CN114002963A - Multi-working-condition suspension support system dynamic modeling method - Google Patents

Multi-working-condition suspension support system dynamic modeling method Download PDF

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CN114002963A
CN114002963A CN202111279623.3A CN202111279623A CN114002963A CN 114002963 A CN114002963 A CN 114002963A CN 202111279623 A CN202111279623 A CN 202111279623A CN 114002963 A CN114002963 A CN 114002963A
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rotor
matrix
vehicle
amplitude
response curve
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朱志莹
李鑫雅
张巍
倪钰惠
綦光鑫
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Nanjing Institute of Technology
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Nanjing Institute of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a dynamic modeling method of a suspension support system under multiple working conditions, which comprises the following steps: preprocessing the dynamic driving state working condition and the road working condition of the vehicle, acquiring an amplitude response curve of APM-BFM under the dynamic driving state working condition and the road working condition of the vehicle in ADAMS, and fitting an electromagnetic force response curve according to the amplitude response curve; establishing a rotor dynamics coarse model, constructing a multi-working-condition suspension support system, arranging a linear quadratic controller (LQR), feeding back a rotor centroid dynamic offset matrix of the rotor dynamics coarse model into the LQR as disturbance, wherein the LQR and the multi-working-condition flywheel rotor dynamics coarse model form the multi-working-condition suspension support system; and dynamically optimizing the suspension support system under multiple working conditions. According to the invention, the dynamic running state working condition and the road working condition of the vehicle are considered, the suspension support control system is dynamically optimized by adopting a differential evolution algorithm and a feedforward neural network, the accuracy of the model is improved, and the stability of the suspension support control system, namely the stability of the operation of the rotor is improved.

Description

Multi-working-condition suspension support system dynamic modeling method
Technical Field
The invention relates to the technical field of magnetic suspension motors, in particular to a dynamic modeling method for a suspension support system under multiple working conditions.
Background
The magnetic suspension bearingless motor which is started in recent years combines the dual advantages of the magnetic bearing and the switched reluctance motor, can simplify the system structure and improve the critical rotating speed and reliability, is used in the field of the flywheel to form the magnetic suspension flywheel motor with unique advantages, is widely researched by domestic and foreign scholars, and sequentially has the structures of radial phase splitting, axial phase splitting and the like, wherein the axial phase splitting structure can realize the radial four-degree-of-freedom suspension only by two sets of suspension windings which are axially distributed without additionally arranging the magnetic bearing while realizing the electric/power generation function, thereby greatly improving the system integration level and the critical rotating speed, and being very suitable for a flywheel energy storage suspension support and energy conversion system.
The vehicle-mounted flywheel battery is a magnetic suspension energy storage flywheel which is installed on a moving vehicle body and works, and all-directional vibration of the vehicle caused by different driving states of the vehicle and unevenness of a road surface can influence the stable operation of a flywheel rotor. Currently, representative modeling methods include: support vector machine method, artificial neural network method. The punishment function and the kernel function selectivity are difficult when the support vector machine is applied, and the punishment function and the kernel function influence the prediction accuracy of the model; the artificial neural network has the characteristics of autonomous learning, strong memory capability, strong fault-tolerant capability and the like, and is widely applied.
Disclosure of Invention
The purpose of the invention is as follows: in view of the above-mentioned shortcomings in the prior art, the present invention provides a dynamic modeling method for a suspension support system with multiple operating conditions.
The technical scheme is as follows: in order to achieve the technical purpose, the invention adopts the following technical scheme.
