Theoretical and experimental investigations on modified LQ terminal control scheme of piezo-actuated compliant structures in finite time

Abstract This study focuses on the open-loop dynamic shape control to realize a rapid and smooth morphing process for a flexible plate which is actuated by a macro fiber composite patch. A finite element model of the system is established and verified for theoretical investigations. Steady-state and dynamic analyses are carried out to satisfy the desired rest-to-test morphing requirement. Spurious oscillations and large overshoots are observed while applying some common voltage signals. The results imply that the voltage profile of the actuator plays a key role in the dynamic morphing behavior of the system. Therefore, a quantitative criterion is proposed to determine the critical voltage slope for evaluating the boundary between quasi-static and dynamic processes. An optimal finite-time feedforward control approach named “modified linear quadratic (LQ) terminal controller” is proposed to optimize the voltage profiles by simultaneously considering the suppression of transient and residual vibration. The superiority of the proposed open-loop control scheme is appreciated when it is compared with the standard LQ terminal controller. An experimental setup is designed for verification. The effectiveness of the theoretical model is validated through modal analysis, static deformation, and dynamic responses. It is indicated by the experiment results that rapid and smooth dynamic shape morphing processes with negligible vibration within a short period of time can be achieved using the optimized voltage profile.

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