参照入力を一般化したILQ最適サーボ系設計法

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  • ILQ Design Method for Optimal Servo Systems with Generalized Reference Inputs

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ILQ (Inverse Linear Quadratic) method is a new design method for optimal control systems based on the result of inverse problem of optimal regulator. This method has been successfully applied to design an optimal servo system with step reference inputs called “ILQ optimal servo system”, which has a special structure with nominal feedback gains and tuning parameters, and has three attractive features from a practical viewpoint as described later. In this paper we extend the existing design method of ILQ optimal servo system with respect to reference inputs. First, we derive two important structures of an optimal servo system with generalized reference inputs, called “basic structure” and “asymptotic structure”, very easily by introducing a new parameter. Secondly, we utilize these structures to design the nominal state feedback gains in such a way that the closed loop transfer matrix of ILQ servo system can be decoupled, and also its poles can be specified as design parameters, asymptotically as the tuning parameters go to infinity. These decoupling and pole assignment are two of the above features. Furthermore the nominal feedback gains can be analytically expressed in terms of the design parameters and the system parameters, which is the remaining feature. Thirdly, we derive an optimality condition of ILQ servo system with respect to the tuning parameters. Finally, we show a design procedure of this method and illustrate a numerical example to verify the validity of the design method proposed here.

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