Vibration Control of an SMA-Cantilever System with Gain Scheduling

Abstract

To eliminate vibration of a flexible cantilever beam, straight SMA wires are used as tendons and are actively controlled. Actuators consist of SMA connected to a spring that is fixed at the end and are obliquely connected to the cantilever beam. The state equations of the mechanical system are formulated from decoupled vibration equation of the cantilever beam on the mode coordinate applying linearized force of the SMA-spring component about the equilibrium point by defining the state variables as modal displacement, velocity of the beam and force of the SMA-spring structure. Since the linearized model of the SMA-spring components includes varying parameter according to amplitude of applied voltage, gain scheduled H∞ controller is designed for the system to obtain high control performance by using SMA under less hysteresis deformation. The simulations and experiments demonstrated that the four vibration modes (three bending and one torsional modes) of the cantilever beam could be simultaneously damped. Furthermore, it was verified that SMAs were stably controlled within less hysteresis deformation that supposed in modeling process.