Robust Gain–Scheduled PID Controller Design For Uncertain LPV Systems

Veselý, Vojtech; Ilka, Adrian

doi:10.1515/jee-2015-0003

Abstract

A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the approach of a parameter varying guaranteed cost is used which allowed to reach for different working points desired performance. Numerical examples show the benefit of the proposed method.

References

[1] HENCEY, B.—ALLEYNE, A.: Robust Gain-Scheduled Control, In American Control Conference (ACC), 2010, pp. 3075–3081.10.1109/ACC.2010.5530440
Search in Google Scholar
[2] GAO, J.—BUDMAN, H. M.: Design of Robust Gain-Scheduled PI Controllers for Nonlinear Processes, Journal of Process Control 15 No. 7 (2005), 807–817.10.1016/j.jprocont.2005.02.003
Search in Google Scholar
[3] BLANCHINI, F.: The Gain Scheduling and the Robust State Feedback Stabilization Problems, IEEE Transactions on Automatic Control 45 No. 11 (2000), 2061–2070.10.1109/9.887627
Search in Google Scholar
[4] STEWART, G. E.: A Pragmatic Approach to Robust Gain Scheduling, In 7th IFAC Symposium on Robust Control Design, vol. 7, Aalborg Congress & Culture Centre, Denmark, 2012, pp. 355–362.10.3182/20120620-3-DK-2025.00168
Search in Google Scholar
[5] De OLIVEIRA, V.—KARIMI, A.: Robust and Gain-Scheduled PID Controller Design for Condensing Boilers by Linear Programming, In Proceedings of IFAC Conference in Advances in PID Control, March 2012, pp. 335–340.10.3182/20120328-3-IT-3014.00057
Search in Google Scholar
[6] KÖROĞLU, H.: Robust Generalized Asymptotic Regulation via an LPV Controller without Parameter Derivative Dependence, In 49th IEEE Conference on Decision and Control (CDC), Dec 2010, pp. 4965–4971.10.1109/CDC.2010.5717033
Search in Google Scholar
[7] FORRAI, A.—KAMIYAMA, K.: Robust Gain-Scheduled Control for Vibration Suppression, Electrical Engineering 87 No. 3 (2005), 151–162.10.1007/s00202-004-0227-5
Search in Google Scholar
[8] WANG, F.—BALAKRISHNAN, V.: Improved Stability Analysis and Gain-Scheduled Controller Synthesis for Parameter-Dependent Systems, IEEE Transactions on Automatic Control 47 No. 5 (May 2002), 720–734.10.1109/TAC.2002.1000267
Search in Google Scholar
[9] MONTAGNER, V. F.—PERES, P. L. D.: State Feedback Gain Scheduling for Linear Systems with Time-Varying Parameters, In Proceedings of the 2004 American Control Conference, vol. 3, 2004, pp. 2004–2009.10.23919/ACC.2004.1383754
Search in Google Scholar
[10] APKARIAN, P.—GAHINET, P.—BECKER, G.: Self-Scheduled H_∞ Control of Linear Parameter-Varying Systems: A Design Example, Automatica 31 No. 9 (1995), 1251–1261.10.1016/0005-1098(95)00038-X
Search in Google Scholar
[11] ADEGAS, F. D.—STOUSTRUP, J.: Structured Control of Affine Linear Parameter Varying Systems, In American Control Conference (ACC), July 2011, pp. 739–744.10.1109/ACC.2011.5991517
Search in Google Scholar
[12] WEN-QIANG, L.—ZHI-QIANG, Z.: Robust Gain-Scheduling Controller to LPV System using Gap Metric, In International Conference on Information and Automation (ICIA), 2008, pp. 514–518.
Search in Google Scholar
[13] SPILLMAN, M. S.—BLUE, P. A.—LEE, L. H.—BANDA, S. S.: A Robust Gain-Scheduling Example User Linear Parameter-Varying Feedback, In Proceedings of the IFAC 13th Triennial World Congress, 1996, pp. 221–226.
Search in Google Scholar
[14] VESELÝ, V.—ROSINOVÁ, D.—ILKA, A.: Decetralized Gain-Scheduling Controller Design: Polytopic System Approach, In 13th IFAC Symposium on Large Scale Complex Systems (LSCS): Theory and Application, 2013, pp. 401–406.10.3182/20130708-3-CN-2036.00064
Search in Google Scholar
[15] VESELÝ, V.—ILKA, A.: Gain-Scheduled PID Controller Design, Journal of Process Control 23 No. 8 (Sep 2013), 1141–1148.10.1016/j.jprocont.2013.07.002
Search in Google Scholar
[16] LEE, S. M.—PARK, J. H.: Output Feedback Model Predictive Control for LPV Systems using Parameter-Dependent Lyapunov Function, Applied Mathematics and Computation 190 No. 1 (2007), 671–676.10.1016/j.amc.2007.01.061
Search in Google Scholar
[17] SATO, M.—PEAUCELLE, D.: Gain-Scheduled Output-Feedback Controllers using Inexact Scheduling Parameters for Continuous-Time LPV Systems, Automatica 49 No. 4 (Apr 2013), 1019–1025.10.1016/j.automatica.2013.01.034
Search in Google Scholar
[18] LEITH, D. J.—LEITHEAD, W. E.: Survey of Gain-Scheduling Analysis and Design, International Journal of Control 73 No. 11 (2000), 1001–1025.10.1080/002071700411304
Search in Google Scholar
[19] RUGH, W. J.—SHAMMA, J. S.: Survey Research on Gain Scheduling, Automatica 36 No. 10 (Oct 2000), 1401–1425.10.1016/S0005-1098(00)00058-3
Search in Google Scholar
[20] VESELÝ, V.—ROSINOVÁ, D.: Robust PID-PSD Controller Design: BMI Approach, Asian Journal of Control 15 No. 2 (2013), 469–478.10.1002/asjc.559
Search in Google Scholar
[21] KUNCEVITCH, V. M.—LYCHAK, M. M.: Controller Design using Lyapunov Function Approach, Nauka, Moskov, 1977. (Russian)
Search in Google Scholar
[22] GAHINET, P.—APKARIAN, P.—CHILALI, M.: Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty, IEEE Transactions on Automatic Control 41 No. 3 (Mar 1996), 436–442.10.1109/9.486646
Search in Google Scholar

Robust Gain–Scheduled PID Controller Design For Uncertain LPV Systems

Abstract

Paradigm

My account