Describing Function Method for Steady- State Analysis of Practical Sliding Mode Controlled Systems

This paper aims to study the steady-state response of the practical sliding mode controlled system (SMC). The nonlinearity of the switching term is approximately characterized by using its equivalent describing function. The parasitic dynamics is modeled as a first order lag transfer function, and the possible transport delay is particularly considered. Subsequently, the frequency domain method is used for the prediction of limit cycles. The stability-equation method accompanying with the parameter plane method is proposed to graphically predict limit cycles in the system coefficient plane. Then the steady-state analyses for system containing imperfect realization of the switching part and the transmission delay are demonstrated. The analysis offers a way to design a practical switching controller to achieve the disturbance-rejection and to maintain the steady-state invariance with respect to plant uncertainties. Index terms limit cycle, parameter plane, sliding mode, stability equation.