A General Technical Route for Parameter Optimization of Ship Motion Controller Based on Artificial Bee Colony Algorithm

Transcription

1 A General Techncal Route for Parameter Optmzaton of Shp Moton Controller Based on Artfcal Bee Colony Algorthm Yanfe Tan, Lwen Huang, and Yong Xong Abstract The most practcal applcaton n ndustral process control s stll the conventonal PID control algorthm. However, PID parameter tunng and optmzng, where the dffculty les n as well, s an mportant ssue n the feld of automatc control. It s the drecton to acheve global optmzaton of PID parameters usng ntellgent optmzaton algorthm. Amng at the dffcult problems n parameter tunng of PID controllers n ndustral control, A parameter tunng and optmzaton method based on artfcal bee colony algorthm s proposed, the parameter of PID controller need to be tuned s seen as the nectar source, the hgh-qualty combnaton of parameters s searched usng the unque role change mechansm of the bees; and the ITAE ndex s selected as the objectve functon for parameter optmzaton. Smulaton mplemented on MATLAB-Smulnk proved the proposed process was of feasblty and avalablty n the optmzaton work. The process and results showed that proposed techncal route was smple and feasble wth strong adaptablty, makng t an effectve computer aded offlne parameter optmzaton method for PID controller. Index Terms Shp engneerng, automaton, PID controller, ntellgent parameter optmzaton, artfcal bee colony algorthm. I. INTRODUCTION At present, the ndustral automaton level has become an mportant symbol to measure the level of modernzaton n all walks of lfe. At the same tme, t also reflects a country's development speed at some pont. Also the development of the control theory has experenced three stages characterzed by the classcal control theory, modern control theory and ntellgent control theory [1]. As control theores rapdly develop, many advanced control algorthms now have appeared. But so far, the most practcal applcaton n ndustral process control s stll the conventonal PID control algorthm. Ths s because the PID control has a smple structure and s easy to be mplemented wth perfect performance and strong robustness. What s more, prncple of PID algorthm s concse, wth clear Manuscrpt receved December 19, 215; revsed February 19, 216. Ths work was supported by: (1) the Fundamental Research Funds for the Central Unverstes (specfcally supported by the self-determned and nnovatve research funds of WUT, Grant No. 214-JL-1), (2) the Natural Scence Foundaton of Hube Provnce (Grant No. 214ZFB878), and (3) the Key Project n the Natonal Scence & Technology Pllar Program (Grant No.215BAG2B5). Yanfe Tan, Lwen Huang, and Yong Xong are wth the School of Navgaton, Wuhan Unversty of Technology (WUT), Chna, and the Hube Key Laboratory of Inland Shppng Technology, WUT, Chna (e-mal: fefe_whut@163.com, lwhuang@whut.edu.cn, bear_brave@163.com). physcs meanngs of the parameters and a complete theoretcal system, whch the majorty of control engneers are famlar wth [2]. However, PID parameter tunng and optmzng, where the dffculty les n as well, s an mportant ssue n automatc control felds. The conventonal PID algorthm especally requres ts parameters hgh-ntegrated and often fals to acheve satsfed control results. Due to a poor parameter settng at the applcaton scene of PID theory or controller, resultng n unsatsfed control effect, people over the years have dedcated to the study parameter settng method and a varety of the methods have been put forward. There are plenty of methods for PID parameter tunng, for example, the classcal Z-N method, smplex method and some ntellgent algorthms such as Artfcal Neural Network (ANN), Genetc Algorthm (GA) [3], etc. The classfcaton of those knds of methods can be seen n [2]. In case of the low effcency and some unsatsfactory, t s the drecton to acheve global optmzaton of PID parameters usng ntellgent optmzaton algorthm [4]. PID controller s wdely used n practce for shp course control. However, the large tme delay, large nerta and nonlnearty of shp moton, make the selecton of PID parameters more dffcult [5]. Amng at the dffcult problems n parameter tunng of PID controllers n ndustral control, we wll propose a general techncal route for parameter optmzaton of shp