Radial basis function neural network chaos control of a piezomagnetoelastic energy harvesting system

Abstract

In this paper, an adaptive chaos control is proposed for a typical vibratory piezomagnetoelastic energy harvesting system to return the chaotic behavior to a periodic one. Piezomagnetoelastic energy harvesting systems show chaotic behaviors in spite of harmonic input. Although, the chaotic behavior of the system gives higher output voltage than the periodic motion, it is preferred to the output voltage as this is periodic for charging a battery or a capacitor efficiently. Therefore, the chaos control is important in this system. The physical model is composed of the upper and lower piezoelectric layers on a cantilever taper beam, one attached tip magnet, and two external magnets (EM). Position of the EM is controlled by inputs. Firstly, chaotic and periodic regions are detected by utilizing the bifurcation diagrams, phase plan portrait, and Poincaré maps. Then an adaptive controller is proposed for controlling of the chaotic behaviors in the presence of uncertainty due to magnetic forces. The control law is derived based on the inverse dynamic method and the uncertainty elements of the controller are estimated using radial basis function (RBF) network. The weights of the RBF network are obtained using an adaptation law. The adaptation laws are derived based on Lyapunov stability theory and a projection operator. The distance of the tip magnet and the EM as well as the gap distance of two EM are used to control the chaotic behavior. Simulation results show that the proposed controller can return the chaotic motion to a periodic one in spite of the uncertainties in the magnetic forces.