Research On Invariant Points Dynamics And Control Of Vehicle Suspension Mechanical Impedance

The suspension system is a multi-body mechanical system,composed of mass,damper,spring,which transmits the force and moment between the vehicle body and wheels,isolates vibration against the ground,and guarantees smooth drive.A quarter car model can be simplified as a two-degree-of-freedom mechanical vibration system under a specific condition for researching ride comfort.The mechanical system's response,which contains the massdamper-spring,is named the mechanical impedance by impedance analogy with the electrical system.As a typical mechanical system,the suspension system could somehow present the properties of mechanical impedance,which is the mechanical system's inherent property.The impedance property reflects the transfer characteristics of the input force and the kinetical parameters of the suspension.Attention would normally be paid to the sprung mass acceleration,suspension deformation as well as tire deformation,as the impedance invariant points would exist in the properties of the three indexes.It is aimed to reveal the mechanism of invariant points,analyze the influence of invariant points against the suspension performance and the influence between the suspension parameters in the current thesis work.The law of the process to the invariant points how comes into being is revealed.The method of designing suspension is introduced into the area of the semi-active suspension by the theory of the invariant points,and both design methodology of the passive suspension and semi-active suspension come together.All-state feedback impedance control is proposed for the improvement of ride comfort and road holding based on the suspension mechanical impedance characteristics.The functional behavior and power economy of the active suspension are developed under the all-state feedback impedance control.The following research will be conducted through these three aspects based on the matters just mentioned:1.Modelling and analysis of non-dimensional mechanical impedance invariant points of passive suspensionIn the passive suspension,the response of the spring-mass acceleration,suspension deformation,as well as the tire deformation against the road excitation is called acceleration impedance and displacement impedance.The invariant points that the damper does not affect appear on the amplitude-frequency curve of the spring-mass acceleration,suspension deformation,and tire deformation.The mathematical function of the invariant points is derived from the aspect of the impedance matrix.The affection of the invariant points on the suspension property is also analyzed as well as the mechanism of invariant points.The nondimensional parameters,stiffness ration,and mass ration are introduced firstly.The impedance invariant points mathematical modelings are derived and corrected further based on the modification of the approximation of invariant points function with the guide of the Jason inequation.The non-dimensional impedance invariant points theory is proposed based on the work above.The non-dimensional parameters could depict the relationship between the codimensional parameters and the impedance matrix coupled with the mass-damper-stiffness parameters,which could reflect the effect of the suspension parameters on the mechanical impedance characteristics.The non-dimensional parameters simplify the expression of the complex function of the traditional suspension invariant points directly and are also helpful for the mechanism analysis of the negative effects of the unsprung-mass,and are helpful for the suspension design and control plant of the distributed drive electric vehicle.The introduction of non-dimensional parameters would reflect the suspension property itself directly and the effect on each other between the suspension parameters by the nondimensional parameters changing.It is the linear relationship between the variable nondimensional parameters and the properties of the invariant points.The vector curve is proposed because of the convenience for calculation factually.It is also helpful for estimating the amplitude-frequency parameters of the invariant points at the actual work of chassis adjusting.2.The semi-active suspension mechanical impedance invariant points dynamics mechanism and control mechanism analysisIn the semi-active suspension,it also exists the mechanical impedance invariant points characteristics as the passive suspension invariant points.The impedance invariant points also would appear when the damper changes under some conditions.When the condition changes accordingly,the suspension would achieve a better attenuation performance.The essence of the impedance invariant points of the semi-active suspension is the change of the effective damper.The effective damper reflects the suspension's impedance characteristics that could work normally after the adjustable part of the shock absorber fails.Based on an effective damper's characteristics,this paper tries to put forward the concept of "damping ellipse".The position of the point on the damping ellipse reflects the essence of the damping shock absorber's performance and the damping relationship between passive suspension and semiactive suspension;The concept of shaft length reflects the relationship between the change of effective damper and the generation of invariant points.The damping ellipse reveals the essential relationship between passive suspension and semi-active suspension damper changes.At the same time,the concept of the effective damper reveals the inherent law formed by the constant points of suspension and semi-active suspension impedance,and the unified explanation of the passive and semi-active suspension invariant points mechanism is pointed out.The movement of the point on the damper ellipse depicts the optimization of the damping coefficient and also points out the law of the semi-active suspension performance varying with the variable damper coefficient.3.The active suspension property and invariant points characteristics performance under all-state feedback impedance controlBased on the research on the impedance invariant points and control law of passive and semi-active suspension,further research on impedance invariant points and all-state feedback impedance control property of active suspension will be conducted later.Impedance control is a fraction of flexible control,which is widely used in robotics.After analyzing the mechanism of impedance invariant points of suspension,feedback of impedance parameters is tentatively introduced into suspension control to obtain a flexible interaction between spring-mass of suspension and ‘environment'.According to the principle of impedance control,unsprung mass and virtual environment can be regarded as ‘environment interaction' which is parallel to the physical environment,and then an all-state feedback impedance control method could be designed.The impedance state of spring-mass is selected as feedback information and therefore the all-state feedback impedance control method obtained model-free modeling and parameter adjustment.Compared with the LQR controller,the all-state feedback impedance control is free from the requirements of precise modeling and parameters of the road.The proposed controller could achieve the same performance compared with the LQR controller,while it would behave much better than that of LQR at some special frequency,and the impedance control achieves a more balanced power distribution in power consumption,especially the instantaneous peak power consumption reduces by 32% compared with the LQR control and deepens the research of active suspension into the direction of the energy consumption economy.Based on the superiority of all-state feedback impedance control,the transfer function of the active suspension time-varying system is deduced by an approximate transfer function,and then the influence of the suspension parameters and impedance control parameters on the impedance invariant points in the impedance characteristic of the active suspension is studied.Both simulation and test results show that impedance control can effectively improve the performance of the suspension and realize the economy of power consumption.Suspension mechanical impedance reflects the coupling characteristic between the suspension self parameters and the road condition.The mathematical model of the invariant points and the numerical simulation of the contact characteristic are modeled and analyzed,the all-state feedback impedance control is proposed based on the results above.The passive mechanical impedance invariant points dynamics mechanism,the unified law of the passive and semi-active suspension,and the function optimization and power economy are all researched.