A dynamic modeling method for a suspension support system with multiple working conditions comprises the following steps:
s1, preprocessing the dynamic driving state working condition and the road working condition of the vehicle: presetting a vehicle Dynamic driving state working condition and a road working condition, leading an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM, Automatic permanent magnet magnetic suspension flywheel motor system) into an ADAMS (Automatic Mechanical system dynamics Analysis of Mechanical Systems), obtaining an amplitude response curve of the APM-BFM under the vehicle Dynamic driving state working condition and the road working condition in the ADAMS, and fitting an electromagnetic force response curve according to the amplitude response curve;
s2, establishing a rotor dynamics coarse model: establishing a rotor dynamics coarse model according to the electromagnetic force response curve in the step S1 and by combining a dynamic equation of the APM-BFM system; a rotor mass center dynamic offset matrix in the rotor dynamics coarse model is related to excitation frequency, acceleration, pitching amplitude, simulation time and speed;
s3, constructing a suspension support system with multiple working conditions: setting a linear quadratic controller (LQR), feeding back a rotor centroid dynamic deviation matrix of the rotor dynamics coarse model in the step S2 into the LQR as disturbance, wherein the LQR and the multi-operating-condition flywheel rotor dynamics coarse model form a multi-operating-condition suspension support system; the suspension support system under multiple working conditions outputs suspension force;
s4, dynamically optimizing the suspension support system under multiple working conditions: and calculating weights of excitation frequency, acceleration, pitching amplitude, simulation time and speed by adopting a differential evolution algorithm and an extreme learning machine, further adjusting a rotor mass center dynamic offset matrix of the rotor dynamics coarse model, realizing dynamic optimization of the rotor dynamics coarse model, controlling stable output of suspension force and improving the stability of the suspension support system under multiple working conditions.
Preferably, the specific process of step S1 is:
s11, presetting the dynamic driving state working condition and the road working condition of the vehicle: the dynamic running state working conditions of the vehicle comprise vehicle starting acceleration, braking deceleration, turning and climbing, and the road working conditions comprise vehicle longitudinal vibration, transverse vibration and pitching vibration caused by uneven road surface;
s12, constructing an equivalent three-dimensional model: an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM) is introduced into an ADAMS to obtain an equivalent three-dimensional model, wherein the equivalent three-dimensional model comprises an equivalent installation base of the APM-BFM, an electromagnetic force application point and a sensor observation point, and the electromagnetic force application point and the sensor observation point are arranged on the equivalent installation base;
s13, obtaining an amplitude response curve of APM-BFM: setting a driving function for the equivalent three-dimensional model constructed in S12 in ADAMS, and simulating the motion conditions of APM-BFM under the preset vehicle dynamic driving state working condition and road working condition to obtain an APM-BFM amplitude response curve; the amplitude response curve is the relation between the rotor mass center amplitude and the excitation frequency, the acceleration, the pitching amplitude, the simulation time and the speed;
and S14, fitting an electromagnetic force response curve according to the amplitude response curve, wherein the electromagnetic force response curve is the relation between the electromagnetic force of the rotor mass center and the amplitude displacement of the rotor mass center relative to the balance point.
Preferably, the electromagnetic force application point and the sensor observation point are changed along with the position change of an equivalent mounting base, the equivalent mounting base is used for simulating the motion condition of a flywheel supporting system base, and gravity and electromagnetic force constraint is added between the equivalent mounting base and the rotor and used for simulating electromagnetic force and rotary driving force.
Preferably, the drive function is:
V＝90000(°/s2)×time
wherein V is the driving speed of the rotor, ° s2Is the unit of acceleration and time is the simulation time.
Preferably, the amplitude response curve comprises:
when the vehicle is in a starting acceleration state, the speed of the APM-BFM starts to increase along the X direction, different accelerations are set, the vehicle is simulated to do acceleration motion, and a response curve of the mass center amplitude and the acceleration of a rotor is obtained;
when the vehicle is in a braking and decelerating state, different acceleration and friction coefficients are set, the vehicle is simulated to do deceleration movement, and a rotor mass center amplitude and simulation time response curve is obtained;
when the vehicle is in a turning state, setting different turning radiuses and speeds, and simulating the vehicle to turn to obtain a response curve of the rotor mass center amplitude, the simulation time and the speed;
when the vehicle is in a climbing state, different climbing speeds and different slopes are set, the vehicle is simulated to do climbing motion, and a response curve of rotor mass center amplitude and simulation time in the X, Y direction is obtained;
when the vehicle vibrates longitudinally: different excitation frequencies are set in the Y direction, longitudinal vibration of the vehicle is simulated, and response curves of the mass center amplitude of the rotor, the simulation time and the excitation frequencies are obtained;
when the vehicle vibrates transversely: different excitation frequencies are set in the X direction, and the transverse vibration of the vehicle is simulated to obtain the response curve of the mass center amplitude of the rotor, the simulation time and the excitation frequency;
when the vehicle vibrates in a pitching mode: excitation frequencies are respectively given in the direction X, Y, different rotor center-of-mass pitching amplitudes are set, and the motion trail of the rotor center-of-mass is obtained, wherein the motion trail is the amplitude response curve of the rotor center-of-mass in the direction X, Y.
