CN105260530A - Modeling method for magneto-rheological damper inverse model and application thereof - Google Patents

Abstract

The present invention discloses a modeling method for a magneto-rheological damper inverse model and application thereof. The modeling method is characterized by deriving a mathematical expression of the magneto-rheological damper inverse model on the basis of a transformation model of a Bouc-Wen model, and establishing a correspondence relationship among an excitation current of a magneto-rheological damper, a controllable damping force, a relative offset of the damper and a relative speed of the damper. A control circuit of the magneto-rheological damper inverse model comprises an implementation circuit of the magneto-rheological damper inverse model, a magneto-rheological damper driving circuit and the magneto-rheological damper, which cooperatively constitute a closed-loop control system of the magneto-rheological damper. According to the modeling method for the magneto-rheological damper inverse model and the application thereof, which are disclosed by the present invention, the modeling process of the magneto-rheological damper inverse model can be simplified, and an error of the damping force of the magneto-rheological damper, which is caused by an inherent non-linear hysteresis characteristic, is reduced, so that control precision of the damping force is improved.

Description

A kind of modeling method of MR damper inversion model and application thereof

Technical field

The present invention relates to vibration control field; Specifically a kind of modeling method and application thereof being applied in the MR damper inversion model in vibration/shock control system as half active actuators.

Background technology

MR damper, a kind of half active actuators part based on magnetic rheology effect, there is the advantages such as energy consumption is low, fast response time, structure simple, damping force continuously adjustabe, be the ideal device implementing semi-active control, be used widely in various vibration/shock control system.But the strong nonlinearity hysteresis characteristic that MR damper is intrinsic, makes MR damper accurate mathematical model and corresponding control system be difficult to set up, brings very large difficulty to the accurate control of the damping force of MR damper.

At present, the inversion model of MR damper mainly contains polynomial expression inversion model and neural network contrary modeling.ChoiS.B. wait and to be divided into by MR damper speed-damping force curve forward to accelerate to accelerate two parts with negative sense carrying out fitting of a polynomial respectively, establish MR damper polynomial expression inversion model.ChangCC etc. are with the displacement of damper, voltage and damping force for input variable, and voltage is output variable, establish MR damper neural network contrary modeling.Wang Daihua etc. generate emulated data as data sample on Bouc-Wen model basis, utilize radial neural network to construct radial neural network reversed model.But polynomial expression inversion model is set up on lot of experimental data basis, and precision is relatively low; Neural network contrary modeling precision is very high, and modeling process is complicated, and the development difficulty of controller is larger.

Chinese invention patent " a kind of controllable current-inducing power supply " publication number: 11789639A discloses a kind of controllable current source induction power supply, in control cycle, the bypass loop of controlled rectification circuit and commutating circuit alternation, control signal regulates the ON time ratio of bypass loop and commutating circuit.This controllable current-inducing power supply output voltage stabilization, adaptable to different loads and current in wire size.Chinese invention patent " a kind of output current controllable current source ", publication number: 1418432A disclose a kind of output current controllable current source, by fundamental current generation unit and fundamental current copy cell, obtain constant electric current to export, improve the output current range of adjustment of current source.Chinese invention patent " a kind of current driver based on BUCK circuit ", publication number: 14276A disclose a kind of current driver based on BUCK circuit, be applicable to different input voltage environment, according to output maximum current and pull-up resistor, the adjustment BUCK loop input voltage upper limit, obtains different maximum output currents.But the above-mentioned current source response time is long, be difficult to the working environment of the quick response adapting to MR damper, specific aim is not strong.

Summary of the invention

The present invention is the weak point for avoiding existing for above-mentioned prior art, a kind of modeling method and application thereof of MR damper inversion model are provided, to the modeling process of MR damper inversion model can be simplified, the error that the damping force reducing MR damper causes due to intrinsic strong nonlinearity hysteresis characteristic, thus the control accuracy improving damping force.

