A new practical method for closed-loop identification with PI control

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1 : 1 815(1) Control Theory & Applications Vol. 7 No. 9 Sep. 1 PI,, (, 5164) : PI,,.,, (SOPDT).,, PI ;,, : ; PI ; ; : TP73 : A A new practical method for closed-loop identification with PI control ZHU Xue-feng, XIAO Shu-jun, WANG Xiu (College of Automation Science and Technology, South China University of Technology, Guangzhou Guangdong 5164, China) Abstract: For a closed-loop system with a PI controller, we propose a method to identify the transfer function of the controlled object. From the under-damped-response of the closed-loop system, we approximate the closed-loop system by a second-order-plus-dead-time(sopdt) transfer function. The transfer function of the PI controller is then removed from the approximate closed-loop transfer function. From the remaining transfer function, the open-loop transfer function of the controlled object is determined through a coefficient-comparison process. Both the simulations and the control experiments on a pilot-equipment show advantages of the proposed method, such as the high identification-accuracy, the low computational complexity and the easy online implementation, thus demonstrating its application potential. Key words: closed-loop identification; proportional-integral control; second-order-plus-dead-time; coefficientcomparison 1 (Introduction),..,, [1].,., R. Manat P.J. Fleming [], (FOPDT) FOPDT. [3,4] R. Manat P.J. Fleming PI PID (SOPDT). Wonhui Cho [5] PI, FOPDT. [6] N (Laguerre) [7,8],,., : 1,. 1 [ 4, 9],. (Identification principle) : Tp s + ζ p T p s + 1. (1) : , : 9 1. : 8 (8B134).

2 9 : PI 141 PI G c (s) = K c(t i s + 1), () T i s M(s) = G p(s)g c (s) 1 + G p (s)g c (s). (3) PI, 1. K cl e d cls M(s) = Tcl s + ζ cl T cl s + 1. (4) Fig. 1 1 PI Typical closed-loop step response under PI control [1],. [1,4,7] : K cl = 1, ζ cl = ρ/(1 + ρ), T cl = t p1 1 ζ cl, π S c d cl = ζ cl T cl. C ss C ρ = ( 1 π ln C p1 C ss ), C ss C S c = (C ss C(t))dt. (5) (6) [9] PI (4) [6], M(s) C(s) = (1 M(s))G c (s). (7) (3) (7) C(s) = G p (s). (8) Fig. Equivalent block diagram of the process Pade [1] : e θs = 1 θs/ 1 + θs/, ()(4)(8) (7), : s(s /d cl ) E s 4 + Ds 3 + Cs + Bs + A, (9) : A = (1 K cl) T i Tcl d =, cl B = 1 ( + 4ζ cl ), T i Tcl T cl d cl C = + 4ζ cl + ( ζ cl + 1 ), Tcl T cl d cl T i T cl d cl D = 1 + ζ cl +, T i T cl d cl E = 1. K c Tcl (1) (1) (9), (1) : (Tp s + ζ p T p s + 1) (T p s + ζ p T p s + 1) s (s + ξ). (11) (11) ξ, [13] (11), ξ,. Pade (11) (9), K p, T p, ζ p, d p : d p = d cl, T p = d p B, K p = T p E, ζ p = 1 T p(d ). d p (1), (1) ζ p, λ(λ ), λ = : ζ p = 1 T p(d d p )λ.

