Research on time-delay-dependent H ∞ /H 2 optimal control of magnetorheological semi-active suspension with response delay

Considering the influence of the magnetorheological damper response time delay on the low-frequency vibration (body vibration) and multi-objective control requirements of the semi-active suspension system, a novel H ∞ / H 2 controller (time-delay-dependent H ∞ / H 2 optimal controller) is proposed in this paper. Based on the Lyapunov–Krasovskii function and robust control theory, a time-delay-dependent H ∞ / H 2 controller in consideration of the MR damper response time delay is designed to reduce and remove the effects of time delay on the semi-active suspension system. To obtain better suspension control performances, the optimal selection strategy of anti-interference coefficients in the time-delay-dependent H ∞ / H 2 controller is proposed. Then, the time-delay-dependent H ∞ / H 2 optimal controller is structured built on the optimal selection strategy. With the application of matrix properties and the cone-compensation linearization algorithm, the nonlinear matrix inequality for controller design is linearized, and the feedback gain matrix of the controller is solved iteratively. Finally, comparative simulation and experimental research are conducted to verify the effectiveness and superiority of the designed optimal controller.