Dynamic Sliding Mode Control Based on a Full–Order Observer: Underactuated Electro–Mechanical System Regulation

This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.