order through theoretic analyses on this system, proved the global stability of the internal dynamics (unobservable part excep

33、t inputoutput part in system dynamics) through the input-output linearization technique, and proposed the region of stability for closed-loop system. Fig.2 shows a control block diagram of the electro-hydraulic position control system with a TDC controller, where s is variable of Laplace transform a

34、nd L is sampling time. The controller is embodied with the three controller gains (E to be system constant, and to decide on error dynamics of the system) in block diagram as shown in the following equation:2.3. Theoretic settings on TDC gains and practical problemsIn general, the gain setting metho

35、d for TDC is as follows: theoretically the controller gains of TDC are not necessary to be tuned. For instance, let us consider a case in which a TDC of 2nd order is designed like Eq. (1). First by setting the values of and to dene the error dynamics of system, poles of the 2nd order system can be d

36、etermined. Then, the frequency responses of system is decided on by specic poles. Secondly the value of E to be system constant is specied to be in the region of stability for the stability of the closed-loop system. Namely, according to the desired control specications, the value of and can be sele

37、cted, and the value of E can be tuned as close as possible to a limit of the region of stability (Youcef-Toumi & Ito, 1990). However, when a TDC is applied to real system, the setting of controller gains on the TDC has several problems. First, when a reference input is given, it is some practical pr

38、oblem how the locations of poles will be assigned. Furthermore though a trajectory is determined in the form of reference model for following the reference input, the ability of the system for following the trajectory is unknown before the controller is applied to real system (Chin et al., 1994). Se

39、condly the value of E is related to the inertia of the system. In real system, the estimation of the system inertia is another hard problem. The error between the system constant and the estimated E directly affects the error dynamics of the closed-loop system, so it becomes a reason why the system

40、does not follow the prescribed reference model with accuracy (Youcef-Toumi & Reddy, 1992). Thirdly the saturation of actuators or a controller, the friction characteristics of the system, etc. are able to become causes to obstruct the trajectory following (Chang & Park, 2003). The results of the exp

41、eriments with the theoretical settings of the TDC controller gains were as follows. Because of the compressibility of the working uid excluded to simplify the system modeling, it is necessary that the damping ratio of the reference model is designed to be over-damped (1). It is very difcult to deter

42、mine proper and due to the friction characteristics on the hydraulic systemthe friction of hydraulic actuator is generally larger than other actuators. Though the controller gains are tuned for the system to have some satised performance via the above mentioned procedures, it is uncertain that they

43、are the optimal gains under a given performance index. Hence, in the case of the real system, the optimal controller gains of TDC can be searched and settled in the given gain regions via the proposed ES-based method.Fig.2.Block diagram of the position control system with a time delay controller.3.

44、Evolution strategiesSince ESs had been developed for solving experimental optimization problems applied to hydrodynamics, they have been successfully applied to various optimization problems. As other evolutionary algorithms, ESs also depend on the concept of a population of individual. Based on ini

45、tial population selected randomly in specied region, the population evolves toward better tness regions of the search space through randomized processes of mutation, recombination, and selection. The tness, given as survivability of each individual, reects the evaluation level of each individual wit

46、h respect to a particular objective function dened in each application. The object of this algorithm is to search the optimal solution that maximizes the objective function. Comparing with other evolutionary algorithms, its unique and important characteristic is to include the standard deviation and

47、 the covariance of each variable as important algorithm parameters for the Gaussian mutation, which are called strategy parameters. Therefore, the optimization not only takes place on object variables, but also on strategy parameters of them. This optimization mechanism exploits an implicit link bet

48、ween internal model and good tness value. The evolution and adaptation of strategy parameters according to the topological surface shape of tness function has been termed self-adaptation by Back and Schwefel (1996). In addition to it, to use naturally the real-valued vector as the individual, to use

49、 the Gaussian mutation as the primary operator for reproduction of the individuals, to be possible to select various recombination operators, and to have stronger selection pressure than the other evolutionary algorithms is the major characteristics of this algorithm.3.1. Differences between genetic

50、 algorithms and evolution strategiesIn recent years, the researches on applications of genetic algorithms (GAs) have been performed for the optimization of the controller gains in hydraulic systems (Jeon et al., 1998; Hyun & Lee, 1998). ESs and GAs are probabilistic optimization algorithms gleaned f

