CN114186473A - Magneto-rheological damper modeling method based on progressive saturation magic formula - Google Patents
Magneto-rheological damper modeling method based on progressive saturation magic formula Download PDFInfo
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Abstract
A magneto-rheological shock absorber modeling method based on a progressive saturation magic formula comprises the following steps: step 1), providing a mechanical characteristic model of a progressive saturation magic formula of the magneto-rheological damper and determining parameters of a forward model; step 2) determining parameters of a reverse mechanical model of the magneto-rheological shock absorber based on a progressive saturation magic formula; wherein, the specific implementation in the step 1) comprises the following steps: step 1.1) testing the mechanical properties of the magnetorheological damper; step 1.2) providing a mechanical characteristic model of a progressive saturation magic formula; step 1.3) determining value ranges of various parameters of a separately fitted progressive saturation magic formula based on different working conditions; 1.4) nonlinear parameter fitting of a peak factor of a progressive saturation magic formula; and 1.5) step by step, satisfying the final determination of each parameter value of the progressive saturation magic formula with the minimum working condition error. The invention enables the newly constructed mechanical property model of the magnetorheological damper to meet the high-precision modeling requirements under different test working conditions.
Description
Technical Field
The invention belongs to the field of magneto-rheological shock absorbers, and particularly relates to a magneto-rheological shock absorber modeling method based on a progressive saturation magic formula.
Background
The magneto-rheological suspension has the advantages of high response speed, controllable damping force, large adjustment range, low energy consumption and the like, and not only attracts researchers' attention, but also gets market acceptance and more extensive development and application. The mechanical properties of the magneto-rheological damper have important influence on the comprehensive performance of the suspension, and an accurate and practical mechanical property model of the magneto-rheological damper is constructed by considering the characteristics of strong nonlinearity, time lag effect, uncertainty and the like of the magneto-rheological damper, so that the accurate control of the magneto-rheological type semi-active suspension is realized.
At present, the mechanical property model of the magnetorheological damper mainly comprises two types: a phenomenological model and a physical model. The image-only model mainly determines the unknown parameters of the model through data obtained by experiments, and the image-only model can be further subdivided into two categories, namely a parametric model and a non-parametric model, wherein the parametric model construction method is widely concerned. Typical parameter models mainly include a Bingham model, a Bouc-Wen model, a hyperbolic tangent function model, a magic formula model and the like. However, the Bingham model often neglects the viscoelastic property of the magnetorheological damper before yielding, so that the nonlinear relation between force and speed when the damper moves at low speed cannot be described; the Bouc-Wen model can only show better hysteresis characteristics of the magnetorheological damper under a single working condition, and related parameters need to be recalculated when the complex and changeable driving working conditions are met, so that the Bouc-Wen model is relatively complex and tedious; although the parameter significance of the hyperbolic tangent model is very clear and the number of the identified parameters is small, the consistency of the fitting parameters under different working conditions is low.
The expression formula of the mechanical characteristic model of the magneto-rheological shock absorber based on the traditional magic formula model is
In the formula FMRThe damping force of the magneto-rheological shock absorber is based on a traditional magic formula; d is the peak factor of the traditional magic formula; c is a traditional magic formula form factor; b is a stiffness factor of a traditional magic formula; e is a curvature factor of the traditional magic formula; k is the stiffness coefficient of the traditional magic formula; c is the viscous damping coefficient of the traditional magic formula; f. of0Is inclined toForce is applied; s is the piston displacement; v is the piston velocity. Compared with other typical models, the traditional magic formula model has the natural advantage of good parameter consistency, but the detailed defects that the fitting accuracy of the hysteresis width of the speed characteristic curve is not high and the speed characteristic curve has a droop phenomenon when the piston speed is higher still exist in the process of fitting the dynamic model of the magnetorheological damper. Therefore, in the process of researching the modeling method of the magneto-rheological shock absorber, how to improve the existing magic formula model to meet the high-precision modeling requirement of the magneto-rheological shock absorber has important research significance.
Disclosure of Invention
The invention provides a magneto-rheological damper modeling method based on a progressive saturation magic formula, aiming at solving the problems that the fitting precision of a traditional magic formula model to the hysteresis width of a speed characteristic curve in the magneto-rheological damper modeling process is not high, and the speed characteristic curve has a droop phenomenon when the piston speed is higher.
