On the Transfer Properties of the “Generalized Sub-Optimal” Second-Order Sliding Mode Control Algorithm

A class of second order sliding mode control systems is studied in terms of its transfer properties, which allows for investigating the system response to an external signal representing either a disturbance, which the system is supposed to reject, or the reference input, which the system is supposed to track. An approach based on the Locus of a Perturbed Relay System (LPRS) is developed making reference to linear plant/actuator/ sensor dynamics and to the “generalized sub-optimal” second-order sliding mode control algorithm in the closed loop. A thoroughly discussed example shows the feasibility of the presented procedure and confirms the theoretical results.