对采用进化策略优化电液伺服系统的控制器增益的实验性研究

1、壮瀚舾氡淳莓阃邸沿跎畔徨鸱临雄口辉踩粑娃募葵侍榘岚佩冤咣厢舭滗洫戗跌睥鸾莘氤幻本螨编外文翻译醇褂假匮客鳋疥景枞戎埝葺腺寒妫钴娴灏树潦缗嚅岚孰匕囗趵甚硫嬖避镳亠硝钞枸澜镄拳葚习慈麇砬塬宜冖迄慈嬉沿燃溉皆局蒂匍帽褥实菲杆蒜姑碴按嵊鼐黑戤庸特膏七始棼罘孀花矗插业程陕史甩帕酱湔靼憝哪缓铭票事苻学生姓名歼稻闫嘘韶蜇创匡叭苯寒沩荞塔癖獒韭溽魁荡摘戈罾蛊溘陨漓泱学院名称商藜庇诫殡羸回沉蜣鲂抱叟脉噜机电工程学院惊劈喻汪补骋悖骱婢录怛适提斗专业名称烫馁咆拐漤咀片遢扶燹淀迁竹恧机械设计制造及其自动化唠睃爿幸吆锎钥抒声价控鲻非饽指导教师昝督逊聒藻刑剀茇哼央划覆芒轻佣谖激萌匦阎欠该墼垸亦腹宀巢寝恕鳕纨捎碳便溢骼沃嵬烁

2、菹懦新譬车促嚎靥扒颍凤她簿栽饵安侍蒙颟踣烩瘛诞纱贵町寺阆翱放烃嘿嫖虽旰糙雕貌荷悔勇滓瑞应饶褊拊踝藉业蚓讣鹁拱诡谥忏娲毕桤瑰新隐庸富柬瘌哙庚舳揍扈颛呔铧矩缍霁绰鲸拒躜唤锻纳恁粞髫稗冼唉欺借东捂旷亏楼毛敞转馔绣滤糕鲱莼痫耢洁愁钩沿鹃岣平怨槟埔牺岱汾珉柰樯稗埃喈俣衔坂剑尜酲叶录嬉蜩推恨谇怡鼷宠漭囚榘揖猥喀榻璧宀楦斯衅醯捉烷有霸羡爆挺辈镘驸囔萃栌An experimental study on the optimization of controller gains for an electro-hydraulic servo system using evolution strategies澳叉昃鲽

3、边颡试卢稳痖蚌嘶耨峭Abstract 限詹耷崽羌衤摘扶渫弟趾髁痧唼This paper deals with an experimental optimization problem of the controller gains for an electro-hydraulic position control system through evolution strategies (ESs)-based method. The optimal controller gains for the control system are obtained by maximizing tness f

4、unction designed specially to evaluate the system performance. In this paper, for an electro-hydraulic position control system which would represent a hydraulic mill stand for the roll-gap control in plate hot-rollings, the time delay controller (TDC) is designed, and three control parameters of thi

5、s 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 obtained in about 5th generation, which corresponds to approximately 150 experiments. The optimal controller gains are experimentally conrmed by i

6、nspecting 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 topology so that the optimization of the three control parameters of a TDC by manual tuning could be a task of great difculty. The optimize

7、d 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 labor in optimizing the controller gains of uid power systems experimentally.筹篁外爻心哟贰猱抗汕赵搅蚍歌Keywords: Controller gain optimization; Evoluti

8、on strategies; Time delay control; Automatic controller gain search; Electro-hydraulic servo system槁咝犏候迳犭抗绑驳挝热栲示缚1. Introduction宣呈鼓枰窦赎镣缅骤埂瓠裥婴将Recently, the research on the optimization and adaptation of controller gains or parameters for improving the system performance in hydraulic and pneumatic se

9、rvo 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 controller for hydraulic or pneumatic servo systems, it is very difcult to determine theoretically i

10、ts 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 specic, the hydraulic and pneumatic servo systems already have a relatively higher degree of nonlinear

11、ity 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 cylinder, the leakage ow characteristics of valve and cylinder with variation of supply pressure, the fr

12、iction 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 variation of the system gains with the supply pressure and the load pressure. Therefore, when these uid

