Design of a variable gain feedback control system for a linear system with bounded control variable.

概要

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In the present paper the design method of a controller for linear system x=Ax+bu with the constraint |u|≤1 is proposed. I=∫∞0x'Qxdt is considered as the performance index. The resultant control law is a nonlinear contral via state-dependent feedback gains, and is not optimal in the sence of minimizing I, but has following desirable properties:(a) The proposed control law gives smaller I than the linear feedback which the constraint is always met.(b) It requires relatively simple calculations and is suitable for closed-loop implementation.The main results obtained in this study are as follows:(1) Defining the feedback gain k(ρ) with one parameter ρ, and varing ρ according to some rule, u(t)=-k(ρ)'x(t) gives smaller I than with fixed ρ. Not only the constraint but also the rule imposed on ρ are able to be met if k(ρ) is an admissible gain for x(t).(2) The piecewise-constant gain and the linear region R make closed-loop implementation easy.(3) The linear region R is represented approximately by polyhedral convex set R. And the method to construct R is given.Some numerical examples turn out the proposed control law to be effective and attractive.
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