51、rom the similar model of natural evolution. Since these algorithms simultaneously evaluate several points on a search space, it is highly possible that they converge to the global optimum solution. Though there are many similarities between these approaches, there are some notable differences (Back

52、& Schwefel, 1996). The differences can be summarized as follows. ESs operate on oating point vectors, whereas classical GAs operate on binary vectors. It makes that optimized results in GAs are limited by resolution of discrete spaces because search spaces are discrete spaces into which real values

53、are coded. However, some researchers have modied to use real-valued vectors in GAs, and recently GA applications frequently use oating point representation for parameter optimization problems (Michalewicz, 1996; Herrera & Verdegay, 1996).對采用進(jìn)化策略優(yōu)化電液伺服系統(tǒng)的控制器增益的實驗性研究摘要本論文通過進(jìn)化的方法解決電液位置控制系統(tǒng)的控制器增益的優(yōu)化問題?？?/p>

54、制系統(tǒng)的優(yōu)化控制器增益可以通過使為評估系統(tǒng)的性能而專門設(shè)計的適應(yīng)函數(shù)最大化來獲得。在本論文中針對以熱軋鋼板中輥縫的控制為代表的液壓軋管機(jī)電液位置控制系統(tǒng)，設(shè)計了時間延時控制器，并且通過基于進(jìn)化策略的一系列實驗直接優(yōu)化了控制器的三個控制參數(shù)。根據(jù)大約150次試驗顯示控制器增益的近優(yōu)值在第五代產(chǎn)生。優(yōu)化的控制器增益可以通過在增益區(qū)間內(nèi)檢查代表系統(tǒng)性能的適應(yīng)函數(shù)的拓?fù)鋪淼玫綄嶒炐缘拇_認(rèn)。由試驗發(fā)現(xiàn)適應(yīng)函數(shù)的拓?fù)溆腥舾删植孔顑?yōu)值以致通過手動調(diào)整得到時間延時控制器的三個控制參數(shù)的最優(yōu)值成了一項艱巨的工作。優(yōu)化的結(jié)果可由進(jìn)化策略和拓?fù)渲械淖畲蠓逯档闹睾宵c獲得。試驗也顯示進(jìn)化策略是優(yōu)化液壓驅(qū)動系統(tǒng)控制器增益

55、的省時省力的高效的方法。關(guān)鍵詞 控制器增益優(yōu)化；進(jìn)化策略；時間延時控制器；自動化控制器增益搜索；電液伺服系統(tǒng)1介紹近幾年來，為提高液壓和氣動伺服系統(tǒng)性能而進(jìn)行的關(guān)于控制器增益的優(yōu)化性和適應(yīng)性研究已經(jīng)成為一個人們?nèi)找娓信d趣的領(lǐng)域（Fleming & Purshouse，2002；Klein，1992；Jeon，Lee，& Hong，1998；Hyun & Lee，1998；Choi，Lee，& Cho，2000）。通常當(dāng)控制工程師為液壓和氣動伺服系統(tǒng)設(shè)計一個控制器是很難從理論上確定它的控制增益從而獲得系統(tǒng)最好的性能。因為液壓驅(qū)動系統(tǒng)高度非線性的特點,所以準(zhǔn)確地模擬這些系統(tǒng)是很困難的。更明確些，液

56、壓和氣動伺服系統(tǒng)比其他的機(jī)械系統(tǒng)比如DC和AC已經(jīng)有相當(dāng)高程度的非線性了。這是多種因素的結(jié)果（Merritt，1976;Watton,1989）:閥的壓力流特性，閥和液壓缸的飽和效應(yīng)，因供油壓力改變而產(chǎn)生閥和液壓缸泄露流量改變的特性，液壓缸的摩擦力特性，以及隨著溫度變化，工作流體粘性和壓縮系數(shù)改變的特性，更主要是因為供油壓力和負(fù)載壓力變化所引起的系統(tǒng)增益的變化。其中，流體的特性是由管道的形狀所決定的。因此，當(dāng)控制液壓驅(qū)動系統(tǒng)時，根據(jù)專家對系統(tǒng)的直觀知識和調(diào)整控制器增益的一般經(jīng)驗來調(diào)整控制器增益。這需要大量的實驗來驗證。但即使獲得了控制器增益，也很難說它是給定條件下的最佳增益。為了研發(fā)液壓驅(qū)動系