Preferably, the mathematical formula of the electromagnetic force response curve is as follows:
Figure BDA0003329105830000031
wherein the content of the first and second substances,
Figure BDA0003329105830000032
is the electromagnetic force of the mass center of the rotor,
Figure BDA0003329105830000033
is an amplitude displacement matrix of the rotor centroid relative to the balance point,
Figure BDA0003329105830000041
in order to control the current matrix,
Figure BDA0003329105830000042
Kxis a displacement stiffness matrix, kxIs the displacement stiffness coefficient, which is a constant number;
Figure BDA0003329105830000043
Kiis a current stiffness matrix, kiFor the current stiffness coefficient, constant quantities, a and B represent motor phases a and B.
Preferably, the kinetic equation of the APM-BFM system in step S2 is:
Figure BDA0003329105830000044
wherein: m is the mass of the rotor in APM-BFM; x and y are translational displacement of the rotor in the x-axis direction and the y-axis direction under the barycentric coordinate, alpha and beta are rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor,
Figure BDA0003329105830000045
Figure BDA0003329105830000046
respectively, its second derivative; f. ofxAnd pxIs the electromagnetic force and moment in the x-direction at the centroid; f. ofyAnd pyIs the electromagnetic force and moment in the y-direction at the centroid; Δ f and Δ p are external disturbance force and disturbance moment; j. the design is a squarezω is angular momentum, H ═ Jzω, ω is the rotor rotation angular velocity, faxAnd fbxElectromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, fayAnd fbyElectromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor respectively; lsaAnd lsbThe distances from the a phase shift sensor and the B phase shift sensor to the centroid point O, respectively.
Preferably, the coarse rotor dynamics model in step S2 is:
Figure BDA0003329105830000047
wherein Kxx＝LfKxLf TThe matrix is a negative stiffness matrix of the bearing,
Figure BDA0003329105830000048
Kxis a displacement stiffness matrix, kxFor the displacement stiffness coefficient, the rotor mass matrix is
Figure BDA0003329105830000051
m is the mass of the rotorAmount Jx、JyRespectively, moment of inertia, Jx＝Jy＝0.0005kg·m2Coordinate vector of rotor centroid
Figure BDA0003329105830000052
x and y are translational displacement of the rotor in the x-axis direction and the y-axis direction under the coordinate of the mass center, alpha and beta are rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor, and the screw matrix
Figure BDA0003329105830000053
H is angular momentum, H ═ Jzω, ω is the rotor rotation angular velocity, JzIs moment of inertia, Jz＝0.001kg·m2Matrix of moment arm coefficients of rotor
Figure BDA0003329105830000054
lsaAnd lsbThe distances from the A phase shift sensor and the B phase shift sensor to the centroid point O respectively,
Figure BDA0003329105830000055
to control the current matrix, iax、ibx、iay、ibvThe control currents of the phase A and the phase B in the x direction and the y direction are respectively.