3 (Simulation experiments),, PI PI, Table 1 1 Simulation examples and the results of identification G p(s) PI K c T i K p T p ζ p d p IAE Rel IAE [3] e 1s 5s [3] [3] [3] [3] e.5s (s + 1)(3s + 1) [3] [3] [3] Fig. 3 Unit step response of FOPDT process and the result of Fig. 4 Unit step response of SOPDT process and the result of the identification the identification : 1), PI,,. ) : d cl,, d cl (1)(13) K p, T p, ζ p, d p d p (

4 9 : PI PI, d cl ). 3) 1 IAE : IAE = ŷ(t) y(t) dt, (13) ŷ, y. IAE, IAE, IAE,,, IAE ;,,, IAE. IAE. IAE(Relative IAE, Rel IAE), IAE Rel IAE = y ss y(t) dt, (14) y ss Rel IAE,. Rel IAE IAE, 4) 1, 4 PI, [3],, 5) [3],,. [3] ), 4 PI. 6), PI, 5%,,3, ). 4 (Identification of the experimental hyperthermia instrument),, 5,., T 3,, T 3. SSR, T 3. Fig. 5 5 Schematic diagram of the experimental hyperthermia instrument,, T 3 PI : K p =, T i = 3, PI 6. Fig. 6 6 Closed-loop response of heat treatment instrument : K p =.199, T p = 87.5, ζ p = 1.875, d p = 1.6,

5 144 7,.199e 1.6s s s Fig. 7 Comparison of open-loop step response of the heat treatment instrument and the identification 7,,. 5 (Conclusion), PI,,.,,. PI.,, [9],,, 3,. (References): [1] LANDAU I D. Identification in closed loop: a powerful design tool(better design models, simpler controllers)[j]. Control Engineering Practice, 1, 9(1): [] MANAT R, FLEMING P J. Method for on-line identification of a first order plus dead-time process model[j]. Electronics Letters, 1995, 31(15): [3],,. PI [J].,, 9(6): 8 83, 96. (CHEN Yongyun, LIU Ailun, CHEN Chengliang. A new closed-loop identification metheod of PI[J]. Control Engineering of China,, 9(6): 8 83, 96.) [4],. PID [J]., 4, (3): 31 3, 48. (CHEN Yongyun, LIU Ailun. A closed-loop identification method under PID control[j], Automation in Perto-Chemical Industry, 4, (3): 1 3, 48.) [5] WONHUI CHO, THOMAS F EDGAR, JIETAE LEE. Closed-loop identification of wafer temperature dynamics in a rapid thermal process[j]. Korean Journal of Chemical Engineering, 6, 3(): [6],,. [J]., 3, 3(6): (LI Chao, HUANG Dexian, JIN Yihui. Robust closed-loop identification of continuous system with dead-time from step response[j]. Control and Instruments in Chemical Industry, 3, 3(6): ) [7],,. Laguerre [J]., 8, 18(6): (CHEN Xiaolong, CHEN Zhengshi, LIU Mei. HSIC based on the Laguerre function prediction control model[j]. Journal of Maoming University, 8, 18(6): ) [8],. Laguerre [J].,, 6(6): (XIA Bokai, YUAN Pu. Predicitve control for large dead-time plants based on Laguerre function model[j]. Journal of the University of Petroleum,, 6(6): 1 11.) [9] SUGANDA P, KRISHNASWAMY P R, RANGAIAH G P. On-line process identification from closed-loop tests under PI control[j]. Transactions of the Institution of Chemical Engineers, 1998, 76(5): [1] LEE J, CHO W, EDGAR T F. An improved technique for PID controller tuning from closed loop tests[j]. AIChE Journal, 199, 36(1): [11],. [M]. :, 3: (GAO Guoshen, YU Wenxiao. Principle of Automatic Control[M]. Guangzhou: South China University of Technology Press, 3: ) [1],. Pade [J]. ( ), 1, 4(1): (Lü Zhimin, ZHOU Maolin. Manipulation of the pure timedelay in digital control system applying Pada approximation[j]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 1, 4(1): ) [13] TSAIA M C, GEDDESB E J M, POSTLETHWAITE I. Pole-zero cancellations and closed-loop properties of an H mixed sensitivity design problem[j]. Automatica, 199, 8(3): : (194 ),,,,, xfzhu@scut.edu.cn; (1985 ),,,, xiaoshujun111@163.com; (1985 ),,,, myxiaoxiuzi@163.com.

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