On selection of nonlinear gain in composite nonlinear feedback control for a class of linear systems

This paper addresses the tuning of the nonlinear function in the composite nonlinear feedback (CNF) control law for single-input single-output linear systems. A new nonlinear function is proposed for the CNF control law. The parameters of the new function are not sensitive to variation of amplitude of the reference input. The parameters can be tuned automatically by solving a minimization problem. Two performance criteria, the integral of absolute-value of error (IAE) and the integral of time multiplied absolute-value of error (ITAE), are investigated. Simulation results show that both performance indexes can be used to tune the parameter, but ITAE criterion results in a smaller overshoot than IAE does. Further more, a feedforward neural network is trained to tune the parameter for double integrator systems. The well trained neural network is applied to design a CNF control law for the HDD servo system.