Design of an adaptive sliding mode controller with a sliding mode Luenberger observer for the MEMS capacitive plates

Abstract

Uncertain parameters in a MEMS tunable capacitor, as one of the fundamental elements in a MEMS AC voltage reference source (VRS) structure, is an important issue for acquisition of a rigorous voltage in the VRS output. The output is mostly supposed to be destroyed by harmful disturbance and noise. Even though the manufacturers make attempts to build MEMS tunable capacitor with desired characteristics in thorough compliance with the initial major design, uncertainties in the parameters inescapably do exist in manufacturing process on the ground of deficiencies in various procedures. This paper mainly remarks an adaptive sliding mode controlling design with a sliding mode Luenberger observer and its application for a MEMS tunable capacitor. The control design is done considering matched and unmatched terms of uncertainties and disturbance. The advantageous outcome is that the VRS could be generating a stable precise regulated output voltage owing to correct distance adjustment of the capacitor charged plates. The design exploits the sliding mode observer to get rid of extra usage of plate position measurement in the control structure. The controller alleviates the system output of the matched and unmatched disturbance which could exist dynamically because of cross stiffness and damping in addition to other inertial and electrostatic disturbing forces. The matched uncertainties, such as stiffness and damping change, might appear due to variation in fabrication procedures or working condition. The simulation yields are satisfactory and depict a persuasive tracking performance as well as regulation about the pull-in point.

Design of a fuzzy PID controller for a MEMS tunable capacitor for noise reduction in a voltage reference source

“…In the similar previous articles [10,34], the convergence-time of the states is longer in comparison with this work. The settling time (convergence) in the proposed controller is also a little shorter (faster) in comparison with [33]. • The proposed FLC has been applied to the MEMS tunable capacitor for voltage regulation for the first time.…”

“…• Unlike similar previous works [33,35] which have used SMC, the proposed method does not suffer from possible excitation of non-modeled modes in the dynamics of the tunable capacitor. This excitation may be brought about by high frequency elements, which are themselves caused by the chattering phenomenon, in the control law enforcing the plate.…”

“…1 a MEMS tunable capacitor lumped model. b Movable plate gets access to one third of its first distance to the fixed plate at the pull-in point [33,35] Vol. :(0123456789) [26].…”

“…Farzanegan et al [10] proposed Model Reference Adaptive Control (MRAC) for the MEMS TC using output feedback. Ranjbar et al [33] proposed an observer-based controller for the MEMS TC to cancel the requirement for measurement circuits of displacement and velocity of the movable capacitive plates. Note that the stability of the pull-in easily remains accessible using a straightforward poleplacement state feedback control design.…”

Robust adaptive sliding mode control of a MEMS tunable capacitor based on dead-zone method

“…(3) Unlike many other works such as [32][33][34][35][36][37], which have been concerned with tracking a sinusoidal displacement trajectory for the displacement of the MEMS movable capacitive plate, this paper addresses displacement control of the movable capacitive plate, regulating its motion about a fixed position. (4) This article deems uncertainty in the movable plate mass which has not been considered in previous works such as [24,29,30,38,39].…”