Multi-discontinuous Functional based Sliding Mode Cascade Observer for Estimation and Closed-loop Compensation Controller

The sliding mode observer is a useful method for estimating the system state and the unknown disturbance. However, the traditional single-layer observer might still suffer from high pulse when the output measurement is mixed with noise. To improve the estimation quality, a new cascade sliding mode observer containing multiple discontinuous functions is proposed in this letter. The proposed observer consists of two layers: the first layer is a traditional sliding mode observer, and the second layer is a cascade observer. The measurement noise issue is considered in the source system model. An alternative method how to design the observer gains of the two layers, together with how to examine the effectiveness of the compensator based closed-loop system, are offered. A numerical example is provided to demonstrate the effectiveness of the proposed method. The observation structure proposed in this letter not only smooths the estimated state but also reduces the control consumption.