moton PID controller based on Artfcal Bee Colony (ABC) algorthm, where the parameters of PID controller need to be tuned and optmzed wll be treated as the nectar source, hgh-qualty combnaton of parameters wll be searched usng the unque role change mechansm of the bees, and the ntegral of tme multpled by the absolute value of error (ITAE) wll be selected as the objectve functon for parameter optmzaton. The proposed general techncal route wll be tested va MATLAB-Smulnk based smulatons. II. THE ARTIFICIAL BEE COLONY (ABC) ALGORITHM A. Glance at ABC Algorthm Introduced by D. Karaboga [6]-[9], the ABC algorthm s a nature-nspred algorthm based on the ntellgent foragng behavor of honey bee swarm and has been used to fnd an optmal soluton n numerc optmzaton problems [1]. Based on many benchmark functons, researches [7]-[9] showed the ABC algorthm was compettve to other populaton-based algorthms, such as GA, Partcle swarm optmzaton (PSO), Dfferental Evoluton (DE), evoluton DOI: /IJET.217.V

2 strateges and Partcle Swarm nspred Evolutonary Algorthm (PS-EA), etc., wth an advantage of employng fewer control parameters [11]. Snce ts nventon n 25, ABC algorthm has attracted a lot of attenton and been appled to solve many knds of problem besde numercal functon optmzaton [1]. A survey about applcatons of ABC algorthm s provded by Karaboga et al. n [12]. Besdes, there are now many types (or mproved versons) of the orgnal ABC due to a large number of researchers ntatve nterests n t and (or) makng t more sutable for varous problems. To dfferentate, we call the algorthm proposed n 25 the standard ABC, what s the one the paper here refers to. B. Basc Prncple Descrpton of ABC Algorthm Accordngly [6]-[1], colony of artfcal bees conssts of three groups of bees to search foods generally, whch ncludes employed bees, onlookers and scouts. The frst half of colony conssts of the employed artfcal bees and the second half ncludes the onlookers. The employed bees search the food around the food source n ther memory. They perform waggle dance upon returnng to the hve to pass ther food nformaton to the other of the colony (the onlookers). The onlookers are watng around the dance floor to choose any of the employed bees to follow based on the nectar amount nformaton shared by the employed bees. The employed bee whose food source has been exhausted by the bees becomes a scout who must fnd new food source. For every food source, there s only one employed bee. In other words, the number of employed bees s equal to the number of food sources around the hve. In ABC algorthm, the poston of a food source represents a possble soluton to the optmzaton problem and the nectar amount of a food source corresponds to the qualty of the assocated soluton (ftness value). C. Implement Steps of ABC Algorthm Brefly and accordngly [6]-[1], the man steps of mplementng the ABC algorthm are gven below. Step 1: Randomly generate the ntal populaton of N food sources wthn the range restrcted by boundares of the varables accordng to Eq. (1). new food source. v x ( x x ) (3) j j j j kj where j s a random nteger wthn [1,D] and k 12,, N s a randomly chosen ndex that s dfferent from. j s a unformly dstrbuted real random number wthn [-1,1]. Step 4: Calculate probablty based on ftness of the solutons n the populaton. Each onlooker selects a food source accordng to Eq. (4) by roulette wheel selecton and generates a canddate soluton accordng to Eq. (3). p SN n1 Step 5: Evaluate the canddate food source and select a better one as the new food source accordng to greedy selecton. Step 6: Memorze the best food source poston (soluton) found so far. Step 7: If the poston of a partcular food source cannot be mproved through the predetermned number of trals lmt, then select t as an abandoned one. Replace the solutons by a new poston that s randomly produced by a scout accordng to Eq. (1). Step 8: Repeat the procedure from step 3 untl the termnaton crteron s met. When the algorthm s termnated, the poston of optmal food source and ts nectar amount are the optmum values of the decson varables and objectve functon for the consdered problem. III. PARAMETER OPTIMIZATION OF SHIP PID CONTROLLER ft ft A. The PID Control System of Shp Course The shp course PID control system drawn n MATLAB-Smulnk lbrary s shown n Fg. 1. n (4) x x rand[,1]( x x ) (1) j j j j mn max mn where =1 N, j=1 D. N s the number of food source and D s the number of varables to be optmzed. Step 2: Evaluate each food source by calculatng ts ftness (.e. calculate the nectar amount) accordng to Eq. (2). 