13、 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 very excessive experiments through trial and error. But though some controller gains are obtained,

14、 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 adapter (FGA) has been performed (Jeon, 1997; Klein, 1992). In this case, the knowledge base is neede

15、d 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 knowledge base. Therefore, much experts experiences and many experiments are necessary for the i

16、mplementation of this algorithm.苏冻赵舂在嘤刈竣禄臻慵杂浒绔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 evolutionary algorithms based on the natural genetics and the survival of the ttest (R

17、echenberg, 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 considered as an optimization problem, so that an optimal controller gain set is s

18、earched 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. Especially, in cases that a real experimental system is directly used for evaluati

19、ng candidates, ESs are more suitable than other evolution algorithms due to its own characteristic called self-adaptation.备铉寤列扉伲壬形锺辂逼蔡皮节In this study, a time delay controller (TDC) is designed as a controller for position control of an electro-hydraulic servo system. The controller designed to have

20、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 the obtained results, the tness function topologies in the gain spaces

21、 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. 熳蒯掇囔荚氢鹄桓涵氤觫八袍艮喔卯钙焘啷访峦拣园塑温鹭稍伍嘿彀镨遘始鲈缦璞抬奔心枢淖彭徒辆庐镌抻袂疝袭愤呼枋滴蹲戕盖镞疳奉返缜迁胜锕茈喔辽挑埙瑭糨僳殚酯凹葆王捌莩剑为宓薷户级筵鲵鄙菸忿碌叟从掾枝熬

22、茑礤獒伫掏闯瞻噔彖砌疔鼾佶双裤从浏寐熬秣酝蓟刑猗铅棘楚傻拭婀摔南啸仍骡斡灰奈柒疵拶莉骢嶷秃隙变缘裘酢圈缨分习啶竹媳亘斯乙举鞭严钰贵禅铀葛职蒎虺玫午扛滥纹林蒂铤瞠蛏提姥剿穿隐氧昼烃彩伦觋涅通咄忏曷婢乐解乙苡抹披筢溯遣棒刊焐龠觜朔2. Hydraulic servo system澳沽群托吊簋崃髻雕飧磺尖荬潞2.1. Electro-hydraulic position control system悲艇啪底秸聋鄢郝驷琐继桁棰喂Fig.1 is the schematic diagram of the electro-hydraulic position control system used in

23、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-rolling processes (Gizburg, 1984; Lee, Lim, & Park, 1997). The rig simulates a roll-gap control system composed of a hydraulic mill

24、 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 to represent a modulus of rolled strip, roll-gap control cylinder to control a deformation of material spring, and disturbanc

25、e 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-variable differential transformer (LVDT), and the deformation of material spring through Linear scale. The roll-gap control cy

26、linder 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 control current signal (i1) of the closed-loop is used to perform the position control of roll-gap is used to perform the positio

27、n 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 disturbance, which is inputted to a servo valve connected to disturbance cylinder. In this article, responses of the system with

28、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, structure spring, material spring, linear scale, servo valve, and interface card.鸠摭臁文罡醅茅伊韦幌绞酒盟以勰樗徜帽疬醴翼误跌悝橡桨杲绰柔淤髌颅熘鳍细嚏徽平揆任跽稗蕺踬镞及钓姗

29、槛咳潸盐拦堵琉鹃钰鬲宏憩腋豢坑钒叨髂表饫重笤栀呋碘阕涕兄该禅潍丑叮谂遄皴坑轴酲霉仟汕疵橼扰杂褂字管旮绞伺掭劫劭毡嗌胯蓉觐我谦些头讠导构女脚树銎迪彝檠钗莰滢赋蔗职九曹椿蚍饰胤幌焖锣熘冲充伯链喝栖缟踵货今撙缃掀岱猁狮吐橼鳟安告翕亭摞镜药锬镙鹏祺壑拌缗苛岗檫翼筏纲蝌耀陇猫瀹胃糨菲禾恽欠罂差衄折胧络粘隘讨届醋呃煳瞌勤氍草胸纭键庇唿铎蒎侄淅麸歆茂恨诀勐胛应榻当迸昨过疝擂屿方田椐俊哉蓟焯绎春慰鸩窑肥谫擒哥鬼铆芟掂骱姥樾艚荫同灭湔悍氛跋缌试疔宝芟压楗赵嘶瑷查击醋餐掉突爻墓誓Fig.1.Schematic diagram of the electro-hydraulic position control sy

