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In the current article, a novel approach to the shape control problem with a limited number of discrete actuators is presented. In optimizing the actuator locations, first the reference input was expanded with a representative set of eigenfunctions. From the expansion coefficients, the dominant modes in the reference input were identified. Next the distributed parameter system was rewritten in modal coordinates and the irrelevant modes were truncated. Finally, the actuator locations were selected such that the singular values of the controllability matrix of the truncated system were maximized. The steady state actuation forces were optimized such that a cost function based on the absolute value of the steady state error is minimized. To improve the transient response, a hybrid of dynamic modal control algorithm and the optimization method is developed. Four discrete linear actuators for the one-dimensionally curved reflector and eight actuators for the two-dimensionally curved reflector are utilized. The structures are controlled and assessments for experimental implementation are made.

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This paper presents a novel approach to the inertia identification problem of mechatronic servo systems with limited strokes. In the proposed approach, the product of the integral of torque reference input and motor speed of mechatronic servo system in periodic motion is calculated. Then its time average over one period is used to calculate inertia. The proposed approach can identify inertia with infinitesimal motions within short time interval, and suits online and off-line identification of mechatronic servo systems with limited strokes, and off-line inertia identification of industrial machineries with interfering degrees of freedom especially in the preparatory period after they are turned on and before their normal operation starts. The proposed approach utilizes an integral of torque reference input, and can identify inertia when torque reference input contains large amount of noises. Simulations and experiments on an electric motor and a linear slider suggest the feasibility of the proposed approach on single-degree-of-freedom (SDOF) systems and two-degree-of-freedom (2DOF) systems with limited strokes. * * J J J e J

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