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Research Papers

Coupled State-Dependent Riccati Equation Control for Continuous Time Nonlinear Mechatronics Systems

[+] Author and Article Information
Xin Wang

Electrical and Computer Engineering,
Southern Illinois University,
Edwardsville, IL 62026
e-mail: xwang@siue.edu

Edwin E. Yaz

Electrical and Computer Engineering,
Marquette University,
Milwaukee, WI 53201
e-mail: edwin.yaz@marquette.edu

Susan C. Schneider

Electrical and Computer Engineering,
Marquette University,
Milwaukee, WI 53201
e-mail: susan.schneider@marquette.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received November 29, 2017; final manuscript received May 10, 2018; published online June 18, 2018. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 140(11), 111013 (Jun 18, 2018) (10 pages) Paper No: DS-17-1590; doi: 10.1115/1.4040295 History: Received November 29, 2017; Revised May 10, 2018

This paper considers a novel coupled state-dependent Riccati equation (SDRE) approach for systematically designing nonlinear quadratic regulator (NLQR) and H control of mechatronics systems. The state-dependent feedback control solutions can be obtained by solving a pair of coupled SDREs, guaranteeing nonlinear quadratic optimality with inherent stability property in combination with robust L2 type of disturbance reduction. The derivation of this control strategy is based on Nash's game theory. Both finite and infinite horizon control problems are discussed. An under-actuated robotic system, Furuta rotary pendulum, is used to examine the effectiveness and robustness of this novel nonlinear control approach.

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Figures

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Fig. 5

Nonlinear quadratic regulator – H CSDRE control state trajectories

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Fig. 1

Setup for mixed NLQR and H control

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Fig. 2

Furuta rotary inverted pendulum

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Fig. 3

State-dependent sliding mode control state trajectories

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Fig. 4

State-dependent sliding mode control torque input

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Fig. 6

Nonlinear quadratic regulator SDRE control state trajectories

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Fig. 7

H SDRE control state trajectories

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Fig. 8

Nonlinear quadratic regulator – H CSDRE control torque input

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Fig. 9

Nonlinear quadratic regulator SDRE control torque input

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Fig. 10

H SDRE control torque input

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