Abstract: A time-delay-dependent H_∞ robust controller considering the response delay of magnetorheological(MR) damper is proposed to solve the negative effect of MR damper response delay on the low frequency vibration control of semi-active suspension control system. The MR semi-active suspension model considering of response time-delay is built, and the time-delay stability of time-delay MR semi-active suspension is analyzed based on Lyapunov-Krasovskii function, the critical time delay for the system is solved by using the cone complementary linearization algorithm. Then a time-delay-dependent H_∞ robust controller considering the response delay of MR damper is designed, the overall response time delay of the MR damper is reduced to be less than the theoretical critical time delay, and the feedback gain of the controller is obtained. Finally, a comparative study of simulation and experiment is carried out, the results show that the time-delay-dependent H_∞ robust controller reduces the peak responses of vehicle body acceleration and wheel dynamic load by 16.4% and 7.4% respectively in compared with the time-delay independent H_∞ robust controller under the bump road excitation, and the wheel grounding performance changes little. Experiment and simulation results validate the effectiveness and superiority of the proposed control method, and provide a theoretical reference for the research of subsequent MR semi-active suspension.

Key words: magnetorheological semi-active suspension, response delay, time-delay-dependent H_∞ robust controller, theoretical critical delay, comparative performance test