The present invention is that technical solution problem adopts following technical scheme:

The modeling method of a kind of MR damper inversion model of the present invention, be applied in the transformation model based on Bouc-Wen model, the mechanical structure of the described transformation model based on Bouc-Wen model is after being connected with the first damping element by hysteresis element, is formed in parallel respectively with flexible member and the second damping element; The described transformation model based on Bouc-Wen model is described by formula (1), formula (2) and formula (3):

$\stackrel{\·}{y}=\frac{\mathrm{\α}z}{c_1}---\left(1\right)$

$\stackrel{\·}{z}=\mathrm{\ρ}(-\mathrm{\σ}|\stackrel{\·}{x}-\stackrel{\·}{y}\left|z\right|z{|}^{n-1}-\left(1-\mathrm{\σ}\right)\left(\stackrel{\·}{x}-\stackrel{\·}{y}\right)|z{|}^n+(\stackrel{\·}{x}-\stackrel{\·}{y}\left)\right)---\left(2\right)$

$F=c_0\stackrel{\·}{x}+\mathrm{\α}z+k_{0}x+f_0---\left(3\right)$

In formula (1), virtual state variable is represented respectively with z; α represents the Steinmetz's constant of described MR damper; c ₁represent described first ratio of damping;

In formula (2), represent the differential of virtual state variable z; ρ, σ and n are respectively the described magnetic hysteresis factor based on the transformation model of Bouc-Wen model; represent the relative velocity of described MR damper;

In formula (3), F represents the controllable damping force of described MR damper; c ₀represent described second ratio of damping; k ₀represent the stiffness coefficient of described MR damper; X represents the relative displacement of described MR damper; f ₀represent the initial displacement elastic force of described MR damper; Be characterized in that the modeling method of described MR damper inversion model is carried out as follows:

Step 1, formula (4), formula (5) and formula (6) is utilized to obtain the k moment respectively, the first ratio of damping c of described MR damper ₁(k), the second ratio of damping c ₀(k) and Steinmetz's constant α (k):

c ₁(k)＝cI(k)+d(4)

c ₀(k)＝aI(k)+b(5)

α(k)＝eI(k)+f(6)

In formula (4), formula (5) and formula (6), I (k) represents the exciting current of MR damper described in the k moment, c and d represents described first ratio of damping c respectively ₁the fitting coefficient of (k) and described exciting current I (k); A and b represents described second ratio of damping c respectively ₀the fitting coefficient of (k) and described exciting current I (k); E and f represents the fitting coefficient of described Steinmetz's constant α (k) and described exciting current I (k) respectively;

Step 2, formula (4) and formula (6) are substituted into formula (1), vertical (2) in parallel, obtain virtual state variable z (k) in k moment; Virtual state variable z (k) in described k moment is approximately the virtual state variable z (k+1) in k+1 moment;

Step 3, formula (3) is transformed to formula (7), the more approximate Steinmetz's constant α (k+1) obtained such as formula the k+1 moment shown in (8):

$\mathrm{\α}\left(k\right)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z\left(k\right)}---\left(7\right)$

$\mathrm{\α}(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z(k+1)}---\left(8\right)$

Step 4, formula (8) is substituted into formula (6), thus obtains the exciting current I (k+1) of MR damper described in the k+1 moment:

$I(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0-z(k+1)f}{ez(k+1)}---\left(9\right)$

Formula (9) represents the relational expression of the exciting current of described MR damper and controllable damping force, relative displacement and relative velocity; With described relational expression, described MR damper inversion model is described.

The feature of the realizing circuit of a kind of MR damper inversion model of the present invention comprises: the first analog to digital converter, the second analog to digital converter, controller, digital to analog converter and displacement transducer;

Receive the controllable damping force F of outside input by described first analog to digital converter and pass to described controller;

Transmitted the relative displacement x of described MR damper by institute's displacement sensors to described second analog to digital converter, and by described second analog to digital converter, described relative displacement x is passed to described controller;

Described controller carries out differential process according to received relative displacement x, obtains the relative velocity of described MR damper , then according to received controllable damping force F and described relative velocity with relative displacement x, utilize formula (9) to calculate the exciting current I obtaining described MR damper, and described exciting current I is passed to described digital to analog converter;

Described exciting current I is converted to corresponding control voltage U and exports by described digital to analog converter.

