Robust Gain–Scheduled PID Controller Design For Uncertain LPV Systems

Open access


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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] HENCEY B.—ALLEYNE A.: Robust Gain-Scheduled Control In American Control Conference (ACC) 2010 pp. 3075–3081.

  • [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.

  • [3] BLANCHINI F.: The Gain Scheduling and the Robust State Feedback Stabilization Problems IEEE Transactions on Automatic Control 45 No. 11 (2000) 2061–2070.

  • [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.

  • [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.

  • [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.

  • [7] FORRAI A.—KAMIYAMA K.: Robust Gain-Scheduled Control for Vibration Suppression Electrical Engineering 87 No. 3 (2005) 151–162.

  • [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.

  • [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] 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.

  • [11] ADEGAS F. D.—STOUSTRUP J.: Structured Control of Affine Linear Parameter Varying Systems In American Control Conference (ACC) July 2011 pp. 739–744.

  • [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.

  • [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.

  • [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.

  • [15] VESELÝ V.—ILKA A.: Gain-Scheduled PID Controller Design Journal of Process Control 23 No. 8 (Sep 2013) 1141–1148.

  • [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.

  • [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.

  • [18] LEITH D. J.—LEITHEAD W. E.: Survey of Gain-Scheduling Analysis and Design International Journal of Control 73 No. 11 (2000) 1001–1025.

  • [19] RUGH W. J.—SHAMMA J. S.: Survey Research on Gain Scheduling Automatica 36 No. 10 (Oct 2000) 1401–1425.

  • [20] VESELÝ V.—ROSINOVÁ D.: Robust PID-PSD Controller Design: BMI Approach Asian Journal of Control 15 No. 2 (2013) 469–478.

  • [21] KUNCEVITCH V. M.—LYCHAK M. M.: Controller Design using Lyapunov Function Approach Nauka Moskov 1977. (Russian)

  • [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.

Journal information
Impact Factor

IMPACT FACTOR 2018: 0.636
5-year IMPACT FACTOR: 0.663

CiteScore 2018: 0.88

SCImago Journal Rank (SJR) 2018: 0.200
Source Normalized Impact per Paper (SNIP) 2018: 0.771

Cited By
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 283 138 2
PDF Downloads 112 58 3