1/ (1 f) f f ft = 1abs( f ) f f where f s the cost value of soluton x. For maxmzaton problems, the cost functon can be drectly used as a ftness functon. Step 3: Each employed bee searches a canddate food source v accordng to Eq. (3). Evaluate the canddate food source and apply greedy selecton to select a better one as the (2) Fg. 1. A PID course control system of shp course. The algorthm of PID controller was represent by Eq. (5). ( t)= K e( t) K e( t)dt K t P I D d et ( ) dt And, et () means the trackng error calculated by Eq. (6). e( t)= y ( t) - y( t) r Addtonally, yr () t represents the command sgnal for (5) (6) 134

3 reference, whle yt () represents the actual sgnal feedback. B. Problem Descrpton of Parameter Optmzaton for the Control System The problem of PID parameter optmzaton for shp course control can be brefly descrbed n a sentence that a set of sutable KP, KI, KD need to be determned to make a certan or more evaluaton ndexes perform best. There are several most wdely used error ntegral performance ndexes (crtera) to evaluate a control system, such as ntegral of absolute value of error (IAE), ntegral of squared error (ISE), ntegral of tme multpled by the absolute value of error (ITAE), ntegral of tme multpled by squared error (ISTE). There s no doubt that such ndexes can be utlzed as the objectve functons. In vew of ths, an objectve functon can be chosen form the followng equatons (7) to (1). optmzed) and constructng an objectve functon. 2) Intalzng algorthm settngs. 3) Amng at optmzng the objectve functon, executng the artfcal bee colony algorthm. 4) Outputtng parameter optmzaton results (the optmal parameters). 5) Applyng the optmal parameters and analyzng the control effect. IV. SIMULATION OF THE MODEL AND CALCULATING FLOW A. A SIMULINK Model Combne Control System and Performance Calculaton The SIMULINK model smulatng step response and calculatng error performance of the system s shown n Fg. 2. JIAE e( t) dt 2 JISE e ( t) dt J t e( t) dt ITAE 2 JISTE t e ( t) dt (7) (8) (9) (1) Fg. 2. Smulnk model of step sgnal based course control system (the lower half) and error performance calculaton (the upper half). where the nonlnear J s the objectve functon correspondng to dfferent error ntegral performance ndexes, and et () s calculated by Eq. (6). C. A Search for Best Solutons Based on ABC Algorthm By analyss, we beleved that exsted the followng correspondence among actual act of honey bees, solvng of optmzaton problems based on ABC algorthm and parameter optmzaton of shp course PID controller, whch was lsted n Table I. TABLE I: CORRESPONDENCE AMONG ACTUAL ACT OF HONEY BEES, SOLVING OF OPTIMIZATION PROBLEMS BASED ON ABC ALGORITHM AND PARAMETER OPTIMIZATION OF SHIP COURSE PID CONTROLLER Actual act of honey bees Nectar source locaton Nuctar source earnng degree The speed of the foragng The maxmum earnng degree Solvng of optmzaton problems based on ABC algorthm Feasble solutons Qualty of the feasble solutons Speed of optmzng fessble solutons The optmal soluton Parameter optmzaton of shp course PID controller Varous values of the parameters KP,KI,KD Performance ndex value n accordance wth dfferent KP, KI, KD Speed of optmzng the performance ndex The optmal KP, KI, KD mnmzng the performance ndex Thus t can be nferenced that the PID controller parameter optmzaton problem was able to be nverted as a nonlnear functon optmzaton problem, and then could be solved usng artfcal bee colony algorthm. The man steps to solve the problem were as follows: 1) Determnng control varables (parameters to be where: 1) The concrete content of TF block calculatng shp moton was gven by convertng the followng dfferental equaton (11) accordng to [13], [14]. T K (11) Takng YULONG as an example, the shp s maneuverng character ndces were: T = and K =. 48 [13]. 