Preferably, in step S3, the linear quadratic controller (LQR) has a state equation:
Figure BDA0003329105830000056
x(t0)＝x0
y(t)＝C(t)x(t)
the performance indexes of the LQR are as follows:
Figure BDA0003329105830000057
wherein A (t) is LQR system matrix, B (t) is control input matrix, C (t) is output matrix, u (t) is optimalControl input vector, i.e. reference displacement of the centroid, x (t) is the state vector, y (t) is the output vector, i.e. actual displacement of the centroid; f (t) is the perturbation input vector, x0、x(t0) Are all initial state vectors, tfAt the intermediate moment, J is the moment of inertia, the weighting matrix Q is a semi-positive definite matrix of dimension n multiplied by n, and R is a positive definite matrix of dimension R multiplied by R; the first integral term represents the integral of the weighted average sum of the dynamic tracking errors of the LQR system; the second integral term represents the total control energy consumption of the LQR system; the LQR is used for solving a gain K of state feedback control, and the gain K is determined by a weighting matrix Q and a positive definite matrix R;
and the weighting matrix Q and the positive definite matrix R are corrected through a fuzzy PID algorithm, and the weighting matrix Q and the positive definite matrix R are corrected through adjusting PID control parameter values in the fuzzy PID algorithm, so that the gain K of the feedback control of the LQR state is adjusted.
Preferably, the calculating the weights of the excitation frequency, the acceleration, the pitch amplitude, the simulation time and the speed by using the differential evolution algorithm and the extreme learning machine specifically comprises:
s41, in the extreme learning machine, selecting excitation frequency, acceleration, pitching amplitude, time and speed as input, selecting suspension force as output, and setting the number and parameters of hidden layer nodes of the extreme learning machine;
and S42, introducing a differential evolution algorithm to optimize the extreme learning machine, and outputting a weight matrix of excitation frequency, acceleration, pitching amplitude, time and speed by the extreme learning machine.
Has the advantages that: according to the invention, the dynamic running state working condition and the road working condition of the vehicle are considered, the suspension support control system is dynamically optimized by adopting a differential evolution algorithm and a feedforward neural network, the accuracy of the model is improved, and the stability of the suspension support control system, namely the stability of the operation of the rotor is improved.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of an equivalent three-dimensional model structure of the present invention;
FIG. 3 is a schematic diagram of the coordinate system of the APM-BFM system in the embodiment;
FIG. 4 is a block diagram of LQR in an embodiment;
FIG. 5 is a diagram showing membership functions in the embodiment;
FIG. 6 is a diagram showing the structure of an ELM of the extreme learning machine in the embodiment;
FIG. 7 is a flow chart of the differential optimization algorithm in an embodiment.
Detailed Description
For a better understanding of the present invention, reference will now be made to the following description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in the attached figure 1, the dynamic modeling method of the suspension support system under multiple working conditions comprises the following steps:
s1, preprocessing the dynamic driving state working condition and the road working condition of the vehicle: presetting a vehicle Dynamic driving state working condition and a road working condition, leading an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM) into an ADAMS (Automatic Mechanical system dynamics Analysis of Mechanical Systems), acquiring an amplitude response curve of the APM-BFM under the vehicle Dynamic driving state working condition and the road working condition in the ADAMS, and fitting an electromagnetic force response curve according to the amplitude response curve.
Specifically, step S1 includes:
s11, presetting the dynamic driving state working condition and the road working condition of the vehicle: the dynamic running state working conditions of the vehicle comprise vehicle starting acceleration, braking deceleration, turning and climbing, and the road working conditions comprise vehicle longitudinal vibration, transverse vibration and pitching vibration caused by uneven road surface;
s12, constructing an equivalent three-dimensional model: an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM) is introduced into an ADAMS to obtain an equivalent three-dimensional model, wherein the equivalent three-dimensional model comprises an equivalent installation base of the APM-BFM, an electromagnetic force application point and a sensor observation point, and the electromagnetic force application point and the sensor observation point are arranged on the equivalent installation base; the dynamic modeling method of the suspension support system under multiple working conditions, which is realized in the embodiment, is applied to a vehicle, the equivalent installation basis of the APM-BFM can be regarded as the mass center of the rotor, the electromagnetic force application point and the sensor observation point are arranged on the mass center of the rotor, and the motion of the mass center of the rotor is equivalent to the motion of the APM-BFM, so that the running state of the vehicle is reflected.
The electromagnetic force application point and the sensor observation point are changed along with the position change of the equivalent installation foundation, the equivalent installation foundation is used for simulating the motion condition of the support system foundation, and controllable force constraints, such as gravity and electromagnetic force constraints, are added on the equivalent installation foundation and are used for simulating electromagnetic force and rotary driving force.
