Increasing accuracy in non-linear sliding-mode observers without decreasing sampling time using frequency domain analysis

This paper presents a method to improve estimation accuracy of sliding-mode observers (SMOs) using frequency domain analysis. First, the high-gain property of the SMO is employed in order to obtain fast convergence of the estimated states. Then, when the system is in the switching condition, signals are decomposed into two parts in the frequency domain: (1) the slow-mode part, which consists of the main signals, and (2) the fast-mode part, which consists of the unwanted high-frequency chatterings. In addition, a linear compensator is designed and added in cascade with the observer based on the relay feedback systems theory. In this approach, without reducing the sampling time, the high-gain property is provided for the slow mode of the observer and at the same time, the amplitude of chatterings becomes effectively smaller. Simulation results show good performance of the proposed method as compared to the conventional SMO, when applied to a bioreactor.