Machine learning based nonlinear adaptive optimal control of capacitive micro-actuator subjected to electrostatic field

Since controlling of parallel-plate micro-actuators and improving their speed and precision is an essential factor for tracking of high frequencies reference inputs, the optimal closed-loop control based on state feedback has been studied to control of mentioned structures. To this end, the adaptive feedback coefficient has been employed due to the intermittent and rapid change in the reference input as well as for enhancing control accuracy. To implement adaptive strategy, machine learning based neural networks have been utilized to update the feedback gain in each step and based on the variation of reference input. In this regard, the applied voltage has been determined according to the updated gain coefficient as well as tracking error. In each step, the gain coefficients are updated using the linear quadratic regulator (LQR) and the step by step linearization method (SSLM), and finally, the calculated control force is applied to the nonlinear system. The control of studied micro-actuator has been examined based on tracking of different reference inputs with different frequencies, and the obtained results has proved that the employed strategy has promising precision and acceptable speed. Also, it has been shown that, tracking error for adaptive optimal controlling is less than that obtained by optimal controller with fixed gains. However, dynamic error for both controller is almost zero and negligible.