S13, obtaining an amplitude response curve of APM-BFM: setting a driving function for the equivalent three-dimensional model constructed in S12 in ADAMS, and simulating the motion conditions of APM-BFM under the preset vehicle dynamic driving state working condition and road working condition to obtain an APM-BFM amplitude response curve; the amplitude response curve is the relation between the rotor mass center amplitude and the excitation frequency, the acceleration, the pitching amplitude, the simulation time and the speed.
And S14, fitting an electromagnetic force response curve according to the amplitude response curve, wherein the electromagnetic force response curve is the relation between the electromagnetic force of the rotor mass center and the amplitude displacement of the rotor mass center relative to the balance point.
As shown in fig. 2, fig. 2 is an equivalent three-dimensional model, and a three-dimensional coordinate system X, Y, Z is established.
The driving function is:
V＝90000(°/s2)×time
wherein, the type of the driving function in ADAMS is set as acceleration, i.e. acceleration, V is the driving speed of the rotor, DEG/s2Is acceleration unit, time is simulation time
The amplitude response curve includes:
when the vehicle is in a starting acceleration state, namely the speed of the APM-BFM starts to increase along the X direction, the rotor correspondingly moves; setting different accelerated speeds, simulating the vehicle to do accelerated motion, and acquiring a response curve of the mass center amplitude and the accelerated speed of the rotor; if setting the starting acceleration to be 2m/s respectively2、3m/s2、4m/s2The simulation time is set to 0.3 second;
setting different acceleration when the vehicle is in braking and decelerating stateSimulating the vehicle to do deceleration movement by the aid of the degree and the friction coefficient to obtain a rotor mass center amplitude and time response curve; if the acceleration is set at 8m/s2The equivalent foundation is made to do deceleration movement with a friction coefficient mumTypically set to 0.8, the simulation time is set to 0.5 seconds;
when the vehicle is in a turning state, different turning radii and speeds are set, the vehicle is simulated to make uniform turning motion, and response curves of the amplitude of the mass center of the rotor, time and speed are obtained; if the turning radius is set to be 5.5m, the vehicle speeds are respectively 55km/h, 65km/h and 75km/h, and the simulation time is set to be 0.3 second;
when the vehicle is in a climbing state, different climbing speeds and different slopes are set, the vehicle is simulated to do climbing motion, and a response curve of the mass center amplitude of the rotor in the direction X, Y and the time is obtained; if the climbing speed is set to be 20km/h, the slope is generally set to be 6 degrees, and climbing is started after 0.2 second;
when the vehicle vibrates longitudinally: setting different excitation frequencies, and simulating the longitudinal vibration of the vehicle to obtain a response curve of the mass center amplitude of the rotor, the time and the excitation frequency; if the excitation frequencies are set to be 7Hz, 13Hz and 19Hz respectively, the time step is 0.5 s;
when the vehicle vibrates transversely: setting different excitation frequencies, and simulating the transverse vibration of the vehicle to obtain a response curve of the mass center amplitude of the rotor, the time and the excitation frequency; if the excitation frequencies are set to be 7Hz, 13Hz and 19Hz respectively, the time step is 0.5 s;
when the vehicle vibrates in a pitching mode: excitation frequencies are respectively given in the direction X, Y, different rotor center-of-mass pitching amplitudes are set, and the motion trail of the rotor center-of-mass is obtained, wherein the motion trail is the amplitude response curve of the rotor center-of-mass in the direction X, Y. For example, when the excitation frequency is given to be 2.5Hz in the X, Y direction, the pitch amplitudes are set to be 0.0015rad, 0.0045rad and 0.0075rad respectively, and the locus of the center of mass of the rotor, namely the amplitude response curve of the center of mass of the rotor in the X, Y direction is obtained.
The setting mode of the excitation frequency is as follows: the sine wave signals with different frequencies are superposed to form road surface random excitation, and the frequency of the road surface random excitation is the excitation frequency.