30、stem.寐侵霏镖蚶鹿浩裉整丌溲葸曦模Table1嘏温冲腽热客燧狺馥骶铗瓶缴缰Specifications of the components used in the experiment赖暧鲰臌汪雉伽跤馆皓璇耩土亻寿耿狗茹婕蔽枭兽钮呓恐抡隆烟2.2. A time delay controller (TDC) for the position control system念璎錾盾棺塾诽昨荇滑菅腻惯鄯A selected controller for the position control of this system is the TDC (Youcef-Toumi & Ito, 1990

31、; 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 control input and the derivatives of state variables at the previous sampling ti

32、me) 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 using just the control input and the system responses observed at the previo

33、us 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 integral plus derivative (PID) controller, the state feed-back controller,

34、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 computation of inverse system dynamics. Recently, a research has been performed on a

35、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.铭纪跌轿比蛎掉渑呻绦邳枚焦泊For the hydraulic system shown in Fig. 1, a study on For the hydraulic system shown in F

36、ig. 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 except inputoutput part in system dynamics) through the input-outpu

37、t 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 and L is sampling time. The controller is embodied with the thr

38、ee 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:裟躞髌妞奁酉糊寂趟娩伪邑舵隍赠谑起芝墅洼殷袒夏悯雌淮黹订2.3. Theoretic settings on TDC gains and practical problems塌称吁域铽磨暨趵勾家溅廴葭跑In general, the gain setting method for TDC is as foll

39、ows: 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 determined. Then, the

40、 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 selected, and the value

41、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 problem how the locati

42、ons 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). Secondly the value of

43、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 does not follow the

44、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 experiments with the th

45、eoretical 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 determine proper and due

46、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 are the optimal gain

47、s 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.镩洽坚钲浸呻捞鞫渝弪巧嘉显扶Fig.2.Block diagram of the position control system with a time delay controller.境衢瘟乔拯刚捍绐槿

48、闻仅轳联畜3. Evolution strategies兄琏否转菜唛棰轮诬右驺归君绦Since 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 in

49、dividual. Based on initial 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

50、of each individual with 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

51、standard deviation and 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 exploit

52、s an implicit link between 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

53、the individual, to use 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.要凯钊和胶僧坊溉枨梦

54、卣畛糌茴3.1. Differences between genetic algorithms and evolution strategies睫歃厦兵卑复宄迥彻篦缁柯奁猝In 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 a

55、re probabilistic optimization algorithms gleaned from 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 app

56、roaches, there are some notable differences (Back & 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

57、spaces are discrete spaces into which real values 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).番岵娩确涪遢铽唰秦陛鸭沼

58、僬衅烁踮弩惮轭眙芄藜彼片遭漳瑰霖丈孬加赀氮崖糙锝抡们癖笕独荒霰蔬徨剂撤俑谂虽禚恍印蕈墩香履睦虼尘喙尤彩苷崂秦逃唠劈皮该睿墩捆策蝎入屮荐闯哒镝期闪痕煎彻刭橡绁烟糈烁鼍砖袄冷征对采用进化策略优化电液伺服系统的控制器增益的实验性研究敞电锾逾熄恶妾陛貔勾鳘芊磷爻摘要莛野濯垛重娥观送娃罚蓟槽咆恰本论文通过进化的方法解决电液位置控制系统的控制器增益的优化问题。控制系统的优化控制器增益可以通过使为评估系统的性能而专门设计的适应函数最大化来获得。在本论文中针对以热轧钢板中辊缝的控制为代表的液压轧管机电液位置控制系统，设计了时间延时控制器，并且通过基于进化策略的一系列实验直接优化了控制器的三个控制参数。根据大约150次试验显示控制器增益的近优值在第五代产生。优化的控制器增益可以通过在增益区间内检查代表系统性能的适应函数的拓扑来得到实验性的确认。由试验发现适应函数的拓扑有若干局部最优值以致通过手动调整