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Polytopic gain scheduled H∞ control for robotic manipulators

Published online by Cambridge University Press:  02 March 2021

Zhongwei Yu ,
Huitang Chen  and
Peng-Yung Woo
Zhongwei Yu
Affiliation:
Information and Control Engineering Dept., Tongji University, Shanghai (China)
Huitang Chen
Affiliation:
Information and Control Engineering Dept., Tongji University, Shanghai (China)
Peng-Yung Woo
Affiliation:
Electrical Engineering Dept., Northern Illinois University, DekalbIL60115 (USA)
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Summary

A new approach to the design of a polytopic gain scheduled H∞ controller with pole placement for n-joint rigid robotic manipulators is presented. With linearization around the equilibrium manifold, the robotic system is transformed into a continuous linear parameter-varying (LPV) system with respect to the equilibrium manifold. A filter is introduced to obtain an augmented system, which is apt to have the polytopic gain scheduled controller designed. This system is put into a polytopic expression by a convex decomposition. Based on the concepts of quadratic D-stability and quadratic H∞ performance, the polytopic features are used to simplify the controller design to be a vertices’ controller design for the polytope. A state feedback gain, which satisfies H∞ performance and dynamic characteristics for each vertex of the polytope, is designed with a Linear Matrix Inequality (LMI) approach. A global continuous gain scheduled controller is then obtained by a synthesis of the vertex gains. Experiments demonstrate the feasibility of the designed controller.

Keywords

Polytopic gain scheduled controlManipulatorsLMI approachVertex gains
Type
Research Article
Information
Robotica , Volume 21 , Issue 5 , October 2003 , pp. 495 - 504
Copyright
Copyright © Cambridge University Press 2003

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