Design of PID Controller for Nonlinear System with Dead-zone and Saturation

doi:10.3969/j.issn.1000-1093.2013.10.016

Abstract

Abstract: Based on the describing function model of dead-zone and saturation and the method of determining the stabilizing region of PID controller for linear system, an approach is presented for the design of PID controller for a given nonlinear system with dead-zone and saturation. The new equivalent inverse Nyquist plots are given for the different sinusoidal input amplitudes of nonlinear component, and the parameters of PID controller are selected from the intersection sets of stabilizing controller parameter region for different sinusoidal input amplitudes. The controller can effectively mitigate the nonlinear effect. For unstable open-loop system, a prefilter is added on the reference input. The proposed approach can be used to stabilize the closed-loop system with nonlinearity. The simulation examples demonstrate the validity of the proposed approach.

Key words: automatic control technology, dead-zone and saturation, inverse Nyquist, PID controller, parameter stable regions, intersection

CLC Number:

TP273

PENG Fu-ming, FANG Bin. Design of PID Controller for Nonlinear System with Dead-zone and Saturation[J]. Acta Armamentarii, 2013, 34(10): 1298-1303.

References

[1] Keel L H, Bhattacharyya S P. Controller synthesis free of analytical models: three term controllers[J]. IEEE Transactions on Automatic Control, 2008,53(6):1353 - 1369. [2] Bajcinca N. Design of robust PID controllers using decoupling at singular frequencies [ J]. Automatica, 2006,42 (11):1943 -1949. [3] Ho M T, Datta A, Bhattacharyya S P. Generalizations of the Hermite-Biehler theorem: the complex case[J]. Linear Algebra and Its Applications, 2000,320(1 -3):23 -26. [4] Ackermann J, Kaesbauer D. Stable polyhedra in parameter space [J]. Automatica, 2003,39(5):937 -943. [5] 方斌. 时滞系统PID 控制器参数稳定域的实现[J]. 电子科技大学学报, 2011,40(3):411 -417. FANG Bin. Realization of PID controller parameter stable regions for time delay systems[J]. Journal of University of Electronic Science and Technology of China, 2011,40 (3): 411 - 417. (in Chinese) [6] 方斌. 时滞系统PID 控制器增℃的稳定范围研究[J]. 信息与控制,2009,38(5):546 -551. FANG Bin. On gain stabilizing regions of PID controller for time delay systems[J]. Information and Control,2009, 38(5):546 -551. (in Chinese) [7] Grimm G, Hatfield J, Postlethwaite I, et al. Antiwindup for stable linear systems with input saturation: an LMI-based synthesis[J].IEEE Transactions on Automatic Control, 2004,48(9):1509 - 1525. [8] Hu T, Teel A R, Zaccarian L. Anti-windup synthesis for linear control systems with input saturation: achieving regional, nonlinear performance[J]. Automatica, 2008,44(2):512 -519. [9] Sajjadi-Kia S, Jabbari F. Scheduled static anti-windup augmentation synthesis for open-loop stable plants[C]//American Control Conference ( ACC), 2010. Baltimore: IEEE, 2010: 6751 -6756. [10] Isayed B M,Hawwa M A. A nonlinear PID control scheme for hard disk drive servo systems [ C] //MED蒺07. Mediterranean Conference on Control & Automation. Athens: IEEE, 2007:1 -6. [11] Huang Y, Yasunobu S. A general practical design method for fuzzy PID control from conventional PID control[C] //The 9th IEEE International Conference on Fuzzy Systems. Texas: IEEE, 2000:969 -972. [12] Mhaskar P, El-Farra N H, Christodes P D. A method for PID controller tuning using nonlinear control techniques [C] //Proceeding of the 2004 American Control Conference. Massachusetts: IEEE, 2004:2925 -2930. [13] Santibanez V, Kelly R, Zavala-Rio A, et al. A new saturated nonlinear PID global regulator for robot manipulators[C]//Proceeding of the 17th IFAC Word Congress. Korea: IFAC, 2008:11690 -11695. [14] Zavala-Rio A,Santibanez V. Simple extensions of the PD-with-gravity-compensation control law for robot manipulators with bounded inputs[J]. IEEE Transactions on Control Systems Technology, 2006,14(5):958 -965. [15] Zavala-Rio A, Santibanez V. A natural saturating extension of the PD with desired gravity compensation control law for robot manipulators with bounded inputs[J]. IEEE Transactions on Robotics, 2007,23(2):386 -391. [16] Alvarez-Ramirez J, Santibanez V, Campa R. Stability of robot manipulators under saturated PID compensation[J]. IEEE Transactions on Control Systems Technology, 2008,16(6):1333 -1341. [17] Fang B. New approach to the realization of PID controller parameter stable regions[C]//IEEE International Conference on Computer Science and Automation Engineering. Shanghai: IEEE,2011:627 -631.