Perturbed Butterworth pole patterns for tracking in the sense of spheres
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The so called “Quantitative Pole Placement” (QPP) identified in the context of guaranteed tracking in the sens of spheres is considered. In the prior literature this pole-placement problem was treated in a somewhat adhoc way. The primary purpose of the present work therefore is to propose a systematic procedure for such pole placement. The approach to the problem is based on a generalization of the standard LQ problem formulation. The preferred pole locations that minimize a crucial operator norm needed for the success of the QPP formulation are shown to be a perturbed version of the Butterworth pole configuration. The results are applied to a 3 d.o.f. robotic manipulator for illustrating the evolving methodology. At the center of the overall design philosophy is the need to directly satisfy performance specifications in uncertain. nonlinear systems.
Key WordsQuantitative Pole Placement Tracking in the Sese of Spheres Generalized LQ Formulation L∞-norm Banach Contraction Mapping Butterworth Pole Configuration
- Barnard, R.D., 1980, “Controller Design Criteria for Servo Tracking in Uncertain System,” Proceedings of 23rd Midwest Symposium on Circuits and Systems, Toledo, OH.Google Scholar
- Barnard, R.D. and Jayasuriya, S. 1982, “Controller Design for Uncertain Nonlinear Sytems,” Proceeding of 1982 American Control Conference, Alington, VA.Google Scholar
- Kee, C.D., 1987, “A Quantitative Ploe-Placement Approach for Robust Tracking,” Ph. D. Dissertation, Michigan State Univ., East Lansing, MI 48823.Google Scholar
- Usoro, P.E., Schweppe, F.C., Wormley, D.N. and Gould, L.A. 1982, “Ellipsoidal Set-Theoretic Control Synthesis,” Journal of Dynamic Systems, Measurement, and Control, Vol. 104, No. 4.Google Scholar