2) The S-functon block (Calculator) was used to calculate error performance accordng to dfferent performance requrements. Selecton of objectve functon should be combned wth the characterstcs of the problem to be solved, and be convenent for applcaton. ITAE s one of the best performance ndexes appled to evaluate a sngle nput and sngle output (SISO) control system and the adaptve control system. And ITAE s always chosen as the objectve functon to be optmzed a conventonal PID control system to obtan better control effect. Here we chose ITAE as the ndex for nvestgaton, thus the man and concrete content of the Calculator block was programmed accordng to Eq. (9). B. Settngs of the ABC Algorthm Meanngs of the varables and ther values used n the program are lsted below. Populaton sze: NP=3. Number of foods: FoodNumber=NP/2. Number of the scouters: SearchNumber=5. Maxmum cycle: maxcycle=1. Tres Lmt: lmt=5. Upper bound of [KP KI KD]: Ub=[3 3 3]. 135

4 Lower bound of [KP KI KD]: Lb=[ ]. C. Parameter Optmzaton Results based n ABC Algorthm Optmzaton processes of controller varables (specfcally KP, KI, K ) can be seen n Fg. 3 and the fnal D optmal values are: KP 159, K and K 3. I D solve the parameter optmzaton problem, the gven the process wth the MATLAB-SIMULINK based smulaton model was workable. Compared wth the results provded by un-optmzed parameters, smulaton showed that the optmal parameters produced: (1) hgh trackng speed (the tme from ntal moment to steady state less than 1 seconds); (2) only one small overshoot (less than 1%, shown n Fg. 4) or undesred, redundant oscllaton elements; and (3) a best performance ( mn J =11.1 ). ITAE Fg. 3. Optmzaton processes of the control varables (PID parameters). For comparson, we ntroduce a set of un-optmzed parameters (e.g. KP=26, KI =1, K D=21 ). And then, system step response correspondng wth the optmal and un-optmzed PID parameters are separately shown n Fg. 4 and Fg. 5. Changes of the system performance ndex correspondng wth the optmal and some un-optmzed PID parameters are shown n Fg. 6 and Fg. 7. Fg. 7. System performance correspondng wth un-optmzed parameters. Generally, t can be summarzed that the ABC algorthm was applcable to solve the problem when appled for parameter optmzaton of shp moton PID controller and the optmzed parameters produced a better effect, reachng the goal of a rapd, accurate and stable control effect, and mnmzng the performance ndex value. V. CONCLUSION AND OUTLOOK ` Fg. 4. System step response correspondng wth optmal PID parameters. Fg. 5. System step response correspondng wth un-optmzed parameters. Fg. 6. System performance correspondng wth the optmal parameters. It can be seen that the ABC algorthm was applcable to A. Conclusons Parameter tunng s an essental part of knds of controllers, a global optmzaton of the parameters can be realzed by applyng optmzaton algorthms, meanwhle overcomng the defects of tradtonal methods. Focusng on such feld, ths paper have launched the followng work: 1) Analyzed and ponted out that achevng global optmzaton of PID parameters usng ntellgent optmzaton algorthm was the development drecton of PID controller parameter tunng and optmzaton. 2) Based on the performance requrements of the control system, analyzed the adaptablty between PID parameters optmzaton problem and ABC algorthm. By specfc descrbng the ABC algorthm based steps on how to optmze PID parameters for shp course control system, the paper ntroduced smultaneously a scheme of optmzng the parameters based on ABC algorthm as well as a MATLAB-SIMULINK based smulaton model. 3) Smulaton mplemented on MATLAB-Smulnk proved the proposed process was of feasblty and avalablty n the optmzaton work. 4) The process and results showed that proposed techncal route was smple and feasble wth strong adaptablty, makng t an effectve computer aded offlne parameter optmzaton method for PID controller. Due to some detals, there exsted some small overshoot n the system. But t does not affect the feasblty of the 136