In order to achieve the purpose, the modeling method of the magneto-rheological damper based on the progressive saturation magic formula improves the fitting precision of the hysteresis width of the speed characteristic curve by additionally arranging the piston acceleration hyperbolic tangent term on the premise of keeping the natural advantage that a traditional magic formula model has good parameter consistency, and eliminates the droop phenomenon of the speed characteristic curve when the piston speed is higher by using the hyperbolic tangent function to replace the sine function of the original magic formula.
A magneto-rheological shock absorber modeling method based on a progressive saturation magic formula comprises the following steps:
step 1), providing a mechanical characteristic model of a progressive saturation magic formula of the magneto-rheological damper and determining parameters of a forward model;
wherein, the specific implementation in the step 1) comprises the following steps:
step 1.1) testing the mechanical properties of the magnetorheological shock absorber to obtain a damping force-speed curve graph and a damping force-displacement relation curve graph of the magnetorheological shock absorber under different working conditions;
step 1.2) providing a mechanical characteristic model of a progressive saturation magic formula;
in the process of modeling the magneto-rheological damper by adopting a traditional magic formula, the fitting precision of the hysteresis width of the speed characteristic curve is not high, and the speed characteristic curve has the technical problem of sagging phenomenon when the piston speed is higher. In order to overcome the problems, a mechanical property model of a progressive saturation magic formula for describing the mechanical properties of the magneto-rheological damper is provided, the fitting precision of the hysteresis width of a speed characteristic curve is improved by additionally arranging a piston acceleration hyperbolic tangent term, the hyperbolic tangent function is used for replacing a sine function of an original magic formula to eliminate the droop phenomenon of the speed characteristic curve when the piston speed is higher, and the magneto-rheological damper model based on the progressive saturation magic formula is described as follows:
in the formula: f'MRThe damping force of the magneto-rheological shock absorber is based on a progressive saturation magic formula; d' is the peak factor of the progressive saturation magic formula; c' is the progressive saturation magic formula form factor; b' is a stiffness factor of a progressive saturation magic formula; e' is a curvature factor of a progressive saturation magic formula; f is a hysteresis loop width factor of a progressive saturation magic formula; m is an inertia factor of a progressive saturation magic formula; k' is the stiffness coefficient of the progressive saturation magic formula; c' is a viscous damping coefficient of a progressive saturation magic formula; f. of0Is a biasing force; s is the piston displacement; v is the piston velocity; a is the piston acceleration;
step 1.3) determining value ranges of various parameters of a separately fitted progressive saturation magic formula based on different working conditions;
1.4) nonlinear parameter fitting of a peak factor of a progressive saturation magic formula;
step 1.5) of final determination of all parameter values of the gradual saturation magic formula with the minimum working condition error;
and step 2) determining parameters of a reverse mechanical model of the magneto-rheological shock absorber based on a progressive saturation magic formula.
Further, the substep 1.1) also comprises the following steps:
the mechanical property test system of the magnetorheological damper is utilized to test the mechanical property of the magnetorheological damper to be tested, in the test process, an input signal is set to be a sine wave signal, the amplitude of the magnetorheological damper is 50mm, the working control current is 0.5-3A, 0.5A is increased each time, the test frequency is 0.5-2.0 Hz, and 0.5Hz is increased each time; and measuring to obtain a damping force-speed curve graph and a damping force-displacement relation curve graph of the magnetorheological shock absorber under 24 different working conditions.
Still further, the substep 1.3) also comprises the following steps:
based on measured data under different test conditions obtained by a mechanical property test of the magnetorheological damper, and by utilizing an lsqcurvefit tool in MATLAB software, the unknown parameters D ', C ', B ', E ', F, M, k ', C ' and f ' to be fitted in the formula (1) are independently fitted0Fitting values under 24 working conditions; the lsqcurvefit tool performs parameter fitting on the magneto-rheological damper model adopting the progressive saturation magic formula according to a minimum variance algorithm, and satisfies the following conditions:
in the formula:
the output force measured in the mechanical property test of the magnetorheological damper is represented;
comparison of D ', C', B ', E', F, M, k ', C' and f separately0And respectively marking the maximum value and the small value of the numerical value under 24 working conditions as an upper limit threshold value and a lower limit threshold value to obtain each parameter determination range of the gradual saturation magic formula.
