1、26 5 湖 南 大 学 学 报 (自然科学版) Vo1. 26, No. 51 9 9 9 M10Journal of Hunan University(Natural Sciences Edition) Oct. 1 9 9 9cI|: 1000-2472(1999) 05-0056-061 ZPIDe null彭楚武1, 钟庆昌2, 贾 青2, 谢剑英2(1. 2v , 2 410082; 2. ZYv1“, Z200030)K1:深入分析了基于极点配置理论和鲁棒控制基本原理而提出的鲁棒PID控制器,导出了该控制器极点配置的约束条件,提出了一种基于对象开环阶跃响应辨识对象参数的控制参数自
2、动整定方法. 就不同的对象(包括null/T= 20的对象)进行的仿真结果表明,该方法是相当有效的,具有广阔的应用前景.1oM:PID控制;自整定;鲁棒控制;极点配置ms |: TP13 DS M : AAutomatic Tuning of Robust PID ControllerPENG Chu-wu1, ZHONG Qing-chang2, JIA Qing2, XIE Jian-ying2( 1.College of Electrical2.Dept of Automation,Shanghai Jiaotong Univ,Shanghai200030,China; )Abstrac
3、t: The robust PID controller, which is presented based on the poleassignment theory and the basic pronciple of robust control,is analyzed in detail. Theconstraints of the desired closed-loop poles and the automatic tuning method, accordingto the parameter identification based on the open-loop step r
4、esponse, are presented.Several plants,including a null/T = 20s one,are simulated to prove the effectiveness andthe bright future of the medthod.Key words:PID control;auto-tuning;robust control;pole assignmentPID e ?s1, 2= - nulljnull, ZPID e Tf= ( 2null+ ( null2+ null2)null/2) - 1, Ti= T+ null/2- Tf
5、,Kp= T iT f(null2+ null2)/K , T d= Tnull/ (2T i)- T f. (4)N H,Q “d( ).f Gc(s)= 1+ nulls/ 2null2s2+ 2nullnulls+ 1e- nulls, (5)Tnull= 1/ null2+ null2,null= null/ null2+ null2. (6) T(5), V“dYy(t) = y0(t- null), y0( t)= 1(t) + e- nullt null/ 2- nullnullnull 1- null2sin( nullt)- cos(nullt). (7)y(t) p,i 7
6、ynull(t)= 0, V p“d rKvym HWtm./ Ttan(nulltm- nullnull)= nullnullnullnull- 2, (8),tm= (km+ 1)null, (9)575 #:1 ZPID e km=1nullnull(null- arctan- 1 nullnull2- nullnull)(0 0). ( 11)V1,V2 null= 0.707null= 0. 5 f /nullnull |Y nullr HWtmY.V1nullnull“d ?Y(null= 0. 707)nullnull km null/%0. 5 5. 640 4. 70. 75
7、 3. 468 5. 41. 0 2. 356 6. 71. 25 1. 689 8. 81. 5 1. 262 11. 91. 75 0. 979 15. 92 0. 785 20. 82. 5 0. 549 32. 33 0. 416 45. 33. 5 0. 333 59. 34 0. 277 73. 95 0. 206 104V2nullnull“d ?Y( null= 0. 5)nullnull km null/%0. 5 3. 023 19. 10. 75 1. 799 23. 41. 0 1. 209 50. 01. 25 0. 880 38. 21. 5 0. 678 47.
