UBC Theses and Dissertations
Multiple objective control with applications to teleoperation Hu, Zhongzhi
Control system design inevitably involves tradeoffs among different and even conflicting performance and robustness specifications. This thesis deals with some multiple objective control system design problems and with applications to teleoperation systems. First, the multiple objective linear-quadratic optimal control problem is solved. By using duality theory, this minimax problem is transformed into a convex optimization problem . In particular, the infinite time problem is shown to be an optimization problem involving linear matrix inequalities. Second, the multiple objective Hoo control problem for SISO systems is studied. Nonsmooth analysis is used to characterize optimality conditions for this problem. Under these conditions, either all-pass properties or the optimal performance values are obtained. Third, numerical solutions of the general multiple objective control system design problem by either convex optimization or non-convex optimization are presented. First, the convex optimization design procedure is described, the effectiveness of the cutting-plane based solver is demonstrated, and some computational issues are discussed. Then a non-convex optimization design procedure is proposed, in which an approximation to the free transfer function in the Q-parametrization is proposed. It is shown, by design examples, that it has the advantage of directly producing low-order controllers. Last, the robust controller design problem for teleoperation systems is investigated. First, a two-port ideal teleoperation model is proposed. It is shown that the model scales both positions and forces, yet is stable when terminated by any strictly passive hand and environment impedances. Then a transparency measure is proposed to be defined as the Hoo-distance to the ideal teleoperator model. Using a four channel control structure, the controller design problem is formulated as a multiobjective optimization problem maximizing transparency subject to robust stability for all passive environments. This problem is shown to be convex in the design parameters for a fixed hand impedance. To demonstrate the design procedure, this thesis treats the design of a controller for a simple one degree-of-freedom system model of a motion-scaling teleoperation system. Both simulations and experiments have been carried out to show the effectiveness of the proposed controller design methodology.
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