New discrete multivariable sliding mode control for multi-periodic disturbances rejection

This paper presents a control strategy using Sliding Mode Control (SMC) and Repetitive Control (RC) for linear multi-input discrete-time systems to reject periodic and multi-periodic disturbances. A new reaching law is used to steer the system trajectories into the sliding surface and then keep them on it without chattering. The repetitive control is used to reject periodic and multi-periodic signals. The combination of SMC and RC improves the performance of these two control laws. A numerical simulation example is presented to illustrate the effectiveness of the proposed multivariable repetitive sliding mode control. The obtained results show good performances in term of harmonic disturbances rejection.