Double Closed-Loop Controller Design of Brushless DC Torque Motor. Based on RBF Neural Network Denghua Li 1,a, Zhanxian Chen 1,b, Shuang Zhai 1,c

Transcription

1 Advanced aterials Research Online: ISSN: , Vols , pp doi:0.4028/ 202 Trans Tech Pblications, Switzerland Doble Closed-Loop Controller Design of Brshless DC Torqe otor Based on RB Neral Networ Dengha Li,a, Zhanxian Chen,b, Shang Zhai,c School of Atomation BISTU Beijing a ldh@bist.ed.cn, b jasoncchen66@sina.com, c sssb987003@63.com Keywords: Brshless DC torqe motor, RB neral networ, doble closed-loop controller Abstract. or the problem of that the traditional brshless DC torqe motor controller position servo system is difficlt to trac accrately the complex and varied location information, an improved doble closed-loop controller is designed in this paper. A self-adaptive PID algorithm based on RB neral networ is employed to design position loop controller and a feed-forward control algorithm is sed in the speed loop controller. The improved doble closed-loop controller validated the feasibility of the new method for the design of brshless DC torqe motor position servo system. Introdction Brshless DC torqe motor can overcome many defects of brsh DC motor, and it is a characteristic of large torqe coefficient, high overloading ability, good heat emission condition, high reliability, flexible control and so on[]. Nowadays, it has been widely sed in the servo-controller field. In order to improve the tracing accracy for the complex and varied location information, design a doble closed-loop controller of brshless DC torqe motor based on RB (Radial Basis nction) neral networ in this paper. The RB neral networ is a three-layer feed-forward neral networ, which inclde a single hidden layer. Acted as a local approximation networ, RB can simlate the local adjstment and the acceptance domain of mtal coverage of hman brain and has the ability to approach any nonlinear fnction with any accracy[2]. This controller has online identification characteristic which are based on dynamic RB neral networ. It can effectively overcome the poor adaptability of traditional PID controller when the system tracs continos position signal. In addition, a feed-forward controller was designed for the speed loop. The atlab simlation reslt shows that this control method can improve the dynamic performance of this system. The mathematical model of Brshless DC torqe motor Assming that three-phase stator of the motor are symmetrical completely, the angle difference between each phase is 20, the waveform of is sine wave, the three-phase resistor parameters are the same and the indctor parameters are also the same. Ignoring the eddy crrent loss, magnetic loss and alveolar effect of motor, the mathematical model of Brshless DC torqe motor can be simplified as follows: All rights reserved. No part of contents of this paper may be reprodced or transmitted in any form or by any means withot the written permission of Trans Tech Pblications, (ID: , Pennsylvania State University, University Par, USA-2/02/6,08:39:55)

2 352 rontiers of anfactring Science and easring Technology II ig. athematical model of brshless DC torqe motor Where, is three-phase inpt crrent of the motor, is the otpt torqe of the motor, R is the total circit resistance of armatre, L is the indctance of armatre, is the torqe coefficient, is the coefficient, J is the total inertia moment and b is the total viscos friction coefficient. According to ig., the transfer fnction of torqe motor can be written as: ( Js+ b) ( Js+ b)( R+ Ls) + () Since the vale of viscos friction coefficient, b is very small, it can be ignored. So the eqation () can be approximated as: aet Js/ JL 2 JR s + s+ JR, which is mechanical time constant of motor, and T L, which is electrical L R time constant of motor, the formla (2) can be written as: (2) Js TTLs Ts In this paper, the inertial trntable is chosen as the controlled object. As the load rotating inertia of the motor is generally large, then T >>T L, the formla (3) can be simplified as: (3) R( T s+ ) L (4) The whole transfer fnction model of control system is shown in igre 2: ig.2 Transfer fnction model of control system Where θ 0 is inpt position signal, θ p is otpt position signal, T is distrbance torqe.

3 Advanced aterials Research Vols Design of the doble closed-loop controller A The design of speed loop controller In order to ensre the anti-interference ability of speed loop, chosen the feed-forward controller as the predictive controller of speed loop. It can predict the next state by calclating the crrent state[3]. The bloc diagram of speed loop is shown as ig Speed controller - eedforward controller R( T s+ ) L T - Js * ig.3 The feed-forward speed loop controller Where ω is inpt position signal, ω * is otpt position signal. B The design of position loop controller As a position servo system, the rapid response performance and anti-interference ability is particlarly important. When a continos and npredictable interference, or step interference is imposed on the system, the control accracy will be redced. In order to ensre the accracy and reliability of position servo system, the self-adaptive PID controller based on RB neral networ is employed. The bloc diagram of position servo system is shown in ig.4. ig.4 The position loop controller with RB neral networ In ig.4, the increment PID algorithm is employed as neral networ controller, it is a discrete algorithm and its three inpts are: error x (5)

