We present an alternative to averaging methods for vibrational control design of second-order systems. This method is based on direct application of the stability map of the linearization of the system at the desired operating point. The paper focuses on harmonic forcing, for which the linearization is Mathieu’s equation, but somewhat more general periodic forcing functions may be handled. When it is applicable, this method achieves significantly greater functionality than previously reported approaches. This is demonstrated on two sample systems. One is the vertically driven inverted pendulum, and the other is an input-coupled bifurcation control problem arising from electrostatic MEMS comb drives.
- Dynamic Systems and Control Division
A Linearization-Based Approach to Vibrational Control of Second-Order Systems
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Wickramasinghe, IPM, & Berg, JM. "A Linearization-Based Approach to Vibrational Control of Second-Order Systems." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control. Palo Alto, California, USA. October 21–23, 2013. V003T48A005. ASME. https://doi.org/10.1115/DSCC2013-4089
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