Still further, the substep 1.4) also comprises the following steps:
through analysis of mechanical property test data of the magnetorheological damper, the fact that compared with other parameters to be fitted, the peak factor D' of the gradual saturation magic formula fluctuates most obviously along with the change of current under different frequencies, and the parameter consistency under different working conditions is poor in performance is found. In order to further improve the model fitting accuracy of the proposed progressive saturation magic formula, the expression of the peak factor D' of the progressive saturation magic formula needs to be re-expressed,
the expression of the modified peak factor D' of the gradual saturation magic formula is as follows:
D′＝D0+D1I+D2I2 (3)
in the formula: d0、D1And D2Respectively representing a constant term coefficient, a first term coefficient and a second term coefficient of a peak factor of the progressive saturation magic formula; i is exciting current;
substituting formula (3) into formula (1), rewriting magneto-rheological damper damping force F 'based on progressive saturation magic formula'MRExpression:
F′MR＝FMR_i+FMR_0+c′v (4)
in the formula: fMR_iControlled damping force for the magnetorheological shock absorber; fMR_0Indicating other damping forces except the controlled damping force and the base value damping force;
based on the mechanical property test data of the magneto-rheological damper, the fitting value of the D' of the peak factor of the progressive saturation magic formula, which is obtained by independent fitting under different working conditions according to the measured value of the actual exciting current I and the substep 1.3), and the constant term coefficient D of the peak factor of the progressive saturation magic formula is fitted by adopting a minimum variance algorithm0First order coefficient D1And coefficient of quadratic term D2At this time, the calculation expression of the minimum variance algorithm satisfies:
in the formula:
representing the fitting value D' of the peak value factor of the progressive saturation magic formula under 24 groups of working conditions obtained in the step 1.3);
d in magneto-rheological damper model finally determining progressive saturation magic formula0、D1And D2The parameter fit value of (2).
Still further, the substep 1.5) also comprises the following steps:
and finally determining the parameter fitting values of the items of the gradual saturation magic formula on the premise of meeting the minimum error of all working conditions. Various multivariate function optimization methods such as genetic algorithm, annealing algorithm and the like can be adopted to carry out the fitting on the rest unknown parameters C ', B ', E ', F, M, k ', C ' and f in the formula (4-6)0And performing parameter fitting. The method takes a genetic algorithm as an example to implement a final determination process of each parameter value of the asymptotic saturation magic formula which meets the minimum error of all working conditions.
In the parameter fitting process, damping force obtained by testing the magneto-rheological shock absorber under 24 working conditions and the Root Mean Square Error (RMSE) output by the model are used as an optimization target function, and the minimum value of the RMSE function is solved based on a genetic algorithm in the meaning. The RMSE function is calculated as follows:
wherein, i is 1, 2, 3 … 24 and represents the serial numbers of 24 different working conditions in table 1;
calculating upper and lower bound thresholds of various unknown parameters to be fitted according to substep 1.3), and taking the thresholds as C ', B ', E ', F, M, k ', C ' and f0Function of (2) takingUpper and lower limits of the value. According to the implementation steps of a genetic algorithm, the initial population size, the maximum algebra, the cross probability, the mutation probability, the iteration termination condition and the like are sequentially determined, operations such as selection, cross, mutation and the like are implemented on the basis of MATLAB software, and finally, the relation C ', B ', E ', F, M, k ', C ' and f with the minimum RMSE function values are obtained0The fitting parameter value of (1).
Further, the step 2) further comprises the following steps:
the sensor and the corresponding state observer can measure and calculate time-varying piston displacement s, piston velocity v and piston acceleration a, the values and the damping force value required by the magneto-rheological shock absorber are input into a current solver, so that the required exciting current can be calculated,
the current solving formula obtained by inverse solution according to the formula (4-6) meets the following requirements:
wherein y satisfies:
the invention has the following beneficial effects: the model also utilizes the hyperbolic tangent function to replace a sine function of the original magic formula to eliminate the phenomenon of droop of the speed characteristic curve when the piston speed is higher, and reduces the change of mechanical characteristic modeling parameters under different test working conditions.