The mathematical formula of the electromagnetic force response curve is as follows:
Figure BDA0003329105830000091
wherein the content of the first and second substances,
Figure BDA0003329105830000092
is the electromagnetic force of the mass center of the rotor,
Figure BDA0003329105830000093
is a matrix of amplitude displacements of the magnetic bearing relative to the balance point,
Figure BDA0003329105830000094
in order to control the current matrix,
Figure BDA0003329105830000095
Kxis a displacement stiffness matrix, kxIs the displacement stiffness coefficient, which is a constant number;
Figure BDA0003329105830000096
Kiis a current stiffness matrix, kiIs a current stiffness matrix, a constant number.
S2, establishing a rotor dynamics coarse model according to the electromagnetic force response curve in the step S1 and by combining a dynamic equation of the APM-BFM system; a rotor mass center dynamic offset matrix in the rotor dynamics coarse model is related to excitation frequency, acceleration, pitching amplitude, simulation time and speed; namely, when starting acceleration, braking deceleration, turning, climbing, longitudinal vibration, axial vibration and pitching vibration states, namely, corresponding rotor dynamics coarse models under various working conditions, namely, the input of the rotor dynamics coarse models is the electromagnetic force of step S1.
As shown in fig. 3, the dynamic equation of the APM-BFM system can be obtained according to the lagrangian equation method in the multi-rigid system dynamic theory by ignoring the external damping and gravity influence of the system:
Figure BDA0003329105830000097
wherein: m is the mass of the rotor in APM-BFM; x and y are translational displacement of the rotor in the x-axis direction and the y-axis direction under the barycentric coordinate, alpha and beta are rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor,
Figure BDA0003329105830000098
Figure BDA0003329105830000101
respectively, its second derivative; j. the design is a squarex、JyRespectively, moment of inertia, Jx＝Jy＝0.0005kg·m2，，Jzω is angular momentum, H ═ Jzω, ω is the rotor rotation angular velocity, JzIs moment of inertia, Jz＝0.001kg·m2，faxAnd fbxElectromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, fayAnd fbyElectromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor respectively; lsaAnd lsbThe distances from the phase shift sensor A and the phase shift sensor B to a mass center point O, wherein O is the mass center of the rotor at the balance position.
Expressing the motion equation of the APM-BFM rotor in a matrix form:
Figure BDA0003329105830000102
namely:
Figure BDA0003329105830000103
wherein: rotor mass matrix of
Figure BDA0003329105830000104
Coordinate vector of flywheel rotor centroid
Figure BDA0003329105830000105
Gyro matrix
Figure BDA0003329105830000106
Rotor moment arm coefficient matrix
Figure BDA0003329105830000107
Magnetic bearing electromagnetic force
Figure BDA0003329105830000108
Substituting the electromagnetic force obtained in step S1:
Figure BDA0003329105830000109
wherein
Figure BDA0003329105830000111
For an amplitude displacement matrix of the rotor center of mass relative to the balance point, the above equation can be converted to:
Figure BDA0003329105830000112
and converting the rotor radial displacement signal detected by the displacement sensor to the center of mass of the rotor, and expressing as follows:
Figure BDA0003329105830000113
namely:
q＝Aqb
wherein the transformation matrix is a, where a,
Figure BDA0003329105830000114
the inverse of the transformation matrix is the transpose of the moment arm matrix, i.e.:
A-1＝Lf T
obtaining:
qb＝Lf Tq
Figure BDA0003329105830000115
finishing to obtain a dynamic coarse model:
Figure BDA0003329105830000116
wherein Kxx＝LfKxLf TAnd is a bearing negative stiffness matrix.
Figure BDA0003329105830000121
KxIs a displacement stiffness matrix, kxIs a displacement stiffness coefficient, is a constant number, and has a rotor mass matrix of
Figure BDA0003329105830000122
m is the mass of the rotor, J is the moment of inertia, Jx、JyRespectively, moment of inertia, Jx＝Jy＝0.0005kg·m2Dynamic offset matrix of rotor centroid
Figure BDA0003329105830000123
x and y are translational displacement of the rotor in the x-axis direction and the y-axis direction under the coordinate of the mass center, alpha and beta are rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor, and the gyro matrix
Figure BDA0003329105830000124
H is angular momentum, H ═ JzOmega, omega is the rotor rotation angular velocity, rotor moment arm coefficient matrix
Figure BDA0003329105830000125
lsaAnd lsbThe distances from the A phase shift sensor and the B phase shift sensor to the centroid point O respectively,
Figure BDA0003329105830000126
to control the current matrix, iax、ibx、iay、ibyThe control currents of the phase A and the phase B in the x direction and the y direction are respectively.
