Sliding Mode Control Design for Nonlinear Systems Without Reaching Phase and its Applications to a Flexible Spacecraft

Abstract

Two new Sliding Mode Control (SMC) design methods for nonlinear systems are presented in order to eliminate the reaching phase in the SMC. The sliding surface design approaches are based on optimal sliding surface selection methods for Linear Time Invariant (LTI) and Linear Time Varying (LTV) systems. The reaching phase is eliminated by confining the LTI/LTV system on a predefined linear level surface that moves to the designed optimal sliding hyperplane exponentially. The methodology is extended to nonlinear systems by using two approaches; the “State Dependent Riccati Equation” (SDRE) and “Approximating Sequence of Riccati equations” (ASRE) methods. Systematic ways are defined to eliminate the reaching phase and to design optimal sliding surface for the nonlinear system. The proposed methods are then applied to a spacecraft model with flexible solar panels in order to control the attitude and to suppress some of the vibration modes of the flexible panels. Numerical simulations are used to illustrate the application of proposed methods which are also compared with each other to reveal the effectiveness in coping with uncertainty and vibration suppression and minimization of the energy cost.