Abstract
This paper addresses the composite nonlinear feedback (CNF) control for a class of singleinput single-output nonlinear systems with input saturation to track a time varying reference target with good transient performance. The CNF control law consists of a tracking control law and a performance compensator. The tracking control law is designed to drive the output of the system to track the time varying reference target rapidly, while the performance compensator is used to reduce the overshoot caused by the tracking control law. The stability of the closed-loop system is established. The design procedure and the improvement of transient performance of the closed-loop system are illustrated with a numerical example and the controlled Van del Pol oscillator.
Similar content being viewed by others
References
Bakkeheim J and Johansen T A, Transient performance, estimator resetting and filtering in nonlinear multiple model adaptive backstepping control, IEE Proceedings — Control Theory and Applications, 2006, 153(5): 536–545.
Kalkkuhl J, Johansen T A, and Ludemann J, Improved transient performance of nonlinear adaptive backstepping using estimator resetting based on multiple models, IEEE Transactions on Automatic Control, 2002, 47(1): 136–140.
Bakkeheim J, Smogeli O N, Johansen T A, et al., Improved transient performance by Lyapunovbased integrator reset of PI thruster control in extreme seas, IEEE Conference on Decision and Control, San Diego, CA, 2006.
Chen M, Wu Q, Jiang C, et al., Guaranteed transient performance based control with input saturation for near space vehicles, Science China Information Sciences, 2014, 57(5): 1–12.
Wang W and Wen C, Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance, Automatica, 2010, 46(12): 2082–2091.
Hu T, Zhu J, and Sun Z, Adaptive neural control for a class of MIMO nonlinear systems with guaranteed transient performance, Advances in Neural Networks — ISNN 2006, Third International Symposium on Neural Networks, Chengdu, 2006.
Yao B and Tomizuka M, Adaptive robust control of MIMO nonlinear systems with guaranteed transient performance, IEEE Conference on Decision and Control, New Orleans, LA, 1995.
Xue W and Huang Y, Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems, ISA Transactions, 2015, 58: 133–154.
Xue W and Huang Y, Performance analysis of 2-DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances, International Journal of Robust and Nonlinear Control, 2017: 1–18.
Chen Z, Cong B L, and Liu X D, A robust attitude control strategy with guaranteed transient performance via modified Lyapunov-based control and integral sliding mode control, Nonlinear Dynamics, 2014, 78(3): 2205–2218.
Kosmatopoulos E B and Piovesan J L, CLF-based control design for unknown multiinput nonlinear systems with good transient performance, IEEE Transactions on Automatic Control, 2010, 55(11): 2635–2640.
Seshagiri S and Khalil H K, Robust output regulation of minimum phase nonlinear systems using conditional servocompensators, International Journal of Robust and Nonlinear Control, 2005, 15(2): 83–102.
Lin Z, Pachter M, and Banda S, Toward improvement of tracking performance nonlinear feedback for linear systems, International Journal of Control, 1998, 70(1): 1–11.
Chen B M, Lee T H, Peng K, et al., Composite nonlinear feedback control for linear systems with input saturation: Theory and an application, IEEE Transactions on Automatic Control, 2003, 48(3): 427–439.
Lan W, Thum C K, and Chen B M, A hard-disk-drive servo system design using composite nonlinear feedback control with optimal nonlinear gain tuning methods, IEEE Transactions on Industrial Electronics, 2010, 57(5): 1735–1745.
Cheng G and Peng K, Robust composite nonlinear feedback control with application to a servo positioning system, IEEE Transactions on Industrial Electronics, 2007, 54(2): 1132–1140.
Cheng G, Peng K, Chen B M, et al., Improving transient performance in tracking general references using composite nonlinear feedback control and its application to high-speed XY-table positioning mechanism, IEEE Transactions on Industrial Electronics, 2007, 54(2): 1039–1051.
Lan W, Chen B M, and He Y, On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation, Systems and Control Letters, 2006, 55(2): 132–138.
Wang J and Zhao J, On improving transient performance in tracking control for switched systems with input saturation via composite nonlinear feedback, International Journal of Robust and Nonlinear Control, 2015, 26(3): 509–518.
Mobayen S, An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique, Nonlinear Dynamics, 2015, 80(1–2): 917–927.
Mobayen S and Tchier F, Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems, Nonlinear Dynamics, 2017, 80(3): 1731–1747.
Khalil H K, Nonlinear Systems, Prentice Hall, 2002.
Sussmann H J and Kokotovic P V, The peaking phenomenon and the global stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 1991, 36(4): 424–440.
Lin Z, Low Gain Feedback, Springer, London, 1999.
Pappas G J, Lygeros J, and Godbole D N, Stabilization and tracking of feedback linearizable systems under input constraints, Proceedings of the IEEE Conference on Decision and Control, New Orleans, LA, 1995.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Nature Science Foundation of China under Grant Nos. 61374035 and 61733017.
This paper was recommended for publication by Guest Editor XIN Bin.
Rights and permissions
About this article
Cite this article
Lu, T., Lan, W. & Li, Z. Transient Performance Improvement in Tracking Control for a Class of Nonlinear Systems with Input Saturation. J Syst Sci Complex 31, 200–214 (2018). https://doi.org/10.1007/s11424-018-7362-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-018-7362-y