NONLINEAR CONTROL MODELING FOR ARRAYS OF COUPLED MECHATRONIC TRANSDUCERS

摘要

A typical mechatronic oscillator involving a tuned resistor-inductor-capacitor circuit driven by a voltage source and coupled to a mass-spring-damper mechanical subsystem is analyzed in order to develop a nonlinear control model. The analysis is approached using the Volterrra/Wiener framework of nonlinear systems combined with the Hilbert Transform. The former is needed since the coupling between the electrical and mechanical parts is lost, should standard linearization is adopted. The latter is needed since a very important characteristic of the system, due to the presence of the capacitance, is frequency selectivity. To use this very frequency selectivity in an application, involving more than one transducer units, modulation of the carrier signal, amplitude modulation in this case, must be implemented. Carrier modulation enables multiple units, structurally identical otherwise but for the capacitance value adjusting the tuning frequency setting, in the same application. Both a low-pass and a band-pass model are developed and subsequently simulation runs are performed. Since the modulation method employed is not of the suppressed-carrier type, the equilibrium point is of dynamic rather than static nature, corresponding to initial values for current and displacement. The model is enhanced by superimposing an external disturbance in form of a baseband force acting on the mass payload of the mechanical subsystem. Then, the response of the system to monochromatic and polychromatic excitations is investigated; making sure among others none of the constraints is violated. The transducer configuration investigated here can be employed as an energy harvesting device in cases where vibrational or oscillatory motion of a mass is involved, e.g. ocean wave energy concepts, Vortex-Induced Vibrations etc., especially if no physical contact between the driving process and the driven circuit is feasible or practical.