Sliding mode control of Lorenz chaotic system of fluid thermal convection between infinite plates based on LMI

Abstract

Aiming at the unpredictability and nonlinearity of the Lorenz chaotic system, this paper takes the fluid thermal convection of the infinite plate as the model, and studies the sliding mode control of the fluid thermal convection of the infinite plate based on LMI. Based on the characteristics of the Lorenz chaotic system, the sliding mode control method is applied to attenuate the effects of some nonlinear factors, and the Lyapunov function is designed to obtain the control law that satisfies the sliding mode conditions. Further, a dynamic compensation algorithm is presented, it can efficiently regulate the poles of a closed-loop system, and ensure that the specific matrix is negative definite. The simulation results show that under the action of the compensator, the dynamic perturbed Lorenz chaotic system has a good state response, which makes the sliding mode control of the Lorenz chaotic system stable.