4 354 rontiers of anfactring Science and easring Technology II 2 x x 3 error T (6) error error T (7) The otpt of neral networ PID controller is: x + x + x (8) p i 2 d 3 Where, p, iand dare parameters of PID controller. In order to achieve the goal of ato-tning online PID controller,the neral networ identification is employed to adjst the three parameters of PID controller. The algorithm is as follows. The objective fnction of RB networ is: 2 error ( y ) 2 rot yot (9) 2 2 And the iterative algorithms of these parameters are: yot p ηerror x yot i ηerror x2 (0) () yot d ηerror x3 (2) The simlation reslts and analysis This doble-loop controller is sed in brshless DC torqe motor position servo system, the parameters of motor are chosen as follows: armatre resistance R0.07Ω, stator indctance of each phase L4.6mH, electrical time constant T L 0.002s, pea torqe T 0.3N m, and torqe coefficient 0.3 N m/a. According to the actal transfer fnction of position loop of brshless DC torqe motor, the actal reference model is:.. y 0 2y + 0 8r (3) rot ot in A platform has been bilt to test the performance of controller sing atlab/simlin software. In the test, the proportion coefficient of speed loop PID controller select as C eed-forward controller is designed as C ( s) 0.0s / s. The self-adaptive PID controller cq which is based on RB neral networ is programmed sing -files[4], and select the learning rate η0.5, inertial coefficient α Based on the model of motor, the initial parameters are designed as p 80, i 20, d 600.

5 Advanced aterials Research Vols Here mae two tests. The first test is that the position inpt signal is nit step signal, the system response of doble closed-loop controller is shown in ig.5. The second test is that the position inpt signal is sinsoidal signal with freqency of 00Hz and amplitde of, the otpt reslt of doble closed-loop controller identification is shown in ig step response response t/s ig.5 Step response of position controller sinsoidal response sinsoidal singal sinsoidal response t/s ig.6 Sinsoidal response of position controller rom the simlation reslts we now that, the step response crve has no overshoot, the response time is 0.004s, the steady-state error is 0.0%, and the sine wave response crve has no overshoot. Compared to the inpt signal, there is little phase difference whose vale is s, and the steady-state error is 0.%. After tests with several sinsoidal signal of different freqency, the bandwidth of the system is determined to be 80Hz. The dynamic control performances of self-adaptive doble closed-loop controller and traditional doble closed-loop controller are tested. The reslts are shown in ig.7 and Table. RB PID,PID sinsoidal singal RB PID PID t/s ig 7 Performance comparison of two types of doble closed-loop controllers

6 356 rontiers of anfactring Science and easring Technology II Controller Table Performance comparison of two controllers Setting time(s) Phase difference (s) Steady-state error (%) Self-adaptive controller Traditional controller rom ig.7 and Table we now that the performances of self-adaptive PID controller based on RB neral networ have been improved significantly compared with the conventional PID controller in the performances of the setting time, phase difference and steady-state error. Conclsion or the problem of that the traditional brshless DC torqe motor controller position servo system is difficlt to trac accrately the complex and varied location information, designed a new doble closed-loop controller in this paper. mploy a self-adaptive PID algorithm based on RB neral networ to design position loop controller and se a feed-forward control algorithm in the speed loop controller. Test the dynamic performances of self-adaptive doble closed-loop controller based on RB neral networ and traditional doble closed-loop controller. The test reslt shown that the performance of PID doble closed-loop controller can be optimized by RB neral networ, the self-adaptive doble closed-loop control system based on RB neral networ is better characteristic of steady and time-varying position tracing compare with the traditional PID control system. Acnowledgment The athors wold lie to than the financial spport by the nding Project for Academic Hman Development in Instittions of Higher Learning nder the Resorces Jrisdiction of Beijing nicipality (PHR , PHR200728) and the Project of Key Constrction Discipline. References [] Zhi Hang, Hong Go, Day Wang, Jinqan Y. The simlation of doble closed-loop brshless DC torqe motor controller. Beijing University of Aeronatics and Astronatics.Vol.37 (20),pp [2] Yanhe Gao. Optimization and application of RB neral networ based hybrid hierarchy genetic algorithm. Sichan University.(2004),pp7-4. [3] Shaoming Li, Wei Zhao. Simlation of PID controller based RB neral networ abot S-fnction. Jornal of anhi vocational college of metallrgy and technology. Vol.8 (2008), pp9-2. [4] Changliang Xia. Brshless DC motor control system. Beijing: Science Press. 2009, pp [5] Xiaoqing Zho. Design and implement of electric actator control system of high-speed nmanned aerial vehicle. Zhejiang University.Vol.8(200), pp-38.

7 rontiers of anfactring Science and easring Technology II / Doble Closed-Loop Controller Design of Brshless DC Torqe otor Based on RB Neral Networ /