The feature of the control circuit of a kind of MR damper of the present invention inversion model comprises: the realizing circuit of described MR damper inversion model, MR damper driving circuit and MR damper;

Described MR damper driving circuit comprises: pulse-width modulation signal generating circuit, amplifying circuit, protection circuit, current output circuit and feedback circuit;

The control voltage U that the realizing circuit that described pulse-width modulation signal generating circuit receives described MR damper inversion model exports also passes to described amplifying circuit after being converted to the controlled pulse-width signal of dutycycle;

Described amplifying circuit passes to described current output circuit after described pulse-width signal being carried out amplification process;

Described protection circuit is for absorbing the peak voltage of power tube in described current output circuit;

Described current output circuit exports exciting current according to amplifying the pulse-width signal after processing and is supplied to described MR damper;

The exciting current that described current output circuit exports is passed to described pulse-width modulation signal generating circuit by described feedback circuit;

Described pulse-width modulation signal generating circuit adjusts the dutycycle of described pulse-width signal according to received exciting current, thus realizes the closed-loop control to described exciting current.

Compared with the prior art, beneficial effect of the present invention is embodied in:

1, when the variation model that the present invention is based on Bouc-Wen model describes MR damper characteristic, the parameter that relative and other models adopt is less, reduce the parameter redundancy of transformation model, but describing precision in the strong nonlinearity hysteresis characteristic that MR damper is intrinsic does not reduce; The expression formula degree of coupling characterizing MR damper characteristic is low, and numerical solution easy to use tries to achieve the expression formula of the inversion model of MR damper, thus simplifies the modeling process of MR damper inversion model;

2, the present invention is based on the strong nonlinearity hysteresis characteristic that the variation model Efficient Characterization of Bouc-Wen model MR damper is intrinsic, thus reduce the nonlinearity erron of MR damper controllable damping force, MR damper Inverse Model Control device utilizes numerical method solution differential equation group, the precision of exciting current control signal needed for MR damper can be controlled under not considering the model error situation based on the variation model of Bouc-Wen model itself, improve the control accuracy of the controllable damping force of MR damper, realize best vibration control;

3, the realizing circuit structure of MR damper inversion model of the present invention is simple, is convenient to the miniaturization of controller and integrated, thus reduces controlling cost of MR damper.

Accompanying drawing explanation

Fig. 1 is the realizing circuit schematic diagram of MR damper inversion model system in the present invention;

Fig. 2 is MR damper inversion model realizing circuit middle controller workflow diagram in the present invention;

Fig. 3 is MR damper inversion model Systematical control schematic diagram in the present invention;

Fig. 4 is pulse-width modulation signal generating circuit schematic diagram in MR damper driving circuit in the present invention;

Fig. 5 is current output circuit schematic diagram in MR damper driving circuit in the present invention;

Fig. 6 is the schematic diagram of the transformation model of MR damper in prior art.

Embodiment

In the present embodiment, a kind of modeling method of MR damper inversion model and application thereof, comprise the control circuit of the modeling method of MR damper inversion model, the realizing circuit of inversion model and inversion model.MR damper inversion model sets up the mathematic(al) representation of MR damper inversion model on the basis of the transformation model of Bouc-Wen model, set up MR damper exciting current and controllable damping force, corresponding relation between relative displacement and speed, the magnetic hysteresis reducing MR damper controllable damping force and damper relative displacement and relative velocity affects.MR damper inversion model in semi-active control aystem based on magnetorheological damping performer and control circuit thereof are carried out integration packaging, not only can simplify the semi-active control aystem based on MR damper, and there is efficient, accurate execution performance.

