The Mechatronics System Control Quality Analysis Using Simulink and GUI in Matlab

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1 Proceeding of the World Congre on Engineering and Computer Science 01 Vol II WCECS 01, October 4-6, 01, San Francico, USA The Mechatronic Sytem Control Quality Analyi Uing Simulink and GUI in Matlab M. uhá, B. uháová, and P. Mydlo Abtract In thi contribution i preented tudy of flexible mechatronic ytem control quality analyi. Control ytem i deigned by variou tandard and advanced method. The different criteria for quality evaluation are ued. The Matlab Simulink imulation model in conjunction with Matlab GUI i ued for experiment realization. Index Term control quality, Matlab GUI, mechatronic ytem control, Simulink I. INTRODUCTION THE contribution deal with flexible mechatronic ytem control quality analyi by the Simulink tool and with GUI utilization created in the Matlab. The impule i ongoing neceity of further advancement of electric drive containing element with different type of paraitic effect control method, in thi cae flexible connection between an actuator and a load. There are different method of mechatronic ytem control deign analyzed in thi article. The control quality i advied on bae of local criterion a well a integral quality criterion. II. CONTROED SYSTEM MODE The permanent magnet ynchronou motor (PMSM) with flexible coupling i choen a analyzed mechatronic ytem. A pecial type of PMSM with the high torion moment by the relatively low evolve torque motor, wa analyzed. If the inertia of the tranmiion mechanim i mall compared to the motor and load, the flexible coupling between the motor and load can be treated a a two-ma motor/load ytem, a hown in Fig. 1. [, 5, 6] Fig. 1 PMSM with flexible join Manucript received une 0, 01; revied uly, 01. M. uhá i with the Intitute of AIAM FMST SUT in Trnava, Hajdóczyho 1, Trnava, Slovak Republic (phone: ; martin_juha@tuba.k). B. uháová i with the Intitute of AIAM FMST SUT in Trnava, Hajdóczyho 1, Trnava, Slovak Republic ( bohulava.juhaova@tuba.k). P. Mydlo i with the Intitute of AIAM FMST SUT in Trnava, Hajdóczyho 1, Trnava, Slovak Republic ( peter.mydlo@tuba.k). ISBN: ISSN: (Print); ISSN: (Online) TABE I ANAYZED SYSTEM PARAMETERS Parameter Unit Decription Value Ra Ω armature current 0.0 a mh reitance and inductance of armature winding 100 cφ Nm/A torque contant 0.3 M kg/m inertia of the motor rotor 10 kg/m inertia of the load 60 b1 Nm damping of the tranmiion 0.1 d1 Nm pring contant of the tranmiion 4 ktm - converter gain 1 TTM - converter time contant The control ytem deign wa baed on idealized condition where the infinitely rigid connection wa conidered intead of flexible connection between actuator and a load. Thi condition i decribed a = M + (1) Overimplified model of ytem a tranfer function of thi adjuted mechatronic ytem ha a form cφ GPMSM() = () (M ) a + (M )R a + cφ A puriou effect caued by reonant frequency and antireonant frequency occurrence in the flexible connection were eliminated by double notch filter [7, 9] in form 1 ξr r G () ωr ω (3) filter = 1 ξ a ωa ωa where reonance: M ω r = d (4) 1 M reonance dumping: b 1 M ξ r = (5) d 1 1M antireonance: d1 ω a = (6) antireonance dumping: b1 ξ a = (7) d III. CONTRO SYSTEM DESIGN AND CONTRO SYSTEM MODE For control ytem deign wa applied different method. [1, 3, 4, 8] Claical feedback control ha been deigned by --Nalin method 1 WCECS 01

