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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.

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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

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