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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January 2016
Research-Article
A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions
Fen Wu,
Fen Wu
Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: fwu@eos.ncsu.edu
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: fwu@eos.ncsu.edu
Search for other works by this author on:
Xun Song,
Xun Song
Science and Technology on Aircraft
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: songxun@asee.buaa.edu.cn
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: songxun@asee.buaa.edu.cn
Search for other works by this author on:
Zhang Ren
Zhang Ren
Science and Technology on Aircraft
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: renzhang@asee.buaa.edu.cn
Control Laboratory,
Beihang University,
Beijing 100191, China
e-mail: renzhang@asee.buaa.edu.cn
Search for other works by this author on:
Fen Wu
Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695
e-mail: fwu@eos.ncsu.edu
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
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
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. Jan 2016, 138(1): 011007 (10 pages)
Published Online: November 12, 2015
Article history
Received:
October 10, 2014
Revised:
October 8, 2015
Citation
Wu, F., Song, X., and Ren, Z. (November 12, 2015). "A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions." ASME. J. Dyn. Sys., Meas., Control. January 2016; 138(1): 011007. https://doi.org/10.1115/1.4031845
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