8、91. 75 0. 545 58. 62 0. 453 69. 92. 5 0. 336 94. 03 0. 266 1193. 5 0. 219 1454 0. 186 1715 0. 143 224VV V A,9 ,“Hq/,null= 0.7071null= 0. 5 z ?,nullnull V4S v.null= 0.707 H,nullnull1j2W V z ?.nullnull 3H ahl1 “ ( 40 %j80 %) V, “d ?4 .2 s1,2= - nulljnull4 T i 0, T d 0,1 pT+ null/2 T f, Tnull 2TiT f= 2
9、T f(T+ null/2- T f), ( 12) m= 1- null2/null, ( 13)* ,null= mnull.BHqNnullnull2m2+ 1( 1+ (m2+ 1)2T/null+ 1- 1). ( 14)=Hqs f 1) null2T H,1 pnullnull2m2+ 1( 1+ null(m2+ 1)2T - 1) , (15 a)58 2v(1 S)1999 M0 4. 5null) ,yN T(15a)Tnull2T Hnullnull4Hq.2) null2T H,1 p2m2+ 1( m2+ 2- 1), (16 a)0 4.5null),yN T(1
10、6b)Tnull2T Hnullnull4Hq.8 ,V1,1 4/ ( null= 0.707):1) null3T H, ?S1 pV1 |nullnull= 1j2;2) 3Tnull8T H, |1+ null/T - 1nullnull2;3) null8T H, |nullnull v1+ null/T- 1.9 , T(3) e,1vB | s1, 2= - nulljnull,v T(4)9 PID e L e, ( V1 i ?.3 ZPID e 13. 1 O M LCPID e 1, ?1 ?O M K , T, null.D34? kE, V “9mKc “ qnull
11、c, N VvZ-NE2PID . 7,ZE k H,i1K,Bt ;7 O,Z-NEPID ,E D 4D,“d v,null/T= 0. 15j0.6 H ? z,null/T 1 H“d 4.7 7Y k图1 典型工业对象的阶跃响应O M,9 e,9E 1C.s1, 2= - nulljnull,v T(4)9 ZPID e K p, Ti, Td, Tf,V7 LCPID 1. 8, 71SWVT MC,“d1V T M e C L e. ,y L e,1v HW V; e “ q5 V O M .ZE k ,“d/ Y, kV B 7 eV.“dBQYV k, z8C o 7 kae
12、p X. |r(t) | H, V| |T k |u0(t)= r(t),“,“dV T M e C H,Cv , 9m1 H,+ V LC M,Wn4_T.4_T4. 1null/T/ B10 s ,_T m3 U.a:e- 10s/( 6s+ 1) ;b:e- 10s/(2s+ 1);c:e- 10s/( 0.5s+ 1). null/TsY :1.67,5,20, % Y 1y Bnull._Vs4 :1(0j30 s); ( t= 70 slF0. 260 2v(1 S)1999 M图 3鲁棒自整定PID控制器用于不同null/ T 的对象);hl0. 6( t= 150 s) .V
13、A, 9m1,8 M e H,+ ; a,b8 HW , ,= ( |nullnull= 2,Y ?Mv;cnull/T= 20, T( 16a)1 pnullnull 3.58, |nullnull=3. 75 O|1 9mhl40 %,“d ?9z.4. 2 9m f K e- s/ (5s+ 1) , 9mK | H,“d1 MYVAm4. 7Y30 s,_ Ht= 30 s M e . 41T,t= 49 s H,“d1. 0M0. 4.图4对象静态增益不同的自动整定与闭环响应Vm V A, 9m1,V M e H,iBV, Q e1 p. A,BVy 7YV, Ov, y ZPID
14、eXg e,vv “d ?.7 Ot= 49 s“d1.0M0. 4 H,9mVC + B“ Y(nullnull= 2). ID: 1Aoyama T,Omatu S.Design of a self-tuning PID control system by neural networksJ .Trans ofthe Institute of Electrical Engineers of Japan,1996, 116-C( 11):1197.2Ziegler J G,Nichols N B. Process lags in automatic control circuitsJ .Tra
15、ns ASME,1943(65) :433. 3Astrom K J, Hagglund T. Automatic tuning of simple regulators with specifications on phase andamplitude marginsJ .Automatica,1984, 20(5) :645j651. 4 i,t, #. ZPID e !9 J. W, 1998,39( 10): 207j209. 5Vandoren V J.How software tools simplify loop tuningJ .Control Engineering,1997, 44(11): 89.615 #:1 ZPID e