57、統(tǒng)控制器增益的自動調(diào)整裝置，人們已經(jīng)對模糊增益適配裝置的應(yīng)用進(jìn)行了研究（Jeon，1997；Klein，1992）。在這個情況下，需要對系統(tǒng)的專業(yè)知識進(jìn)行移植以及一些因控制器增益變化而使系統(tǒng)反應(yīng)發(fā)生變化的一般規(guī)則的基礎(chǔ)知識。因此，算法的實施必須要有大量專家的經(jīng)驗和實驗。在這個研究中，作為電液伺服系統(tǒng)控制器增益的自動優(yōu)化方法，本人建議采用進(jìn)化策略。ES是一種基于自然遺傳學(xué)和適者生存法則的進(jìn)化算法（Rechenberg ，1973；Schwefel，1981；Back & Schwefel，1994，1996）。當(dāng)給出一個作為候選對象生存能力的合適的適應(yīng)函數(shù)就代表一個潛在的解決方法，所以控制器增益

58、的調(diào)節(jié)問題可考慮成一個優(yōu)化問題，也就是在操作者具體給定的增益區(qū)間范圍內(nèi)尋找優(yōu)化的控制器增益設(shè)置值。這樣的一個主要的優(yōu)點是不需要對控制系統(tǒng)做大量的增益調(diào)節(jié)實驗，并且只需要系統(tǒng)最少量的信息。特別是在真實的實驗性系統(tǒng)中對候選對象進(jìn)行進(jìn)化的情況下，由于ES的自適應(yīng)特點所以ESs比其他進(jìn)化算法都合適。在本研究中，設(shè)計時間延時控制器（TDC）作為電液伺服系統(tǒng)的位置控制器。設(shè)計的第二代順序誤差動態(tài)控制器有三個隱性的控制增益。采用ES作為優(yōu)化算法，可通過在線實驗在特定的增益區(qū)間確定優(yōu)化的控制器增益設(shè)定值。為了驗證獲得的結(jié)果，做出增益區(qū)間內(nèi)適應(yīng)函數(shù)的拓?fù)渚仃嚥⒎治?。最后通過ESs方法尋找到的結(jié)果顯示與在特定的增

59、益區(qū)間內(nèi)有最優(yōu)適應(yīng)值的優(yōu)化峰值重合。術(shù)語 Z 目標(biāo)變向量，Z=Z1,Z2,Z3=E,A 獨立變量 E 與已知系統(tǒng)慣量有關(guān)的TDC控制增益 希臘字母e 隨Xd變化的X位置誤差，e= Xd-X 代數(shù)i1 伺服閥1的控制電流 u 父母數(shù)i2伺服閥2的控制電流 E增益的策略參數(shù)L 控制系統(tǒng)采樣時間 增益的策略參數(shù)n 目標(biāo)變量個數(shù) 增益的策略參數(shù) 策略變量參數(shù) （0）策略參數(shù)慣量值，i1,2,3PS液壓驅(qū)動系統(tǒng)變量拉普拉斯變換后提供的壓力 策略參數(shù)向量，= 1， 2，3=S 拉普拉斯變換變量 ，U 控制系統(tǒng)的控制輸入 代表閉環(huán)系統(tǒng)的TDC控X 滾錕液壓缸的位置 制增益的自然頻率Xd滾錕控制液壓缸的工作位

60、置 代表閉環(huán)系統(tǒng)TDC控制增益的阻尼率2液壓伺服系統(tǒng)圖1所示為本研究中所使用的電液位置控制系統(tǒng)示意圖。這個系統(tǒng)是液壓軋管機(jī)的輥縫控制的試驗機(jī)。它用來改善在熱軋鋼板工藝中的厚度控制性能（Gizburg，1984；Lee，Lim & Park，1997）。試驗機(jī)是仿真由在熱軋工藝中有大量自動檢具控制系統(tǒng)的液壓軋管機(jī)組成的輥縫控制系統(tǒng)。該系統(tǒng)由表示軋管機(jī)模量的結(jié)構(gòu)彈簧，表示軋鋼模量的材料彈簧，控制材料彈簧形變的輥縫控制液壓缸和給控制系統(tǒng)干擾的干擾液壓缸組成。加載在輥縫液壓缸上的壓力通過負(fù)載單元測得。結(jié)構(gòu)彈簧的形變現(xiàn)行差動變壓器（LVDT）測得。材料彈簧的形變通過線性比例測得。輥縫控制液壓缸在實際的熱