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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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References

1. Doyle, J.C. and Stein, G., “Multivariable feedback design: concepts for a classical/modern synthesis”, IEEE Trans. on Automatic Control 26(1), 4–16 (1981).CrossRefGoogle Scholar
2. Apkarian, P. and Adams, R.J., “Advanced gain-scheduling techniques for uncertain systems”, IEEE Trans. on Control Systems Technology 6(1), 21–32 (1998).CrossRefGoogle Scholar
3. Queiroz, M.S., Dawson, D.W. and Agarwal, M., “Adaptive control of robot manipulators with controller/update law modularity”, Automatica 35(7), 1379–1390 (1999).CrossRefGoogle Scholar
4. Tang, Y. and Arteaga, M.A., “Adaptive control of robot manipulators based on passivity”, IEEE Trans. on Automatic Control 39(9), 1871–1875 (1994).CrossRefGoogle Scholar
5. Chen, B., “A nonlinear H∞ control design in robotic systems under parameter perturbation and external disturbance”, Int. J. of Control 59(2), 439–461 (1994).CrossRefGoogle Scholar
6. Choi, Y., “Robust control of manipulators using Hamiltonian optimization”, Proc. of the IEEE Int. Conf. on Rob. and Autom., Albuquerque, New Mexico (1997) pp. 2358–2364.Google Scholar
7. Watanabe, K., “A nonlinear robust control using a fuzzy reasoning and its application to a robot manipulator”, J. of Intelligent and Robotics Systems 20(2), 275–294 (1997).CrossRefGoogle Scholar
8. Karakasoglu, A., “A recurrent neural network-based adaptive variable structure model-following control of robotic manipulator”, Automatica 31(10), 1495–1507 (1995).CrossRefGoogle Scholar
9. Shamma, J.S. and Athans, M., “Analysis of nonlinear gain scheduled control systems”, IEEE Trans. on Automatic Control 35(8), 898–907 (1990).CrossRefGoogle Scholar
10. Shamma, J.S. and Athans, M., “Gain scheduling: potential hazards and possible remedies”, IEEE Control Systems 101–107 (June, 1992).CrossRefGoogle Scholar
11. Jiang, J., “Optimal gain scheduling controller for a diesel engine”, IEEE Control System 42–48 (August 1994).CrossRefGoogle Scholar
12. Gahinet, P. and Apkarian, P., “A Linear matrix inequality approach to H∞ control”, J. of Robust and Nonlinear Control 4, 421–448 (1994).CrossRefGoogle Scholar
13. Nesterov, Y. and Nemirovski, A., “An interior-point method for generalized linear-fractional problems”, Math. Programming Ser. B (1996).Google Scholar
14. Gahinet, P., Arkadii, N. et al. “The LMI control Toolbox”, Proc. of 33rd Conf. on Decision and Control, Lake Buena Vista, Florida (Dec. 1994) pp. 2038–2041.Google Scholar
15. Chilali, M. and Gahinet, P., “H∞ design with pole placement constraints: an LMI approach”, IEEE Trans. on Automatic Control 41(3), 358–367 (1996).CrossRefGoogle Scholar
16. Yu, Z.-W. and Chen, H.-T., “Friction adaptive compensation scheme based on sliding-mode observer”, Robot 21(7), 562–568 (1999).Google Scholar