S3, constructing a suspension support system: as shown in fig. 4, a linear quadratic controller (LQR) is arranged, a centroid dynamic deviation matrix is fed back to the LQR as a disturbance, and the LQR and a multi-operating-condition flywheel rotor dynamics coarse model jointly form a suspension support system; the output of the suspension supporting system is suspension force;
s31, constructing a linear quadratic controller (LQR) -based dynamic deviation matrix q of the rotor dynamics coarse model center of mass obtained in the step S2 to be [ x beta y alpha ]]TInput to LQR as a perturbation;
s32, the weighting matrix parameter Q and the positive definite matrix R of the LQR in the step S31 are corrected by the fuzzy PID control logic design, and the linear quadratic controller and the suspension support control system with online adjustable control parameters are realized.
The linear quadratic control system state equation is as follows:
Figure BDA0003329105830000131
x(t0)＝x0
y(t)＝C(t)x(t)
the performance indexes of the LQR are as follows:
Figure BDA0003329105830000132
wherein, a (t) is an LQR system matrix, b (t) is a control input matrix, c (t) is an output matrix, u (t) is an optimal control input vector, i.e., a reference displacement of a centroid, x (t) is a state vector, and y (t) is an output vector, i.e., an actual displacement of the centroid; f (t) is the perturbation input vector, x0、x(t0) Are all initial state vectors, tfAt the intermediate moment, J is the moment of inertia, the weighting matrix Q is a semi-positive definite matrix of dimension n multiplied by n, and R is a positive definite matrix of dimension R multiplied by R; the first integral term represents the dynamic tracking error of the LQR systemIntegration of the difference weighted average sum; the second integral term represents the total control energy consumption of the LQR system; LQR is used to find the gain K of the state feedback control, which is determined by the weighting matrix Q and the positive definite matrix R.
The selection of Q and R is particularly important in order to minimize the performance indicator function J, where K is uniquely determined by the weighting matrices Q and R.
Wherein: k (t) ═ R-1(t)BT(t) P (t), P (t) may be calculated by Riccati (Riccati) differential equation.
Figure BDA0003329105830000133
The weighting matrix Q and the positive definite matrix R are corrected through a fuzzy PID algorithm, and the weighting matrix Q and the positive definite matrix R are corrected through adjusting PID control parameter values in the fuzzy PID algorithm, so that the gain K of the LQR state feedback control is adjusted.
And establishing a membership relation between the fuzzy quantity and the grade quantity, wherein the membership function image is shown in the figure 4. The membership functions are defined as:
Figure BDA0003329105830000134
where A is called fuzzy set, uA(x) Indicating the extent to which x belongs to the fuzzy set a.
The fuzzy set A can now be represented as:
A＝u1/x1+u2/x2+…+ui/xi+…
the common membership functions mainly include three types of membership functions, namely gaussian membership function (gausssmf), S-type membership function (smf), triangular membership function (trimf), and the like, and fuzzy subset membership functions of input variable error e (t) and error change rate ec ═ e (t) — e (t-1) are shown in fig. 5. S-type membership functions are selected on the fuzzy subsets on the two sides, so that the adaptability is improved, and the advantages of different membership functions are fully exerted; seven language variable values, such as "negative large", "negative middle", "negative small", "zero", "positive small", "middle" and "positive large", are generally used for confirming the fuzzy variable values of the input and output of the fuzzy controller, and are generally abbreviated as { NB, NM, NS, ZO, PS, PM and PB };
the fuzzy quantization processing is to introduce a quantization factor and a scale factor in order to map the input variable into the fuzzy domain.
