0
Technical Brief

Guaranteed Performance State-Feedback Gain-Scheduling Control With Uncertain Scheduling Parameters

[+] Author and Article Information
Ali Khudhair Al-Jiboory

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: aljiboor@egr.msu.edu

Guoming G. Zhu

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: zhug@egr.msu.edu

Jongeun Choi

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: jchoi@egr.msu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 10, 2014; final manuscript received September 20, 2015; published online October 29, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 138(1), 014502 (Oct 29, 2015) (7 pages) Paper No: DS-14-1518; doi: 10.1115/1.4031727 History: Received December 10, 2014; Revised September 20, 2015

State-feedback gain-scheduling controller synthesis with guaranteed performance is considered in this brief. Practical assumption has been considered in the sense that scheduling parameters are assumed to be uncertain. The contribution of this paper is the characterization of the control synthesis that parameterized linear matrix inequalities (PLMIs) to synthesize robust gain-scheduling controllers. Additive uncertainty model has been used to model measurement noise of the scheduling parameters. The resulting controllers not only ensure robustness against scheduling parameters uncertainties but also guarantee closed-loop performance in terms of H2 and H performances as well. Numerical examples and simulations are presented to illustrate the effectiveness of the synthesized controller. Compared to other control design methods from literature, the synthesized controllers achieve less conservative results as measurement noise increases.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Daafouz, J. , Bernussou, J. , and Geromel, J. , 2008, “ On Inexact LPV Control Design of Continuous Time Polytopic Systems,” IEEE Trans. Autom. Control, 53(7), pp. 1674–1678. [CrossRef]
Sato, M. , 2010, “ Gain-Scheduled State-Feedback Controllers Using Inexactly Measured Scheduling Parameters: Stabilizing and H ∞ Control Problems,” SICE J. Control, Meas. Syst. Integr., 3(4), pp. 285–291. [CrossRef]
Wu, F. , Yang, X. H. , Packard, A. , and Becker, G. , 1996, “ Induced L 2-Norm Control for LPV Systems With Bounded Parameter Variation Rates,” Int. J. Robust Nonlinear Control, 6(9–10), pp. 983–998. [CrossRef]
Sato, M. , Ebihara, Y. , and Peaucelle, D. , 2010, “ Gain-Scheduled State-Feedback Controllers Using Inexactly Measured Scheduling Parameters: H 2 and H ∞ Problems,” American Control Conference, pp. 3094–3099.
Sato, M. , 2013, “ Robust Gain-Scheduled Flight Controller Using Inexact Scheduling Parameters,” American Control Conference (ACC), pp. 6829–6834.
Lacerda, M. J. , Tognetti, E. S. , Oliveira, R. C. , and Peres, P. L. , 2014, “ A New Approach to Handle Additive and Multiplicative Uncertainties in the Measurement for H ∞ LPV Filtering,” Int. J. Syst. Sci. (published online).
Agulhari, C. , Tognetti, E. , Oliveira, R. , and Peres, P. , 2013, “ H ∞ Dynamic Output Feedback for LPV Systems Subject to Inexactly Measured Scheduling Parameters,” Proceedings of American Control Conference, pp. 6060–6065.
Al-Jiboory, A. K. , and Zhu, G. G. , 2015, “ Robust Gain-Scheduling H 2 Control With Imperfectly Measured Scheduling Parameters,” (submitted).
Oliveira, R. C. L. F. , Bliman, P. , and Peres, P. L. D. , 2008, “ Robust LMIs With Parameters in Multi-Simplex: Existence of Solutions and Applications,” 47th IEEE Conference on CDC, pp. 2226–2231.
Oliveira, R. , and Peres, P. , 2007, “ Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations,” IEEE Trans. Autom. Control, 52(7), pp. 1334–1340. [CrossRef]
Oliveira, R. , de Oliveira, M. , and Peres, P. , 2011, “ Robust State Feedback LMI Methods for Continuous-Time Linear Systems: Discussions, Extensions and Numerical Comparisons,” IEEE International Symposium on CACSD, pp. 1038–1043.
Oliveira, R. C. L. F. , Bliman, P.-A. , and Peres, P. L. , 2009, “ Selective Gain-Scheduling for Continuous-Time Linear Systems With Parameters in Multi-Simplex,” European Control Conference.
Geromel, J. C. , and Colaneri, P. , 2006, “ Robust Stability of Time-Varying Polytopic Systems,” Syst. Control Lett., 55(1), pp. 81–85. [CrossRef]
de Souza, C. E. , and Trofino, A. , 2006, “ Gain-Scheduled H 2 Controller Synthesis for Linear Parameter Varying Systems Via Parameter-Dependent Lyapunov Functions,” Int. J. Robust Nonlinear Control, 16(5), pp. 243–257. [CrossRef]
Sato, M. , 2008, “ Design Method of Gain-Scheduled Controllers Not Depending on Derivatives of Parameters,” Int. J. Control, 81(6), pp. 1013–1025. [CrossRef]
Pipeleers, G. , Demeulenaere, B. , Swevers, J. , and Vandenberghe, L. , 2009, “ Extended LMI Characterizations for Stability and Performance of Linear Systems,” Syst. Control Lett., 58(7), pp. 510–518. [CrossRef]
Scherer, C. W. , 2006, “ LMI Relaxations in Robust Control,” Eur. J. Control, 12(1), pp. 3–29. [CrossRef]
Scherer, C. W. , and Hol, C. W. J. , 2006, “ Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs,” Math. Program., 107, pp. 189–211. [CrossRef]
Peaucelle, D. , and Sato, M. , 2009, “ LMI Tests for Positive Definite Polynomials: Slack Variable Approach,” IEEE Trans. Autom. Control, 54(4), pp. 886–891. [CrossRef]
Montagner, V. F. , Oliveira, R. C. , Peres, P. L. , and Bliman, P.-A. , 2009, “ Stability Analysis and Gain-Scheduled State Feedback Control for Continuous-Time Systems With Bounded Parameter Variations,” Int. J. Control, 82(6), pp. 1045–1059. [CrossRef]
Agulhari, C. M. , de Oliveira, R. C. L. F. , and Peres, P. L. D. , 2012, “ Robust LMI Parser: A Computational Package to Construct LMI Conditions for Uncertain Systems,” XIX Brazilian Conference on Automation (CBA 2012), pp. 2298–2305.
Löfberg, J. , 2004, “ YALMIP: A Toolbox for Modeling and Optimization in MATLAB,” CACSD Conference.
Sturm, J. , 1999, “ Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over Symmetric Cones,” Optim. Methods Software, 11(1), pp. 625–653. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Performance versus ϵ with ζ = 0.2

Grahic Jump Location
Fig. 2

Guaranteed performance

Grahic Jump Location
Fig. 3

Simulation: (a) measured and exact scheduling parameters and (b) disturbance attenuation responses associated with exact and noisy scheduling parameter

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In