MR damper is linear reciprocating damper, is made up of piston rod, field coil, magnetic flow liquid, barrel and compensation air bag.A kind of modeling method of MR damper inversion model, be applied in the transformation model based on Bouc-Wen model, based on the transformation model of Bouc-Wen model mechanical structure as shown in Figure 6, be after being connected with the first damping element by hysteresis element, be formed in parallel with flexible member and the second damping element respectively; Hysteresis element is connected with damping element and is described the hysteresis characteristic of damper, and flexible member describes the elastic property of damper, and damping element describes the damping characteristic of damper.Transformation model based on Bouc-Wen model is described by formula (1), formula (2) and formula (3):

$\stackrel{\·}{y}=\frac{\mathrm{\α}z}{c_1}---\left(1\right)$

$\stackrel{\·}{z}=\mathrm{\ρ}(-\mathrm{\σ}|\stackrel{\·}{x}-\stackrel{\·}{y}\left|z\right|z{|}^{n-1}-\left(1-\mathrm{\σ}\right)\left(\stackrel{\·}{x}-\stackrel{\·}{y}\right)|z{|}^n+(\stackrel{\·}{x}-\stackrel{\·}{y}\left)\right)---\left(2\right)$

$F=c_0\stackrel{\·}{x}+\mathrm{\α}z+k_{0}x+f_0---\left(3\right)$

In formula (1), virtual state variable is represented respectively with z; α represents the Steinmetz's constant of MR damper; c ₁represent the first ratio of damping;

In formula (2), represent the differential of virtual state variable z; ρ, σ and n are respectively the magnetic hysteresis factor of the transformation model based on Bouc-Wen model; represent the relative velocity of MR damper;

In formula (3), F represents the controllable damping force of MR damper; c ₀represent the second ratio of damping; k ₀represent the stiffness coefficient of MR damper; X represents the relative displacement of MR damper; f ₀represent the initial displacement elastic force of MR damper;

ρ, σ, n, c ₀, c ₁, k ₀, f ₀parameter identification acquisition is carried out, for specific MR damper ρ, σ, n, k by the experimental data of MR damper with α ₀and f ₀for definite value, n=1 in the present embodiment, has nothing to do with MR damper exciting current size, c ₀, c ₁with the linear function that α is MR damper exciting current, change along with exciting current change.Experimental data is by MR damper being arranged on exciting stand, apply sinusoidal displacement excitation signal, the electric current that the field coil of damper applies different amplitude is obtained simultaneously, the size that parameter identification and data fitting obtain the parameters in transformation model is carried out to the controllable damping force data of many group dampers.Concrete grammar is with reference to journal article Principleandvalidationofmodifiedhystereticmodelsformagne torheologicaldampers [J]. (SmartMaterialsandStructures, 2015,24 (8): 085014.)

A kind of modeling method of MR damper inversion model is carried out as follows:

Step 1, formula (4), formula (5) and formula (6) is utilized to obtain the k moment respectively, the first ratio of damping c of MR damper ₁(k), the second ratio of damping c ₀(k) and Steinmetz's constant α (k):

c ₁(k)＝cI(k)+d(4)

c ₀(k)＝aI(k)+b(5)

α(k)＝eI(k)+f(6)

In formula (4), formula (5) and formula (6), I (k) represents the exciting current of k moment MR damper, c and d represents the first ratio of damping c respectively ₁the fitting coefficient of (k) and described exciting current I (k); A and b represents the second ratio of damping c respectively ₀the fitting coefficient of (k) and exciting current I (k); E and f represents the fitting coefficient of Steinmetz's constant α (k) and exciting current I (k) respectively;

Be under the original state of zero at k, order: the exciting current I (0) of MR damper is zero, obtains the first ratio of damping c of original state MR damper respectively ₁(0), the second ratio of damping c ₀and Steinmetz's constant α (0) (0):

c ₁(0)＝d

c ₀(0)＝b

α(0)＝f

Step 2, formula (4) and formula (6) are substituted into formula (1), vertical (2) in parallel, use classical quadravalence Runge-Kutta numerical solution, obtain virtual state variable z (k) in k moment; When the size of double calculating z (k) is within the scope of accuracy requirement, virtual state variable z (k) in k moment is approximately the virtual state variable z (k+1) in k+1 moment;