Drawings
FIG. 1 is a flow chart of a modeling of a magnetorheological damper based on a progressive saturation magic formula.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
As shown in FIG. 1, the modeling method of the present invention is mainly composed of two steps: step 1), providing a mechanical characteristic model of a progressive saturation magic formula of the magneto-rheological damper and determining parameters of a forward model; and step 2) determining parameters of a reverse mechanical model of the magneto-rheological shock absorber based on a progressive saturation magic formula. Wherein, the specific implementation in the step 1) comprises the following steps: step 1.1) testing the mechanical properties of the magnetorheological damper; step 1.2) providing a mechanical characteristic model of a progressive saturation magic formula; step 1.3) determining value ranges of various parameters of a separately fitted progressive saturation magic formula based on different working conditions; 1.4) nonlinear parameter fitting of a peak factor of a progressive saturation magic formula; and 1.5) step by step, satisfying the final determination of each parameter value of the progressive saturation magic formula with the minimum working condition error.
The specific workflow of each step is as follows:
step 1.1) mechanical property test of the magnetorheological damper:
the mechanical property test system of the magnetorheological damper is utilized to test the mechanical property of the magnetorheological damper to be tested, in the test process, an input signal is set to be a sine wave signal, the amplitude of the magnetorheological damper is 50mm, the working control current is 0.5-3A, 0.5A is increased every time, the test frequency is 0.5-2.0 Hz, and 0.5Hz is increased every time. The mechanical property test working conditions of the 24 magnetorheological shock absorbers are shown in table 1.
TABLE 124 test conditions for mechanical properties of magnetorheological shock absorbers
And measuring to obtain a damping force-speed curve graph and a damping force-displacement relation curve graph of the magnetorheological shock absorber under 24 different working conditions.
Substep 1.2) the proposition of the mechanical property model of the progressive saturation magic formula:
in the process of modeling the magneto-rheological damper by adopting a traditional magic formula, the fitting precision of the hysteresis width of the speed characteristic curve is not high, and the speed characteristic curve has the technical problem of sagging phenomenon when the piston speed is higher. In order to overcome the problems, a mechanical property model of a progressive saturation magic formula for describing the mechanical properties of the magneto-rheological damper is provided, the fitting precision of the hysteresis width of a speed characteristic curve is improved by additionally arranging a piston acceleration hyperbolic tangent term, the hyperbolic tangent function is used for replacing a sine function of an original magic formula to eliminate the droop phenomenon of the speed characteristic curve when the piston speed is higher, and the magneto-rheological damper model based on the progressive saturation magic formula is described as follows:
in the formula: f'MRThe damping force of the magneto-rheological shock absorber is based on a progressive saturation magic formula; d' is the peak factor of the progressive saturation magic formula; c' is the progressive saturation magic formula form factor; b' is a stiffness factor of a progressive saturation magic formula; e' is a curvature factor of a progressive saturation magic formula; f is a hysteresis loop width factor of a progressive saturation magic formula; m is an inertia factor of a progressive saturation magic formula; k' is the stiffness coefficient of the progressive saturation magic formula; c' is a viscous damping coefficient of a progressive saturation magic formula; f. of0Is a biasing force; s is the piston displacement; v is the piston velocity; a is the piston acceleration.
Step 1.3) determining the value range of each parameter of a progressive saturation magic formula based on independent fitting under different working conditions:
based on measured data under different test conditions obtained by a magnetorheological damper mechanical property test, each unknown parameter (D ', C ', B ', E ', F, M, k ', C ' and f ' to be fitted in the formula (1) is fitted independently by using an lsqcurvefit tool in MATLAB software0) Fitting values under 24 conditions. The lsqcurvefit tool performs parameter fitting on the magneto-rheological damper model adopting the progressive saturation magic formula according to a minimum variance algorithm, and satisfies the following conditions:
in the formula:
and the output force measured in the mechanical property test of the magnetorheological damper is shown.
