Fourier-transform-based composite intelligent control for high-frequency-response voice coil motor

During to the non derivability for triangle wave reference trajectory, whose high-frequency harmonics will stimulate the resonant modes in the high-frequency voice coil motor (VCM), the traditional speed and acceleration feed forwards can not be achieved. In this paper, the triangle wave was Fourier transformed to get its Fourier series composed of several sine functions, which are high order differential. After derivation calculus to the sum function of the series, the first and second order derivatives of the sum function were obtained. By making the inverse Fourier transform to the derivatives of sum function, the first and second order differential of the triangle wave were obtained and the speed and acceleration feed forwards under triangle wave reference were achieved. In the feedback controller, an incomplete differential PID-like neural network controller was introduced and improved. The dynamic recurrent neural network (DRNN) was used to real-timely identify the system's Jacobian information. The feedback controller was used to compensate the approximation error in the feedforward and suppress the high frequency harmonic components in order to stabilize the systems and eliminate the residual error. The simulation results show that the system is of small steady-state error and high positioning accuracy, and the system requirements are also met under high-frequency inputs.