Robustness control for nonlinear systems based on homogeneous prescribed sliding mode control

Abstract

This paper presents a new homogeneous control using dual sliding mode control, and robustness control using linear matrix inequality (LMI) constraints. The controller is applied for the severe disturbance. A sliding surface function, which relates to an exponential function and itself t-norm, is applied to save the energy consumption of the control system. The constraints related LMI are proposed with the matrices and vectors of the systems following the chosen matrices in control the energy for control. Solution of the constraints is also presented with new approach to save the time of calculation. In addition, the proof for the proposed controller is also presented by using the candidate Lyapunov function. In the input control function, the t-norm type is embedded to improve its performance in control disturbance. Besides of the t-norm, the modified sliding surface in the input control is also improve the energy for controlling. The combination of these robustness control elements would bring a new view for the design of control. The advantages of the controller are demonstrated via computer simulation for a seat suspension system. A magneto-rheological fluid seat suspension with its random disturbances is used. To prove the flexibility of the controller, the proposed approach is compared with an existing controller. The compared control has the same structure as shown in the proposed model. However, its design has a disadvantage in control the severe disturbance. The comparison between two controls is a clear view of distinct improvement. The results of simulations show that the controller provides better performance and stability of the system. The stability is also analyzed through the variation of the input control and power spectral density related energy consumption.