Barrier Lyapunov Function-Based Output Regulation Control of an Electromagnetic Micromirror With Transient Performance Constraint
Weijie Sun, Hui Chen, John T. W. Yeow
Abstract
This article investigates the controller design problem for an electromagnetic torsional micromirror with guaranteed transient performance constraint. Specifically, the developed solution works under the output regulation framework and utilizes the internal model principle for model parameter uncertainties and general reference trajectories tracking, incorporated with barrier Lyapunov function (BLF) method to prevent the tracking constraint violation. We first formulate the micromirror model as an output feedback system with relative degree two and unknown control coefficient, and further turn it into a lower triangular system with an extension transformation. Then, using the extended internal model design, we transform the output regulation problem of the transformed system into the stabilization problem of an augmented system. Finally, based on the BLF technique, we develop a stabilization controller for the augmented system to realize the asymptotic tracking of reference trajectory with transient performance constraint, where the effects of the main design parameters on the control performances are also investigated. By such a technical treatment, the entire control architecture is independent of the angular velocity information of the micromirror, which reduces the measurement complexity in practical. This feature behind the control scheme is important since the velocity information is difficult to be available in many microelectromechanical systems (MEMS). Moreover, the enhanced transient performance is beneficial for improving the scanning quality of the packaged micromirror system. The developed control solution is verified on an experimental platform using a field programmable gate array (FPGA)-based hardware, where the scanning and imaging applications are both conducted.