2 Proceeding of the World Congre on Engineering and Computer Science 01 Vol II WCECS 01, October 4-6, 01, San Francico, USA --Modulu Optimum Method --Method of Invere Dynamic Next, the combination of claical feedback control and one of intelligent control method ha been applied --Fuzzy controller An advanced control method in form of cacade control with utilization --x Modulu Optimum Method --Modulu Optimum Method and Symmetric Optimum Criterion wa alo ued. A. Feedback control of angular velocity The imulation wa performed by imulation model (Fig. ) [10] conit of --controlled ytem actuator electrical part (Fig. 3) and flexible join of actuator with load (Fig. 4) --controller G R () --double notch filter Fig. Simulation model of angular velocity feedback control Fig. 3 Analyzed ytem imulation model of electrical part Fig. 4 Analyzed ytem imulation model of flexible join PI controller Nalin method For controller of PI type in form r 1 GR () = r0 + (8) i the cloed control loop in form 0.3r r 1 Gc() = (9) ( r0 ) + 0.3r 1 According thi, for α = and maximum overhooting 5% following a Nalin method are valid inequalitie a1 α 0 a αa1a a a : ( r0 ) = * 0.3r 1 * 1. 4 (10) :.4 = * ( r ) * 7 (11) For PI controller coefficient calculation i ued a boundary tate equality and the reulting value are TABE II PI (NASIN) CONTROER PARAMETERS r r PID controller Modulu Optimum Method For controller of PID type in form r 1 GR () = r0 + + r1 (1) ha an opened control loop form 0.3r r r 1 Go() = (13) Following an aumption that ideal cloed control ytem tranfer function ha a value approaching to one, the equation involving real part of open control loop frequency repone ha form 4 ω (0.4r1.1r 0 ) + ω (0.07r0 0.4r 1) Go() = ω + 0.7ω ω Go() = 0.5 (14) The coefficient of PID controller are olved baed on equation ytem in matrix form olution r = r (15) r1 49 The coefficient of PID controller deigned by Modulu Optimum Method are TABE III PID (MOM) CONTROER PARAMETERS r r r PID controller Method of Invere Dynamic For poibility to calculate controller coefficient by Method of Invere Dynamic wa tranfer function of an actuator rigidly connected with a load modified to the form 0.3 K GPMSM() = = (16) T0 + ξt0 + 1 where K = 0.3 / 0.09 ; T 0 = 7/0. 09 ; 1.4 ξ = (17) 0.09 * * T 0 The coefficient of PID controller in form Ti GR () = P(1 + + Td) (18) are for defined time contant T w =0.1 calculated according to equation Ti = ξt 0 ; T0 T = ; Ti d P = (19) ξ KTw The coefficient of PID controller deigned by Method of Invere Dynamic are ISBN: ISSN: (Print); ISSN: (Online) WCECS 01

3 Proceeding of the World Congre on Engineering and Computer Science 01 Vol II WCECS 01, October 4-6, 01, San Francico, USA TABE IV PID (MID) CONTROER PARAMETERS P T i T d 5 Fuzzy control The fuzzy controller wa deigned by experimental variation of k e, k de and k du coefficient baed on ITAE quality criteria tracking and evaluation. The imulation model of fuzzy controller, which wa ued in thi imulation experiment, i hown in Fig. 5. Fig. 5 Simulation model of fuzzy controller The reultant value of fuzzy controller are TABE V PD (FUZZY) CONTROER PARAMETERS k e k de k du B. Cacade control The mot frequently ued control tructure in the controlled drive i the cacade control. In the cae of peed control of PMSM are uing two loop namely --current (eventually torque) loop --peed loop Fig. 6 Simulation model of PMSM cacade control Current controller The tuning method baed on the Modulu Optimum optimization criterion wa ued for current controller deign. According to thi criterion wa pecified PI controller in form TiPI + 1 RPI = k (0) PI Ti PI ISBN: ISSN: (Print); ISSN: (Online) with coefficient defined a TiPI k PI = ;TiPI = a / Ra;k = k TM / R (1) a kttm The coefficient of cacade control ubordinate PI current controller deigned by Modulu Optimum Method are TABE VI PI (MOM) CURRENT CONTROER PARAMETERS k PI 0.05 Ti PI 5 Speed controller I The tuning method baed on the Symmetric Optimum Criterion wa ued for firt verion of peed controller deign. According to the Symmetric Optimum Criterion wa pecified PID controller in form: TiPID RPID = kpid + + TdPID () with coefficient defined a ( 4TTM + ) kpid = ; Ti PID = ; 8cφTTM 8cφTTM (3) TdPID = cφttm The coefficient of cacade control mater PID angular velocity controller deigned by Symmetric Optimum Criterion are TABE VII PID (SOC) CURRENT CONTROER PARAMETERS k PID Ti PID Td PID Speed controller II The tuning method baed on the Modulu Optimum criterion wa ued for econd verion of peed controller deign. According to the Modulu Optimum criterion wa pecified PD controller in form: RPD = k PI ( 1+ TdPI) (4) with coefficient defined a 1 k PI = ;TdPI = T (5) TM cφ TTM The coefficient of cacade control mater PD angular velocity controller deigned by Modulu Optimum Method are TABE VIII PD (MOM) CURRENT CONTROER PARAMETERS k PD Td PD 4 IV. GRAPHICA USER INTERFACE FOR QUAITY ANAYSIS For operation rejuvenation by the evaluation of analyzed ytem quality control the graphical uer interface (GUI) wa created (Fig. 7). [11] Deigned WCECS 01