Comparison of D ', C', B ', E', F, M, k ', C' and f separately0In the values under 24 working conditions, the maximum and minimum values are respectively recorded as upper and lower threshold values, and the determination ranges of the parameters of the progressive saturation magic formula shown in table 2 are obtained.
Table 2 shows the parameter ranges of the progressive saturation magic formula
Wherein, D'maxAnd D'minUpper and lower bound thresholds for parameter D', respectively; c'maxAnd C'minUpper and lower bound thresholds for parameter C', respectively; b'maxAnd B'minUpper and lower bound thresholds for parameter B', respectively; e'maxAnd E'minUpper and lower bound thresholds for parameter E', respectively; fmaxAnd FminUpper and lower bound thresholds for parameter F, respectively; mmaxAnd MminUpper and lower bound thresholds for parameter M, respectively; k'maxAnd k'minUpper and lower bound thresholds for parameter k', respectively; c'maxAnd c'minUpper and lower bound thresholds for parameter c', respectively; f. of0_maxAnd f0_minAre respectively related to the parameter f0Upper and lower bound thresholds.
Substep 1.4) nonlinear parameter fitting of the peak factor of the progressive saturation magic formula:
through analysis of mechanical property test data of the magnetorheological damper, the fact that compared with other parameters to be fitted, the peak factor D' of the gradual saturation magic formula fluctuates most obviously along with the change of current under different frequencies, and the parameter consistency under different working conditions is poor in performance is found. In order to further improve the model fitting accuracy of the proposed progressive saturation magic formula, the expression of the peak factor D 'of the progressive saturation magic formula needs to be re-expressed, and the expression of the modified peak factor D' of the progressive saturation magic formula is as follows:
D′＝D0+D1I+D2I2 (3)
in the formula: d0、D1And D2Respectively representing a constant term coefficient, a first term coefficient and a second term coefficient of a peak factor of the progressive saturation magic formula; and I is an exciting current.
Substituting formula (3) into formula (1), rewriting magneto-rheological damper damping force F 'based on progressive saturation magic formula'MRExpression:
F′MR＝FMR_i+FMR_0+c′v (4)
in the formula: fMR_iControlled damping force for the magnetorheological shock absorber; fMR_0Indicating the damping forces other than the controlled damping force and the base value damping force.
Based on the mechanical property test data of the magneto-rheological damper, the fitting value of the D' of the peak factor of the progressive saturation magic formula, which is obtained by independent fitting under different working conditions according to the measured value of the actual exciting current I and the substep 1.3), and the constant term coefficient D of the peak factor of the progressive saturation magic formula is fitted by adopting a minimum variance algorithm0First order coefficient D1And coefficient of quadratic term D2At this time, the calculation expression of the minimum variance algorithm satisfies:
in the formula:
representing the fitting value of D' of the peak value factor of the progressive saturation magic formula under 24 groups of working conditions obtained in the substep 1.3).
D in magneto-rheological damper model finally determining progressive saturation magic formula0、D1And D2The parameter fit value of (2).
Substep 1.5) the final determination of the parameter values of all the progressive saturation magic formulas with the minimum working condition errors is met:
and finally determining the parameter fitting values of the items of the gradual saturation magic formula on the premise of meeting the minimum error of all working conditions. Various multivariate function optimization methods such as genetic algorithm, annealing algorithm and the like can be adopted to carry out the fitting on the rest unknown parameters C ', B ', E ', F, M, k ', C ' and f in the formula (4-6)0And performing parameter fitting. The method takes a genetic algorithm as an example to implement a final determination process of each parameter value of the asymptotic saturation magic formula which meets the minimum error of all working conditions.
In the parameter fitting process, damping force obtained by testing the magneto-rheological shock absorber under 24 working conditions and the Root Mean Square Error (RMSE) output by the model are used as an optimization target function, and the minimum value of the RMSE function is solved based on a genetic algorithm in the meaning. The RMSE function is calculated as follows:
wherein, i is 1, 2, 3 … 24 and indicates the serial numbers of 24 different working conditions in table 1.