Step 3, formula (3) is transformed to formula (7), the more approximate Steinmetz's constant α (k+1) obtained such as formula the k+1 moment shown in (8):

$\mathrm{\α}\left(k\right)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z\left(k\right)}---\left(7\right)$

$\mathrm{\α}(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z(k+1)}---\left(8\right)$

Step 4, formula (8) is substituted into formula (6), thus obtains the exciting current I (k+1) of k+1 moment MR damper:

$I(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0-z(k+1)f}{ez(k+1)}---\left(9\right)$

Formula (9) represents the relational expression of the exciting current of MR damper and controllable damping force, relative displacement and relative velocity; With relational expression, described MR damper inversion model is described.

A realizing circuit for MR damper inversion model, as shown in Figure 1, comprising: the first analog to digital converter, the second analog to digital converter, controller, digital to analog converter and displacement transducer;

Receive the controllable damping force F of outside input by the first analog to digital converter and pass to controller;

Transmitted relative displacement x to the second analog to digital converter of MR damper by displacement transducer, and by the second analog to digital converter, relative displacement x is passed to controller;

Controller carries out differential process according to received relative displacement x, obtains the relative velocity of MR damper , then according to received controllable damping force F and relative velocity with relative displacement x, utilize formula (9) to calculate the exciting current I obtaining MR damper, and exciting current I is passed to digital to analog converter;

Exciting current I is converted to corresponding control voltage U and exports by digital to analog converter.

Controller software program circuit, as shown in Figure 2, because controller relates to many control modules, initial period needs to arrange various control register; Meanwhile, define multiple variable in the controller, need to define and initialization it.Cycle interruption is adopted to carry out acquisition and processing to data point in this example.After initialization is carried out to timer, start timer, wait for down trigger.When down trigger, obtain controllable damping force and damper relative shift signal, and controllable damping force and damper relative displacement signal are carried out computing by above-mentioned algorithm obtain damper exciting current control voltage signal, control voltage signal is after digital-to-analog conversion, access MR damper driving circuit, provides the exciting current needed for MR damper, after completing this process, etc. triggering again to be interrupted, realize the process to next group data point.

A control circuit for MR damper inversion model, comprising: the realizing circuit of MR damper inversion model, MR damper driving circuit and MR damper, its MR damper inversion model Systematical control schematic diagram, as shown in Figure 3, the realizing circuit of MR damper inversion model receives controllable damping force signal F and damper relative displacement x, required exciting current control signal U is exported after the inversion model of controller calculates, MR damper driving circuit receives the exciting current control signal U that damper inversion model realizing circuit exports, the voltage control signal U of exciting current is changed into actual exciting current and exports by MR damper driving circuit, be linked into MR damper, exciting current needed for MR damper is provided.

MR damper driving circuit comprises: pulse-width modulation signal generating circuit, amplifying circuit, protection circuit, current output circuit and feedback circuit;

Pulse-width modulation signal generating circuit, as shown in Figure 4, the control voltage U that the realizing circuit receiving MR damper inversion model exports also passes to amplifying circuit after being converted to the controlled pulse-width signal of dutycycle; The exciting current control voltage U of the realizing circuit output of MR damper inversion model is through signal condition, access pulse-width signal generation chip (as Tl494 chip etc.), parallel filtering electric capacity between chip controls voltage signal inputs and ground simultaneously, the electrochemical capacitor response time is longer, inapplicable working environment herein, here electric capacity adopts polarity free capacitor, and eliminate the shake of control signal, the larger effect of capacitance is better; Pulse-width signal produces the controlled pulse-width signal of chip Parallel opertation dutycycle, and chip 15,16 pin is for comparing input positive and negative terminal, and 15 pin connect 5V reference voltage, and 16 pin connect feedback voltage signal, thus realize the dutycycle of pulse-width signal.

