On non-reduced order model of averaged motions in sliding mode control

For the averaged motions in a sliding mode system with parasitic dynamics, a model of the order equal to the original order of the system is obtained via the use of the locus of a perturbed relay system (LPRS) method. This model proves that averaged motions in a sliding mode system differ from those in the reduced-order model. In particular, such phenomena as nonideal disturbance rejection and non-ideal input tracking are observed in the non-reduced-order model. It is shown that the non-reduced-order model transforms into the reduced one when the parasitic dynamics are removed. An example is provided that illustrates the proposed approach