Nonlinear Control With State-Dependant Reset Integrator for a Class of Singularly Perturbed Interconnected Nonlinear Systems

Abstract

In this paper, we present nonlinear control with a state-dependant reset integrator (RI) for a class of singularly perturbed interconnected nonlinear system. There are many approaches to use integrator reset. But, it has not been reported yet how to design the reset surface influencing the performance of servo system. In this paper, we introduce how to design the reset surface using a Lyapunov function based on the slow subsystem. We design the reset surface, which is a function of a threshold for output tracking error, to guarantee that the Lyapunov function decreases at every reset time. Given the Lyapunov function, we introduce an optimization process to get the lowest bound of threshold. It is proven that the proposed method ensures the globally exponential stability of tracking errors. The proposed method provides the guidelines on how to determine the control gains and reset surface. A numerical example using a permanent magnet stepper motor is given to illustrate the design process for the proposed controller. We performed the experiments for a comparative study with the previous RIs. The experimental results validate the effectiveness of the proposed method.