Sliding Mode Control of Nonlinear Systems Under Nonstationary Random Vibrations via an Equivalent Linearization Method Using Block Pulse Functions

Abstract

This chapter proposes a sliding mode control (SMC) method for nonlinear systems subjected to stationary and nonstationary excitations. The equivalent linearization (EL) method is commonly used as an effective tool in seeking approximate solutions to nonlinear systems, and SMC has numerous successful applications in the field of nonlinear system control due to its robustness in handling uncertainties in dynamic systems. In the current study, the nonlinear system is first linearized by a proposed block pulse (BP) function-based equivalent linearization method, then a continuous form of SMC method is developed to control the linearized nonlinear system. Numerical simulations reveal that compared to other existing methods, the proposed BP function-based EL method can predict the nonlinear system responses more accurately at lower computational cost, and the chattering-free SMC approach can effectively improve the performance of a nonlinear system when subjected to various types of random excitations including seismic load.