| Magnetorheological semi-active suspensions have received extensive commercial and academic attention due to their low energy consumption,fast response,wide adjustment range of force value,and high safety.However,the complex hysteresis behavior of damping force makes the force tracking of the magnetorheological damper still face the problem of low control accuracy.At the same time,when modern general control strategy is applied to the suspension control,too many input variables are needed and some are not readily available.Therefore,the paper extracts strict constraint expressions and builds an accurate reversible model of the magnetorheological damper according to the damping force aggregation characteristics;a three-polar current driver that can provide reverse voltage in time is designed,and combined with the constructed inverse model,the accurate control of the force value tracking of the magnetorheological damper is realized;the dynamic constraints of the suspension system are fully considered in the control laws of LQR and H_∞control,and a dual damping control strategy is derived that is highly equivalent to the LQR and H_∞control and only requires the relative velocity of the suspension and the absolute velocity of the sprung mass.Combined with the force value tracking method based on the inverse model of the magnetorheological damper,the dual damping controller design of the semi-active suspension is realized,which effectively solves the key problems in the control system of the magnetorheological semi-active suspension.To accurately describe the force characteristics of magnetorheological dampers,a reversible model based on sigmoid function is constructed.Firstly,a bench test was carried out on a typical magnetorheological damper.On the basis of analyzing the experimental data of its damping characteristics,the basic model of the magnetorheological damper is constructed by translating and scaling the sigmoid function;then,according to the damping force aggregation characteristics under harmonic excitations,assuming that the damping force at zero speed under constant current has nothing to do with the maximum speed,the constraint relationship between the translation amount of the sigmoid function and the maximum speed is introduced,and the preliminary model of the magnetorheological damper is obtained by combining the constraint relationship with the basic model;finally,the important parameters are selected according to the influence of the parameters of the preliminary model on the damping force,and the relationship between the important parameters and the current are established by coupling the linear function and the exponential function,and a final invertible model with an overall error of 8.62%and only 9 parameters is obtained.To accurately realize the damping force tracking of the magnetorheological damper,an open-loop controller based on the proposed inverse model is designed.Firstly,the motion state of the damper is collected and estimated by the angle sensor and the acceleration sensor;then the current corresponding to the expected damping force is accurately calculated according to the proposed inverse model,and a floating current limiting method based on maximum speed is proposed,which adaptively suppresses the distortion of damping characteristics;subsequently,a three-polarity current driver based on a full-bridge circuit that can switch between positive,zero and negative voltages is designed,and a control method based on PI algorithm for two independent PWM signals is proposed to achieve fast and stable control of the current;the designed open-loop control system is used for bench tests,and it is verified that the controller has high force tracking accuracy when achieving different desired damping characteristics,and analyzes the reason for the system error in the process.To reduce the number of input variables required for typical optimal control(LQR and H_∞control)in suspension control applications,a dual damping control strategy that only needs the relative velocity of the suspension and the absolute velocity of the sprung mass and is equivalent to the optimal control is proposed.The paper takes the single-degree-of-freedom and two-degree-of-freedom suspension models as the objects,and conducts a comprehensive demonstration.Firstly,by combining the control law and its derivative of the typical optimal control with the state equation of the suspension,keeping the relative terms of speed and ignoring the tiny terms,the equivalent relationship between the dual damping control and the optimal control is deduced;then a parameter optimization is proposed to confirm and optimize the accuracy of the equivalence relation;finally,the equivalence of the dual damping control and the LQR or H_∞control in the reasonable parameters range is verified by numerical simulation under random excitation,which shows that the dual damping control based on two input variables can achieve the same control effect as LQR or H_∞control.To verify the effectiveness of the inverse model of the magnetorheological damper,the force tracking method and the dual damping control strategy in the control system of the automobile semi-active suspension,a dual damping controller for the automobile magnetorheological semi-active suspension is designed.The influence of the parameters of the upper-layer dual damping control strategy on the performance index of the suspension is analyzed,and the appropriate parameter values are determined;in the bottom layer implementation,the force value tracking method based on the inverse model of the magnetorheological damper is adopted.The difference between the proposed inverse model and the real magnetorheological damper’s mechanical behavior is reflected by the Spencer positive model,and the Simulink model of the magnetorheological semi-active suspension system is established.Finally,taking random road excitation as an example,the simulation analysis verifies that the proposed suspension control method has good force tracking accuracy and vibration reduction effect.However,the force tracking error of the magnetorheological damper still has a significant impact on the vibration reduction effect of the semi-active suspension.According to the idea of hypothesis deduction,the LQR and H_∞control parameters equivalent to the dual damping control parameters are found in reverse,and it is verified that the dual damping control and the typical optimal control still have good equivalence in the semi-active suspension. |
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