Chattering Free with Noise Reduction in Sliding-Mode Observers Using Frequency Domain Analysis

Sliding-mode observers are known to be robust against presence of disturbances and modeling uncertainties [1−3]. Although these observers are highly robust with respect to noises in system inputs, it turned out that the corresponding stability degrades in systems that exhibit output noise or mixed uncertainties [4]. When the measurements are noisy, because the time derivatives cannot be accurately calculated, it can lead to poor closedloop performance or instabilities in the estimation procedure. Sliding-mode observers are known as high-gain observers, which have appropriate behavior in disturbance rejection [5−7]. Vasiljevic and Khalil have shown that a high-gain observer acts as a differentiator in the limit as the gain approaches infinity [8]. Hence, in the presence of the measurement noise, it magnifies the noise in the estimated states. Therefore, there is a trade-off between the observer gain and the noise effect in the state estimation. In addition, they have showed that a bound on the estimation error exists that depends on the maximum amplitude of the measurement noise. Recently, Ahrens and Khalil have introduced a high-gain observer, where the gain matrix switches between two values [9]. In this method, when the estimation error reaches a steady-state threshold, it switches to a second gain to reduce the effect of the measurement noise. The idea of gain switching in observers has been employed before by other researchers for noise cancellation in the state estimation [10]. Since the main source of the sliding phenomena is the relay element, researchers use relay feedback systems to analyze sliding properties [11]. Due to the interesting characteristics of relay feedback systems, research in this area is fast developing. A number of analyzing methods for the modeling of relay feedback systems as well Chattering Free with Noise Reduction in Sliding-Mode Observers Using Frequency Domain Analysis