Amplifying circuit, is made up of power amplifier chip (as IR2111 chip etc.) and filter capacitor, passes to current output circuit after pulse-width signal being carried out amplification process; Power amplifier chip amplifies its driving force, the pulse-width signal identical by the output terminal output duty cycle of power amplifier chip after receiving pulse-width signal, controls the turn-on and turn-off time of power tube in current output circuit.

Protection circuit is used for the peak voltage of power tube in Absorption Current output circuit; by buffer resistance, buffer capacitor connect after and fast recovery diode compose in parallel; when in current output circuit, power tube turns off; in major loop wiring, the existence of inductance and HF switch produce very large peak voltage; power tube drain-source extremely oppositely safe voltage may be exceeded after this peak voltage and direct current supply voltage superposition, cause misleading of power tube.When power tube turns off, fast diode conducting, reduces the duration of charging of buffer capacitor, better absorbs peak voltage; During power tube conducting, fast diode ends, and buffer resistance limits the discharge current of buffer capacitor, reduces the current stress of power tube, the work that guaranteed output pipe is safe and reliable.

Current output circuit, as shown in Figure 5, exports exciting current according to the pulse-width signal after amplifying process and is supplied to MR damper; Comprise power tube, fast recovery diode, sampling resistor, filter inductance and filter capacitor.During power tube conducting, fast recovery diode oppositely ends, filter inductance and filter capacitor charging, store electrical energy, and power tube is operated in linear zone, constant current output; When power tube turns off, fast recovery diode, filter inductance, filter capacitor and load composition continuous current circuit, fast recovery diode forward conduction, the electric energy that filter inductance and filter capacitor release store, there is provided the electric current flowing through load, the alternation of power tube turn-on and turn-off.The pulse-width signal of different duty is input to the grid of power tube, controls the time of power tube turn-on and turn-off, thus realizes the controlled continuously of output current.

The exciting current that current output circuit exports is passed to pulse-width modulation signal generating circuit by feedback circuit; By sampling resistor, the current value that current output circuit exports is converted to voltage signal, utilizes the subtractor circuit of operational amplifier to obtain feedback voltage, feedback voltage is linked into the comparison end of pulse-width signal generation chip, the size of regulation output electric current.When the electric current that current output circuit exports is greater than setting value, pulse-width signal generation chip is the pulse-width signal of zero by output duty cycle after the effect of feedback circuit, and close current exports, and plays the effect of current-limiting protection.

Pulse-width modulation signal generating circuit according to the dutycycle of received exciting current adjustment pulse-width signal, thus realizes the closed-loop control to exciting current.

Claims (3)

1. the modeling method of a MR damper inversion model, be applied in the transformation model based on Bouc-Wen model, the mechanical structure of the described transformation model based on Bouc-Wen model is after being connected with the first damping element by hysteresis element, is formed in parallel respectively with flexible member and the second damping element; The described transformation model based on Bouc-Wen model is described by formula (1), formula (2) and formula (3):

$\stackrel{\·}{y}=\frac{\mathrm{\α}z}{c_1}---\left(1\right)$

$\stackrel{\·}{z}=\mathrm{\ρ}(-\mathrm{\σ}|\stackrel{\·}{x}-\stackrel{\·}{y}\left|z\right|z{|}^{n-1}-\left(1-\mathrm{\σ}\right)\left(\stackrel{\·}{x}-\stackrel{\·}{y}\right)|z{|}^n+(\stackrel{\·}{x}-\stackrel{\·}{y}\left)\right)---\left(2\right)$

$F=c_0\stackrel{\·}{x}+\mathrm{\α}z+k_{0}x+f_0---\left(3\right)$

In formula (1), virtual state variable is represented respectively with z; α represents the Steinmetz's constant of described MR damper; c ₁represent described first ratio of damping;

In formula (2), represent the differential of virtual state variable z; ρ, σ and n are respectively the described magnetic hysteresis factor based on the transformation model of Bouc-Wen model; represent the relative velocity of described MR damper;

