Chattering free with noise reduction in sliding-mode observers using frequency domain analysis

This paper presents analysis and regulation of switching in the sliding-mode observers for nonlinear systems. First, the high gain property of the sliding observer is employed in order to obtain fast convergence of the estimated states to the system ones. Then, when the system is in the switching condition, signals are decomposed into two modes: the slow-mode and the fast-mode. The observer parameters are designed based on the relay feedback systems such that the high gain property is provided for the slow-mode operation. This ensures fast convergence of the estimated states and at the same time, by controlling the fast-mode of the observer, the high frequency oscillations (i.e. the chattering phenomena) can be rejected by a simple low-pass filter. In addition, the behavior of the proposed observer is analyzed in the presence of the measurement noise. Moreover, a Variable Relay-Equivalent Gain technique will be introduced to make the proposed observer less sensitive to measurement noises and to maintain good estimation of the states. The proposed nonlinear observer is tested through simulations in an illustrative example involving a bioreactor. Simulation results show good performance of the proposed method as compared to the conventional sliding-mode observer.