Active sliding mode control of vibration in a class of nonlinear system

Based on the theory of sliding mode control, the active control of vibration in a class of nonlinear system with multi-degrees of freedom under disturbance forces is studied. The sliding control law is derived from reaching conditions of sliding mode. The estimated upper bound of the magnitude of disturbance force is adopted to eliminate uncertainties of control law due to unmeasurable disturbance forces. The sliding surface is designed by the H_∞ optimal control theory. Simulation results show that vibration amplitudes of the controlled and uncontrolled degrees of freedom can be greatly reduced by using the proposed control strategy, especially in the case that disturbance forces meet the matching condition.