In formula (3), F represents the controllable damping force of described MR damper; c ₀represent described second ratio of damping; k ₀represent the stiffness coefficient of described MR damper; X represents the relative displacement of described MR damper; f ₀represent the initial displacement elastic force of described MR damper; Described in its feature, the modeling method of MR damper inversion model is carried out as follows:

Step 1, formula (4), formula (5) and formula (6) is utilized to obtain the k moment respectively, the first ratio of damping c of described MR damper ₁(k), the second ratio of damping c ₀(k) and Steinmetz's constant α (k):

c ₁(k)＝cI(k)+d(4)

c ₀(k)＝aI(k)+b(5)

α(k)＝eI(k)+f(6)

In formula (4), formula (5) and formula (6), I (k) represents the exciting current of MR damper described in the k moment _,c and d represents described first ratio of damping c respectively ₁the fitting coefficient of (k) and described exciting current I (k); A and b represents described second ratio of damping c respectively ₀the fitting coefficient of (k) and described exciting current I (k); E and f represents the fitting coefficient of described Steinmetz's constant α (k) and described exciting current I (k) respectively;

Step 2, formula (4) and formula (6) are substituted into formula (1), vertical (2) in parallel, obtain virtual state variable z (k) in k moment; Virtual state variable z (k) in described k moment is approximately the virtual state variable z (k+1) in k+1 moment;

Step 3, formula (3) is transformed to formula (7), the more approximate Steinmetz's constant α (k+1) obtained such as formula the k+1 moment shown in (8):

$\mathrm{\α}\left(k\right)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z\left(k\right)}---\left(7\right)$

$\mathrm{\α}(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0}{z(k+1)}---\left(8\right)$

Step 4, formula (8) is substituted into formula (6), thus obtains the exciting current I (k+1) of MR damper described in the k+1 moment:

$I(k+1)=\frac{F\left(k\right)-c_0\left(k\right)\stackrel{\·}{x}\left(k\right)-k_{0}x\left(k\right)-f_0-z(k+1)f}{ez(k+1)}---\left(9\right)$

Formula (9) represents the relational expression of the exciting current of described MR damper and controllable damping force, relative displacement and relative velocity; With described relational expression, described MR damper inversion model is described.

2. a realizing circuit for MR damper inversion model, its feature comprises: the first analog to digital converter, the second analog to digital converter, controller, digital to analog converter and displacement transducer;

Receive the controllable damping force F of outside input by described first analog to digital converter and pass to described controller;

Transmitted the relative displacement x of described MR damper by institute's displacement sensors to described second analog to digital converter, and by described second analog to digital converter, described relative displacement x is passed to described controller;

Described controller carries out differential process according to received relative displacement x, obtains the relative velocity of described MR damper again according to received controllable damping force F and described relative velocity with relative displacement x, utilize formula (9) to calculate the exciting current I obtaining described MR damper, and described exciting current I is passed to described digital to analog converter;

Described exciting current I is converted to corresponding control voltage U and exports by described digital to analog converter.

3. a control circuit for MR damper inversion model, its feature comprises: the realizing circuit of described MR damper inversion model, MR damper driving circuit and MR damper;

Described MR damper driving circuit comprises: pulse-width modulation signal generating circuit, amplifying circuit, protection circuit, current output circuit and feedback circuit;

The control voltage U that the realizing circuit that described pulse-width modulation signal generating circuit receives described MR damper inversion model exports also passes to described amplifying circuit after being converted to the controlled pulse-width signal of dutycycle;

Described amplifying circuit passes to described current output circuit after described pulse-width signal being carried out amplification process;

Described protection circuit is for absorbing the peak voltage of power tube in described current output circuit;

Described current output circuit exports exciting current according to amplifying the pulse-width signal after processing and is supplied to described MR damper;

The exciting current that described current output circuit exports is passed to described pulse-width modulation signal generating circuit by described feedback circuit;

Described pulse-width modulation signal generating circuit adjusts the dutycycle of described pulse-width signal according to received exciting current, thus realizes the closed-loop control to described exciting current.