4 Proceeding of the World Congre on Engineering and Computer Science 01 Vol II WCECS 01, October 4-6, 01, San Francico, USA application utilize imulation and analyi of created imulation model to view variou qualitative indicator. It alo allow analyzing influence of elimination element double notch filter application on control proce quality increae. --Integral Square Error (ISE) --Integral Time Square Error (ITSE) --Integral Abolute Error (IAE) --Integral Time Abolute Error (ITAE) Fig. 7 GUI for PMSM Control Quality Analyi V. ANAYSIS RESUTS The plot of angular velocity of particular imulation experiment are diplayed extra for enabled (Fig. 8) and extra for diabled (Fig. 9) paraitic frequency filtration. Fig. 10 Simulation ubytem for integral criteria meaurement The reult of experiment, coniting of evaluating of different quality marker for different method of flexible mechatronic ytem control deign are hown in TABE IX TABE IX SIMUATION RESUTS Fig. 8 Angular velocity with filtration Reached reult were repreented in graphical form (Fig. 11, Fig. 1, Fig. 13 and Fig. 14) becaue of analye requirement. Graphical repreentation doe not contain abolute numerical expreion of reult, but becaue of comparability they were tranformed to percentage repreentation of pecific part relative to entirety. Fig. 9 Angular velocity without filtration The quality of control proce ha been evaluated baed on local criteria of quality --Settling Time --OverShoot --OverShoot Time a well a baed on integral criteria of quality for control error pace, acquired through the imulation ubytem [10] hown in Fig. 10. Fig. 11 Simulation reult Integral criteria of quality with filtration ISBN: ISSN: (Print); ISSN: (Online) WCECS 01

5 Proceeding of the World Congre on Engineering and Computer Science 01 Vol II WCECS 01, October 4-6, 01, San Francico, USA Fig. 1 Simulation reult Integral criteria of quality without filtration are of advantage in term of local criterion epecially by uing them without filtering of paraitic element, but according to quality integral criterion i their application markedly inept; --according to integral criteria, a an optimal method for control deign wear the cacade control with PI current controller and PID angular velocity controller, which i however at leat advantageou in the term of maximal overhooting value; --uage of advanced control method, repreented by fuzzy control in thi cae conidering dynamic and ytem tructure wear a diadvantageou; --after evaluation of combination of all indicator i poible to aert, that the one of optimal method of flexible mechatronic ytem control deign i poible to conider the claical deign method - method of invere dynamic and advanced method - cacade control contain combination of PI current controller and PD angular velocity controller. Thee two method how ign of robutne furthermore, in term of unacceptable frequencie elimination without uing of upplementary filter too. Fig. 13 Simulation reult ocal criteria of quality with filtration Fig. 14 Simulation reult ocal criteria of quality without filtration REFERENCES [1]. Balátě, Automatické řízení, BEN technická literatura, Praha, 003 [] D.A. Bradley, D. Dawon, N.C. Burd, A.. oader, Mechatronic, Chapman & Hall, ondon, ISBN [3] I. Švarc, R. Matoušek, M. Šeda and M. Vítečková, Automatické řízení, Akademické nakladateltví CERM,.r.o. Brno, 011 [4] M. Vítečková, A. Víteček, Modulu optimum for digital controller, Acta Montanitica Slovaca, 003, vol. 8, no. 4, pp [5] S. Vukoavic, M. Stojic, Suppreion of Torional Ocillation in a High-Performance Speed Servo Drive, IEEE Tran. on Indutrial Electronic, vol. 45, pp , an [6]. Vittek, P. Briš, P. Makyš, M. Štulrajter and V. Vavruš, Control of Flexible Drive with PMSM employing Forced Dynamic, 13th EPE-PEMC 008, pp IEEE [7]. ovankovič, M. Žalman, Mechatronické pohybové ytémy (), AT&P journal, 006, vol. XIII, no. 3, pp ISSN [8] G. Elli, Control ytem deign guide, San Diego: Elevier Academic Pre, pp. ISBN [9]. Kalou, C. Kratochvíl and P. Heriban, Dynamic of Rotary Electromechanical Drive, ÚT AVČR Centrum mechatroniky, Brno, 007. ISBN: X. [10] MathWork. (01, May 0). Simulink [Online]. Available: [11] MathWork. (01, May 0). Matlab GUI [Online]. Available: VI. CONCUSION The et of experiment, conit of imulation of flexible mechatronic ytem with control ytem deigned by different method, ha been performed. The quality of control proce wa evaluated baed on different marker. According to achieved reult i poible to tate, that: --for control deign neceity i poible to ue a ubtitution of infinitely rigid join intead of flexible join in the concurrency with utilization of filter for flexible ytem antireonant and reonant frequency; --claical principle of control deign (Nalin, MOM) ISBN: ISSN: (Print); ISSN: (Online) WCECS 01