Calculating upper and lower bound thresholds of various unknown parameters to be fitted according to substep 1.3), and taking the thresholds as C ', B ', E ', F, M, k ', C ' and f0The function of (d) is upper and lower. According to the implementation steps of a genetic algorithm, the initial population size, the maximum algebra, the cross probability, the mutation probability, the iteration termination condition and the like are sequentially determined, and selection and cross are implemented on the basis of MATLAB softwareFork, mutation, etc., and finally obtaining the minimum function values of the RMSE-based functions of C ', B ', E ', F, M, k ', C ' and f0The fitting parameter value of (1).
Step 2) determining parameters of a reverse mechanical model of the magneto-rheological shock absorber based on a progressive saturation magic formula:
the sensor and the corresponding state observer can measure and calculate time-varying piston displacement s, piston velocity v and piston acceleration a, the values and the damping force value required by the magneto-rheological shock absorber are input into a current solver, so that the required exciting current can be calculated, and a current solving formula obtained by reverse solving according to the formula (4-6) meets the following requirements:
wherein y satisfies:
the present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.
Claims (6)
1. A magneto-rheological damper modeling method based on a progressive saturation magic formula is characterized by comprising the following steps: the method comprises the following steps:
step 1), providing a mechanical characteristic model of a progressive saturation magic formula of the magneto-rheological damper and determining parameters of a forward model;
step 1.1) testing the mechanical properties of the magnetorheological shock absorber to obtain a damping force-speed curve graph and a damping force-displacement relation curve graph of the magnetorheological shock absorber under different working conditions;
step 1.2) providing a mechanical characteristic model of a progressive saturation magic formula;
the fitting precision of the hysteresis width of the speed characteristic curve is improved by additionally arranging a piston acceleration hyperbolic tangent term, the hyperbolic tangent function is used for replacing a sine function of an original magic formula to eliminate the droop phenomenon of the speed characteristic curve when the piston speed is higher, and the magneto-rheological damper model based on the progressive saturation magic formula is described as follows:
in the formula: f'MRThe damping force of the magneto-rheological shock absorber is based on a progressive saturation magic formula; d' is the peak factor of the progressive saturation magic formula; c' is the progressive saturation magic formula form factor; b' is a stiffness factor of a progressive saturation magic formula; e' is a curvature factor of a progressive saturation magic formula; f is a hysteresis loop width factor of a progressive saturation magic formula; m is an inertia factor of a progressive saturation magic formula; k' is the stiffness coefficient of the progressive saturation magic formula; c' is a viscous damping coefficient of a progressive saturation magic formula; f. of0Is a biasing force; s is the piston displacement; v is the piston velocity; a is the piston acceleration;
step 1.3) determining value ranges of various parameters of a separately fitted progressive saturation magic formula based on different working conditions;
1.4) nonlinear parameter fitting of a peak factor of a progressive saturation magic formula;
step 1.5) of final determination of all parameter values of the gradual saturation magic formula with the minimum working condition error;
and step 2) determining parameters of a reverse mechanical model of the magneto-rheological shock absorber based on a progressive saturation magic formula.
2. The modeling method of the magnetorheological damper based on the progressive saturation magic formula as claimed in claim 1, wherein: the substep 1.1) also comprises the following steps:
the mechanical property test system of the magnetorheological damper is utilized to test the mechanical property of the magnetorheological damper to be tested, in the test process, an input signal is set to be a sine wave signal, the amplitude of the magnetorheological damper is 50mm, the working control current is 0.5-3A, 0.5A is increased each time, the test frequency is 0.5-2.0 Hz, and 0.5Hz is increased each time; and measuring to obtain a damping force-speed curve graph and a damping force-displacement relation curve graph of the magnetorheological shock absorber under 24 different working conditions.
3. The modeling method of the magneto-rheological damper based on the progressive saturation magic formula as claimed in claim 2, wherein: the substep 1.3) also comprises the following steps:
based on measured data under different test conditions obtained by a mechanical property test of the magnetorheological damper, and by utilizing an lsqcurvefit tool in MATLAB software, the unknown parameters D ', C ', B ', E ', F, M, k ', C ' and f ' to be fitted in the formula (1) are independently fitted0Fitting values under 24 working conditions; the lsqcurvefit tool performs parameter fitting on the magneto-rheological damper model adopting the progressive saturation magic formula according to a minimum variance algorithm, and satisfies the following conditions:
in the formula:
the output force measured in the mechanical property test of the magnetorheological damper is represented;
comparison of D ', C', B ', E', F, M, k ', C' and f separately0And (3) respectively recording the maximum value and the minimum value of the numerical values under 24 working conditions as an upper bound threshold value and a lower bound threshold value, and obtaining each parameter determination range of the gradual saturation magic formula.
