Stability Analysis Of Time-delay System And Its Application In ISD Semi-active Suspension Control Strategy

The stability problem of time-delay systems is a fundamental theoretical problem in the field of control and an open problem that is clearly recognized internationally.Time-delay phenomenon exists in all kinds of engineering systems and is one of the main causes of system instability.Therefore,exploring the full time-delay stability condition and the time-delay dependent stability condition of the system plays a theoretical role in guiding the design of control strategy.The performance of traditional semi-active suspension is obviously affected by time delay,and there is a possibility of "wheel jump".The ISD semi-active suspension composed of "inerter,spring and damping" shows better low-frequency vibration suppression effect due to the introduction of inertial element.However,due to the control involved,the time-delay instability risk cannot be ignored.Therefore,it is of significant engineering value and practical significance how to apply frequency domain analysis method to accurately study the time-delay vibration mechanism of such new suspension and design the control strategy accordingly.Firstly,based on the semi-active control mechanism,the reasons for the time delay were analyzed,and the dynamic models with time delay of the traditional semi-active suspension and ISD semi-active suspension were established.The stability conditions without time delay were obtained by Routh criterion.Based on the characteristics of the model,the stability switching theory and polynomial discriminant theory were used to derive the time-delay stability conditions for two types of suspension systems with delay.The stability and performance analysis of sinusoidal and random pavements with different response time delays were carried out to reveal the dynamic corresponding relationship among the inerter coefficient,controllable damping and minimum critical time delay,and the influence of time delay on the performance indexes of the two types of suspension under different stable states was explored.Reasonable use of time delay can improve the ride comfort of the vehicle in the stable state with full time delay.The control concept of real-time switching damping is proposed for the time-delay dependent instability.Secondly,the three parameters of PID control were iteratively optimized by particle swarm optimization algorithm(PSO)combined with the root mean square values of the three performance indexes of the suspension.Considering the existence of response time delay,fuzzy control rules were designed based on the influence characteristics of PID control parameters on the system output to realize the intelligent control of the initial parameters.The damping switching control strategy is designed according to the response law of controllable damping and minimum critical delay and the adjusting range of controllable damping with full delay to realize the effective correction of the output force of fuzzy PID control.Under the random road input,compared with the passive control,the fuzzy PID damping switching controller based on PSO optimization can significantly improve the ride comfort of the vehicle and the low-frequency resonance phenomenon,thus realizing the improvement of the comprehensive performance of the suspension under the condition of small delay.Finally,in the case of considering damping viscoelasticity,fractional derivative is introduced to model the ISD semi-active suspension with adjustable damping with time delay.Based on the variable substitution,the stability criterion of fractional suspension system without time delay is derived and the time-delay stability condition of fractional ISD semi-active suspension system is investigated by using the Gao-Zhe method.The sinusoidal road input was selected for stability verification and compared with the integer-order system to reveal the influence law of nonlinear factors on the adjustment range of stable controllable damping with full time delay and the minimum critical time delay,which provides theoretical support for subsequent research.To sum up,this paper applies frequency domain analysis method to study the timedelay stability of integer order ISD semi-active suspension system and fractional order ISD semi-active suspension system respectively.A fuzzy PID damping switching control strategy based on PSO optimization was designed to solve the instability caused by time delay and to effectively suppress the low frequency vibration.In the absence of time delay and small delay,the vibration isolation performance of the vehicle can be greatly improved,which has good practical application value.