9Điều khiển trượt thích nghi phân ly

JOURNAL OF S( IFNCE & TEC HNOUOCJY * No 79B - 2010 DECOUPLED ADAPIIVE SLIDINCJ MODE CONTROL DIED KHIl'.N IRlK.yi' fllicil NGHI PHAN LY i\giiyen Due Minh, Nguyen Due Thanh, Duonfj Hoai llo ('hi Minh University ofTcclinology Nghia ABSTRAC T This paper proposes a controller for a class of nonlinear unknown dynamic systems First, based on the Sliding l\/lode Control (SMC) theory and neural network technique we introduce a new Adaptive Sliding Mode Control (ASMC) for SI SO systems The purpose is to find the optimal control rule, which can overcome the chattering phenomenon and help the system to resist the disturbance without knowing its parameters Second, we present a Decoupled Adaptive Sliding Mode Control (DASMC) to develop the ASMC technique for the 4"' order multivariable system Finally, we apply the above-mentioned theory to handle the two dimensional inverted pendulum, keeping it balanced in upright position and moving along reference trajectories on the horizontal plan The simulation results confirm the effectiveness of the proposed controller TOM TAT Bdi bdo ndy gidi thieu mpt phwgng phdp diiu khiin cho Idp cdc he thdng phi tuyin khdng ro md hinh ddng hoc Diu tien, diiu khiin ASMC dwgc gidi thieu di/a trdn ly thuyit diiu khiin trwgt va ky thudt mang no- rdn dp dung de diiu khiin cdc hd thing SISO Bd diiu khiin ASMC khdng nhirng khic phuc dwgc hien twgng chattering md cdn cd kha ndng khdng nhieu Sau dd bdi bdo gidi thieu diiu khiin phdn ly biin sd di cd thi phat triin ky thudt diiu khiin ASMC cho cdc he thing da biin bac bdn Cudi cimg, ly thuyit diiu khiin trwgt thich nghi ndi tren dwgc dp dung di diiu khiin he thing xe lie ngwgc hai chiiu, giw dwgc thang bdng ngwgc, bdm theo mdt quy dao mong mudn cho trwdc tren mat phing ngang Mdt sd kit qud md phdng da cho thiy tiim ndng ciia bd diiu khiin dwgc di nghi controller, is developed to compute the corrective and equivalent controls, without the !"'.:!1 a\aikibilit> VM " the model parameters Furthermore, adaptive neural sliding mode control is a continuous control, so there is no more chattering phenomenon on the input control I INTRODUCTION Variable Structure Control (VSC) with sliding mode, or SMC is a nonlinear control strategy that is well known for its robust characteristic However, conventional sliding mode control has two disadvantages, which arc 1) the chattering (phenomenon), and 2) the obligation to delimit in advance the model parameters To solve this problem, in recent years, the neural or fu//y-neural network has been proposed to estimate the unknown motlel functions [1] -[3], or to compensate the uncertain components of the plant 14]-[5] However, these training algorithms for neural network are complicated and although the chattering phenomenon has been reduced, this phenomenon still exists on the control signal B> combining the decoupled control theorv and the ASMC technique, this paper also presents a decoupled ASMC to develop the ASMC for a class of " order multivariable sv stems, which is quite usual in practice, like the cart inverted pendulum Ihe rest of this paper is organized as follows Section presents the traditional sliding mode control Section introduces the structure and update rule for the DASMC Section provides simulation results Finally, the conclusion is given in Section In this paper, a neural network based Adaptive Sliding Mode Controller (ASMC) is proposed Based on the sliding mode control theory, a simple updated rule for multilayer neural network, which is used as a direct II SILIDING MODE CONTROL 2.1 Control problem 70 JOURNAL OF SCIENCE & TECHNOLOGY * No 79B - 2010 Consider a nonlinear system 5{x) = y'"'=f{x) + g{x).u + d (c„.„e"'-"+ +c,e g(x) + cf'+ f{x)-r + d)\ (2.1) u is the control input; Let X = {y\ v>'f""'^ ]' is the state vector; with p =rf(,v)+ /?jj, /3,>0 y is the output; /(^)' functions ; ^(^) unknown III ADAPTIVE CONTROL It follows that u^ =f„ =N{e,w) (2.2) = e'"-" +c,„_,)e"'"'' + + c.e + c,e (3.1) where e is the input vector, w is the weight vector of the network Based on the sliding mode control theory, the weights should be updated online so that 5- > as / - > 00 (2.3) The coefficients, c, C(„_,p are chosen the polynomial C-,/^-l-C] is Hurwitz This From (2.3) it can be seen that s->Q as /->oo if condition ensures that if = then e - > as r->oo (3.2) V = s.s ' j • From (3.3), (3.4), (3.5) and (3.6) we have 73 lOl KNAI 4.3 Simiiialioii I I I N I U I h , i i k e' Ii,i\e |u-i ll ll i i u d miller ,ii i i p l il i i i h " , i(N) |H-,ik l o |K-,ik ,il I h e I iMiliul i i i | i i i | ' , oulpillx V ,, ,lie (r e o s ( D.I / ) /)' , \ _, llld -^ J-^ I s" l> W)" I'iyf> (I \ Iriijit />fi nIII rr\/iri liisl li.iiiiiii!' p e i i i u l hi.'eii JiiiiMij 'Jiuw loi iiieil IIK' lliiid /'ITKHI ileMied Mll( I / ) ;(()) I h e K-Mihx ll I'll! Ill' Ii,i\ e troinin',' \ pi,in I lie i n i l i i l •.l.iles ,ire 1(0) Mie 2010 Si I- i h e ( l e i i e d l i ; i | e ^ h H v i il i h e e,ii IN llie e n e l e Ii , K k m i x \(ll) * N o 7'>|{ /••/;,.' 1" Third usiills I h e Miiiiil.ilH 111 I i M i l l ' e\li.Mii.il O l S< II N ( i:>Si r i : ( I N K ) ! , ( ) ( , \ l