4. The modeling method of the magneto-rheological damper based on the progressive saturation magic formula as claimed in claim 3, characterized in that: the substep 1.4) also comprises the following steps:
through analysis of mechanical property test data of the magneto-rheological damper, the peak factor D' of the gradual saturation magic formula fluctuates most obviously along with the change of current under different frequencies and the parameter consistency under different working conditions is poor compared with other parameters to be fitted; in order to further improve the model fitting accuracy of the proposed progressive saturation magic formula, the expression of the peak factor D 'of the progressive saturation magic formula needs to be re-expressed, and the expression of the modified peak factor D' of the progressive saturation magic formula is as follows:
D′＝D0+D1I+D2I2 (3)
in the formula: d0、D1And D2Respectively representing a constant term coefficient, a first term coefficient and a second term coefficient of a peak factor of the progressive saturation magic formula; i is exciting current;
substituting formula (3) into formula (1), rewriting magneto-rheological damper damping force F 'based on progressive saturation magic formula'MRExpression:
F′MR＝FMR_i+FMR_0+c′v (4)
in the formula: fMR_iControlled damping force for the magnetorheological shock absorber; fMR_0Indicating other damping forces except the controlled damping force and the base value damping force;
based on the mechanical property test data of the magneto-rheological damper, the fitting value of the D' of the peak factor of the progressive saturation magic formula, which is obtained by independent fitting under different working conditions according to the measured value of the actual exciting current I and the substep 1.3), and the constant term coefficient D of the peak factor of the progressive saturation magic formula is fitted by adopting a minimum variance algorithm0First order coefficient D1And coefficient of quadratic term D2At this time, the calculation expression of the minimum variance algorithm satisfies:
in the formula:
representing the fitting value D' of the peak value factor of the progressive saturation magic formula under 24 groups of working conditions obtained in the step 1.3);
d in magneto-rheological damper model finally determining progressive saturation magic formula0、D1And D2The parameter fit value of (2).
5. The modeling method of the magneto-rheological damper based on the progressive saturation magic formula as claimed in claim 4, characterized in that: the substep 1.5) also comprises the following steps:
finally determining the parameter fitting values of the items of the progressive saturation magic formula on the premise of meeting the minimum error of all working conditions, and performing genetic algorithm on the rest unknown parameters C ', B ', E ', F, M, k ', C ' and f to be fitted in the formula (4-6)0Performing parameter fitting;
in the parameter fitting process, damping force obtained by testing the magneto-rheological shock absorber under 24 working conditions and the Root Mean Square Error (RMSE) output by a model are used as an optimization target function, the minimum value of an RMSE function is solved based on a genetic algorithm in the meaning, and the RMSE function calculation formula is as follows:
wherein, i is 1, 2, 3 … 24 and represents the serial numbers of 24 different working conditions in table 1;
calculating upper and lower bound thresholds of various unknown parameters to be fitted according to substep 1.3), and taking the thresholds as C ', B ', E ', F, M, k ', C ' and f0Upper limit of the function value of (1)And a lower limit, sequentially determining the initial population size, the maximum algebra, the cross probability, the mutation probability and the iteration termination condition according to the implementation steps of the genetic algorithm, implementing selection, cross and mutation operations based on MATLAB software, and finally obtaining the relation C ', B ', E ', F, M, k ', C ' and f with the minimum RMSE function value0The fitting parameter value of (1).
6. The modeling method of the magneto-rheological damper based on the progressive saturation magic formula as claimed in claim 5, characterized in that: the step 2) further comprises the following steps:
the sensor and the corresponding state observer can measure and calculate time-varying piston displacement s, piston velocity v and piston acceleration a, the values and the damping force value required by the magneto-rheological shock absorber are input into a current solver, so that the required exciting current can be calculated, and a current solving formula obtained by reverse solving according to the formula (4-6) meets the following requirements:
wherein y satisfies:
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