Multi input versus single input sliding mode for closed-loop control of capacitive micro structures

Considering the importance of closed-loop control for control of capacitive microstructures and the high capability of the sliding-mode controllers in control of nonlinear systems, the present study has investigated the closed-loop control of these structures using the sliding-mode controller. For this purpose, the sliding-mode controller was designed for single- and double-input cases, and the applied voltages between the capacitive electrodes was considered as the control inputs. The simulation results for both single- and double-input cases have been extracted and presented, and it was concluded that achieving an accurate control for the single input case is not always feasible given that the sign of the sliding surface changes and the control parameter assume positive definite values. Moreover, it has been shown that an accurate control could be achieved by employing the double-input controller without any limitations. The chattering phenomenon was also thoroughly studied in the initial controller design. To eliminate this phenomenon, a smooth variation has been applied to the switching of the sliding surface. In addition to tracking, the capacitive microstructure has been investigated to reduce the relative distance between the two electrodes (in order to increase the capacitive storage), and the obtained results have been presented.