Time-delayed feedback control of vehicle suspension system based on state transformation

Vehicle active/semi-active suspension is added with control force by actuators based on vehicle driving condition to achieve the purpose of improving vehicle ride comfort and safety. However, time delay is inevitable in control system because of the factors such as signal acquisition, transmission, controlling calculation and actuator actuation. It is found that time delay has a great influence on system control and even can lead to the system instability and divergence. In order to improve the ride comfort and stability of the vehicle, and study the effect of time delay compensation control in the suspension system, 2 degrees of freedom vehicle semi-active suspension system is established based on the suspension system of Sail sedan in this paper. And a time-delayed feedback controller is designed. Moreover, the method of combining theory and experiment is used to study the characteristics of the system with time-delayed feedback control. Firstly, a dynamic model of suspension system with time delay is established. The stability of the system is analyzed by the ordinary differential theory and polynomial discrimination method. According to this method, the time delay stable interval (0, 0.0143 s) of the system is got under the feedback gain obtained by the classic quadratic optimal control. The simulation results show that the system remains stable when the inherent time delay is 0.01 s, and when the inherent time delay is 0.0143, 0.05 or 0.065 s, the system is unstable and diverges after control. And the amplitude frequency characteristic curve of the system can also explain this phenomenon. So the results of the theoretical analysis are verified by the simulation calculation. In a word, when the time delay of the system exceeds the critical delay, the qualitative features of the suspension system with time delay may be changed and become unstable and divergent under the classic quadratic optimal control. And the structure of the system will be damaged in this time. In order to ensure the stability of the system, the state transform method and optimal control theory are applied to design the optimal time-delayed feedback controller. The controller can not only guarantee the stability of the system, but also improve the damping characteristics of the system. It can be seen that the most important evaluation index, i. e. the amplitude of the spring mass acceleration, decreases from 2.70 to less than 1.50 m/s2 when comparing the simulation results under time-delayed feedback control with the uncontrolled results. When the inherent time delay in the system is 0.065 s, the amplitude of the spring mass acceleration is about 1.40 m/s2. It is noted that the amplitude of the spring mass acceleration decreases by 48.15% compared with passive control. Therefore, the damping performance of the suspension system is improved effectively with time delayed feedback control, and the time-delayed feedback controller designed through integral transformation is very reasonable and effective. Finally, in order to verify the reliability of the analysis in this paper, a suspension time delay control platform is designed and assembled. Then the experimental results are compared with the simulation results under the same working conditions to verify the effectiveness of the results. In the experiment, the inherent delay of the suspension system is divided into 2 parts. One is the time lag of the signal from the acquisition to the time point before input into magneto rheological damper and it can be identified based on time domain signal. The other is the reaction delay of the actuator. Hence, the inherent time delay of the system measured is approximately equal to 0.065 s. It is found from the experiment that the experimental results and simulation results are stable, and the experimental results are slightly larger than the simulation results, but the error is less than 15%, which meets the engineering requirements. It indicates that the research is highly reliable. It provides an effective control method for suspension damping, and has a great value in engineering application. © 2018, Editorial Department of the Transactions of the Chinese Society of Agricultural Engineering. All right reserved.