This paper describes control design and stability analysis for a horizontal pendulum using translational control of the pivot. The system is a one-link mechanism subject to linear damping and moving in the horizontal plane. The goal is to drive the system to a desired configuration such that the system oscillates in an arbitrarily small neighborhood of that desired configuration. We consider two cases: prescribed displacement inputs and prescribed force inputs. The proposed control law has two parts, a proportional-derivative part for control of actuated coordinates, and a high-frequency, high-amplitude oscillatory forcing to control the motion of unactuated coordinate. The control system is a high-frequency, time-periodic system. Therefore we use averaging techniques to determine the necessary input amplitudes and control gains. We show that using a certain oscillatory input, the amplitudes of that input must follow a constraint equation. We discuss the geometric interpretation of constraint equation and stability conditions of the system. We also discuss the effects of damping and relative phase of the oscillatory inputs on the system and their physical and geometric interpretation.
- Dynamic Systems and Control Division
On Vibrational Stabilization of a Horizontal Pendulum
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Tahmasian, S, Jafari, F, & Woolsey, CA. "On Vibrational Stabilization of a Horizontal Pendulum." Proceedings of the ASME 2016 Dynamic Systems and Control Conference. Volume 2: Mechatronics; Mechatronics and Controls in Advanced Manufacturing; Modeling and Control of Automotive Systems and Combustion Engines; Modeling and Validation; Motion and Vibration Control Applications; Multi-Agent and Networked Systems; Path Planning and Motion Control; Robot Manipulators; Sensors and Actuators; Tracking Control Systems; Uncertain Systems and Robustness; Unmanned, Ground and Surface Robotics; Vehicle Dynamic Controls; Vehicle Dynamics and Traffic Control. Minneapolis, Minnesota, USA. October 12–14, 2016. V002T24A004. ASME. https://doi.org/10.1115/DSCC2016-9675
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