Disturbance attenuation for systems with second-order sliding modes via linear compensators

Non-ideal disturbance attenuation emerges in systems with sliding mode controllers when parasitic dynamics are present. In this work, the problem of non-ideal disturbance attenuation in systems controlled by second-order sliding modes is considered. Describing function and locus of a perturbed relay system (LPRS) methods are used for analysis of non-ideal disturbance attenuation. The proposed solution is to introduce a linear compensator (series or parallel) in the control loop to modify the system frequency response, that is, the Nyquist plot or LPRS. The design methodology for both parallel and series compensators is presented. The proposed solution allows one to improve disturbance attenuation and tracking quality, thereby reducing the effect of parasitic dynamics which is reflected in the system frequency response. Experiments supporting the proposed approach and simulations are provided.