0
Research Papers

A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

[+] Author and Article Information
Fen Wu

Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: fwu@eos.ncsu.edu

Xun Song

Science and Technology on Aircraft
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: songxun@asee.buaa.edu.cn

Zhang Ren

Science and Technology on Aircraft
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: renzhang@asee.buaa.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 10, 2014; final manuscript received October 8, 2015; published online November 12, 2015. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 138(1), 011007 (Nov 12, 2015) (10 pages) Paper No: DS-14-1408; doi: 10.1115/1.4031845 History: Received October 10, 2014; Revised October 08, 2015

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

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

References

Shamma, J. S. , and Athans, M. , 1991, “ Guaranteed Properties of Gain Scheduled Control for Linear Parameter Varying Plants,” Automatica, 27(3), pp. 559–564. [CrossRef]
Packard, A. , 1994, “ Gain Scheduling Via Linear Fractional Transformations,” Syst. Control Lett., 22(2), pp. 79–92. [CrossRef]
Becker, G. , and Packard, A. , 1994, “ Robust Performance of Linear Parametrically Varying Systems Using Parametrically Dependent Linear Dynamic Feedback,” Syst. Control Lett., 23(3), pp. 205–215. [CrossRef]
Apkarian, P. , and Gahinet, P. , 1995, “ A Convex Characterization of Gain-Scheduled H ∞ Controllers,” IEEE Trans. Autom. Control, 40(9), pp. 853–864. [CrossRef]
Apkarian, P. , and Adams, R. J. , 1998, “ Advanced Gain-Scheduling Techniques for Uncertain System,” IEEE Trans. Control Syst. Technol., 6(1), pp. 21–32. [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]
Shamma, J. S. , and Cloutier, J. R. , 1993, “ Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations,” AIAA J. Guid. Control Dyn., 16(2), pp. 256–263. [CrossRef]
Wu, F. , Packard, A. , and Balas, G. , 2002, “ Systematic Gain-Scheduling Control Design: A Missile Autopilot Example,” Asian J. Control, 4(3), pp. 341–347. [CrossRef]
Marcos, A. , Veenman, J. , and Scherer, C. W. , 2010, “ Application of LPV Modeling, Design and Analysis Methods to a Re-Entry Vehicle,” AIAA Paper No. AIAA-8192.
Mohammadpour, J. , and Scherer, C. W. , eds., 2012, Control of Linear Parameter Varying Systems With Applications, Springer, New York.
Rugh, W. J. , and Shamma, J. S. , 2000, “ Research on Gain Scheduling,” Automatica, 36(10), pp. 1401–1425. [CrossRef]
Rugh, W. J. , 1991, “ Analytical Framework for Gain-Scheduling,” IEEE Control Syst. Mag., 11(1), pp. 79–84. [CrossRef]
Nichols, R. A. , Reichert, R. T. , and Rugh, W. J. , 1993, “ Gain Scheduling for H-Infinity Controllers: A Flight Control Example,” IEEE Trans. Control Syst. Technol., 1(2), pp. 69–79. [CrossRef]
Lawrence, D. A. , and Rugh, W. J. , 1995, “ Gain Scheduling Dynamic Linear Controllers for a Nonlinear Plant,” Automatica, 31(3), pp. 381–390. [CrossRef]
Kaminer, I. , Pascoal, A. M. , Kargonekar, P. P. , and Thompson, C. , 1995, “ A Velocity Algorithm for the Implementation of Gain Scheduled Controllers,” Automatica, 31(8), pp. 1185–1191. [CrossRef]
Lawrence, D. A. , and Sznaier, M. , 2004, “ Nonlinear Compensator Synthesis Via Linear Parameter-Varying Control,” American Control Conference, Boston, MA, pp. 1356–1361.
Isidori, A. , and Byrnes, C. I. , 1990, “ Output Regulation of Nonlinear Systems,” IEEE Trans. Autom. Control, 35(2), pp. 131–140. [CrossRef]
Gajic, Z. , 2003, Linear Dynamic Systems and Signals, Prentice Hall, Upper Saddle River, NJ.
Wu, F. , 1995, “ Control of Linear Parameter Varying Systems,” Ph.D. dissertation, University of California, Berkeley, CA.
Lee, L. H. , 1997, “Identification and Robust Control of Linear Parameter-Varying Systems,” Ph.D. dissertation, University of California, Berkeley, CA.
Hauser, J. , Sastry, S. , and Kokotovic, P. V. , 1992, “ Nonlinear Control Via Approximate Input-Output Linearization: The Ball and Beam Example,” IEEE Trans. Autom. Control, 37(3), pp. 392–398. [CrossRef]
Song, X. , Ren, Z. , and Wu, F. , 2013, “ Gain-Scheduling Compensator Synthesis for Output Regulation of Nonlinear Systems,” American Control Conference, (ACC) Washington, DC, June 17–19, pp. 6078–6083.

Figures

Grahic Jump Location
Fig. 1

The nonlinear ball and beam system [21]

Grahic Jump Location
Fig. 2

Ball tracks a constant-velocity position change: (a) ball position response, (b) position tracking error, (c) beam angle response, and (d) control torque

Grahic Jump Location
Fig. 3

Ball tracks a piecewise linear position reference input: (a) ball position response, (b) position tracking error, (c) beam angle response, and (d) control torque

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