5 proposed scheme. Addtonally, although a practcal control system s far more complcated than the above gven example, but the optmzaton prncple of a number of parameters s the same or smlar. Thus t can be speculated that the developed scheme can be referenced for parameters optmzaton of not only a PID but also the other knds of controllers. B. Outlooks In the follow-up studes, we wll focus on: 1) Further study on prncples and mprovement of ABC algorthm to mprove ts performance, such as the convergence speed as well as the search precson. 2) Deeper analyss of the control system tself and mprovement the objectve functon, n order to make the optmzaton goal meet the dynamc requrements of performance ndcators as well as Enhance dynamc performance of the control system. 3) Expandng applcaton scope of the proposed techncal route for parameter optmzaton based on ABC Algorthm, and optmzng other knds of controllers appled n practce, to conform to the actual demands. ACKNOWLEDGMENT Specal thanks are gven to the research projects for ther nfrastructural and fnancal support. Sncere apprecates are delvered to scholars of the references for ther outstandng contrbutons. REFERENCES [1] T. Yang and Y. Shan, Smulaton of PID controller parameter tunng, Urban Constructon Theory Research (Electronc Verson), vol. 5, no. 16, June 215. [2] Z. Lu, X. Jang, and D. L, Overvew of the tunng methods of the pd controller parameters, Automaton of Electrc Power Systems, vol. 2, no. 8, pp , [3] C. Ca and W. Zhou, Self-tunng PID parameters by usng artfcal bee colony algorthm, Process Automaton Instrumentaton, vol. 36 no. 8, pp , August 215. [4] B. Guo, L. Zou, and X. Qan, The optmzaton of PID tunng based on model smulaton technology, Manufacture Automaton, vol. 37, no. 8, pp , August 215. [5] Y. ZHU, Parameters optmzaton of shp course PID control, Dalan Martme Unversty, 212. [6] D. Karaboga, An dea based on honey bee swarm for numercal optmzaton, Techncal Report (TR6), Computer Engneerng Department, Ercyes Unversty, Kayser, Turkey, 25. [7] D. Karaboga and B. Basturk, A powerful and effcent algorthm for numercal functon optmzaton: Artfcal bee colony (ABC) algorthm, Journal of Global Optmzaton, vol. 39, no. 3, pp , 27. [8] D. Karaboga and B. Basturk, On the performance of artfcal bee colony (ABC) algorthm, Appled Soft Computng, vol. 8, no. 1, pp , 28. [9] D. Karaboga and B. Akay, A comparatve study of artfcal bee colony algorthm, Appled Mathematcs and Computaton, vol. 214, no. 1, pp , 29. [1] P. Guo, W. Cheng, and J. Lang, Global artfcal bee colony search algorthm for numercal functon optmzaton, n Proc. 211 Seventh Internatonal Conference on Natural Computaton, vol. 3, pp , July, 211. [11] W. Chen, An artfcal bee colony algorthm for uncertan portfolo selecton, The Scentfc World Journal, vol. 214, pp. 1-12, 214. [12] D. Karaboga, B. Gorkeml, C. Ozturk et al., A comprehensve survey: Artfcal bee colony (ABC) algorthm and applcatons, Artfcal Intellgence Revew, vol. 42, pp , 214. [13] X. Zhang, X. Ja, and C. Lu, Research on respondng shp moton mathematcal model, Journal of Dalan Martme Unversty, vol. 3, no. 1, pp , February 24. [14] J. Yu and Z. Shao, Knetc smulatng study on the model of the shp maneuverng moton, Journal of Jme Unversty (Natural Scence), vol. 7, no. 3, pp , September 22. Yanfe Tan was born n 1983 and Now He s a Ph.D canddate n School of Navgaton, Wuhan Unversty of Technology (WUT), majorng n transportaton nformaton engneerng and control and devotng hmself to ntellgent navgaton and smulaton technology, marne rsk evaluaton and safety guard. He receved hs master's degree from WUT n 213. Tan had been also crew member on board shp and he s a 2nd brdge offcer now. Lwen Huang was born n 1965 and he s a professor and a doctoral supervsor n School of Navgaton, Wuhan Unversty of Technology (WUT), devotng hmself to ntellgent navgaton and smulaton technology, martme safety guard, etc., He receved hs doctor's degree from Qngdao Ocean Unversty (now renamed Ocean Unversty of Chna) n Prof. Huang had been a postdoctor n the Shp and Ocean Engneerng Post-doctoral Research Staton located n Wuhan Transportaton Unversty (WTU, whch s one of the predecessors of the current WUT) from to 2.7, and n the Insttute of Atmospherc Physcs, Chnese Academy of Scences. 28. Yong Xong was born n 1976 and he s an assocate professor and a master's supervsor n School of Navgaton, Wuhan Unversty of Technology (WUT), devotng hmself to control theory, control engneerng and shp ntellgent control technology, receved hs doctor's degree from Zhejang Unversty n 25. Prof. Xong had been a postdoctor n the Computer Applcaton Post-doctoral Research Staton located n South Chna Unversty of Technology from 26 to 137