While most of the present modeling and control schemes adopt lumped-parameter models for the rod-type solid-state actuators, in this article we develop a distributed-parameters modeling and control approach for the multiple-mode tracking control of such systems. Using the extended Hamilton’s principle, the system’s equations of motion are derived and truncated to finite-mode state-space representation through standard vibration analysis techniques. A novel asymptotic feedback control law is then developed for the high-bandwidth tracking control of the system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller over a wide frequency range. It is shown that the closed-loop system bandwidth can be improved by incorporating the system’s higher modes in the control law. To improve the tracking performance against uncertainties and disturbances, we upgrade the controller to a robust variable structure form, and show that desirable results can be obtained in the presence of perturbations.
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