Variable domain table:
variables of e ec ΔKp ΔKi ΔKd
Linguistic variables E Ec Kp Ki Kd
Fundamental discourse domain [-0.035，0.035] [-0.035，0.035] [-3，3] [-0.04，0.04] [-3，3]
Universe of fuzzy discourse [-0.35，0.35] [-0.35，0.35] [-3，3] [-0.04，0.04] [-3，3]
Quantization factor 10 10 1 1 1
The input variable and the output variable of the fuzzy PID controller are fuzzified into 7 fuzzy subsets, and a control rule pair K is establishedp、Ki、KdAnd (6) adjusting.
ΔKpFuzzy rule table of (1):
Figure BDA0003329105830000141
Figure BDA0003329105830000151
ΔKifuzzy rule table of (1):
Figure BDA0003329105830000152
ΔKdfuzzy rule table of (1):
Figure BDA0003329105830000153
the fuzzy relation operation is:
R1＝[(NB)E×(NB)EC]T×(PB)Kp×(NB)Ki×(PS)Kd
by n fuzzy relations Ri(i ═ 1, 2, 3, … n), the control rule may be represented by an overall fuzzy relationship R:
Figure BDA0003329105830000161
the fuzzy quantities of the input variables are E and EC, respectively, and the synthesized fuzzy inference rule is as follows:
U＝(E×EC)·R
the fuzzy relation R comprises the fuzzy relation of proportion, integral, differential and input variable, so the fuzzy inference output U comprises delta Kp、ΔKi、ΔKdThree fuzzy quantity results.
The clarification is carried out by adopting a gravity center method:
Figure BDA0003329105830000162
wherein the content of the first and second substances,
Figure BDA0003329105830000163
represents various combinations KpiDegree of membership. For Ki、KdThe method can also be obtained through a sharpening process according to a fuzzy reasoning method and a gravity center method. Finally, the adjustment value delta K is obtained by multiplying the sharpening quantity by the corresponding quantization factorp、ΔKi、ΔKdActual PID parameter values:
Kp＝Kp0+ΔKp
Ki＝Ki0+ΔKi
Kd＝Kd0+ΔKd
wherein, Kp0、Ki0、Kd0Is the initial value of the PID control parameter. Kp0＝0.3，Ki0＝0.002，Kd010. And the weighting matrix can be adjusted on line by completing PID fuzzy control to realize control parameters.
S4, dynamically optimizing the suspension support system under multiple working conditions: and calculating weights of excitation frequency, acceleration, pitching amplitude, simulation time and speed by adopting a differential evolution algorithm and an extreme learning machine, further adjusting a rotor mass center dynamic offset matrix of the rotor dynamics coarse model, realizing dynamic optimization of the rotor dynamics coarse model, controlling stable output of suspension force and improving the stability of the suspension support system under multiple working conditions.
According to the step S3, "unmodeled dynamic information" having a large influence on the levitation force is selected as a sample space, such as excitation frequency, acceleration, pitch amplitude, time, and velocity. The method is characterized in that an extreme learning machine is adopted to identify an unmodeled dynamic sample space, the number and parameters of network hidden layer nodes in the extreme learning machine are dynamically optimized by introducing a differential evolution algorithm, and a dynamic model of the suspension support system capable of reflecting the unmodeled dynamic is constructed.
And S41, selecting the excitation frequency, the acceleration, the pitching amplitude, the time and the speed as input, using the suspension force as output, and setting the number of hidden layer nodes and parameters of the extreme learning machine. As shown in fig. 6, for NaA plurality of arbitrary samples, wherein xi＝[xi1，xi2，...，xin]T∈Rn，n≤5，ti＝[ti1，ti2...，tim]T∈RmM ≦ n, the output of the feedforward neural network with L hidden nodes and the excitation function G (X) may be expressed as follows:
Figure BDA0003329105830000171
wherein, ai＝[ai1，ai2，…，αin]TIs input layer to ith hidden layer nodeInput weight, xi∈Rn，ai∈Rn，βi∈Rm，biIs the deviation, β, of the ith hidden layer nodei＝[βi1，βi2，...，βim]TIs the output weight of the ith hidden layer node, ai·xiRepresenting the inner product, the excitation function G (X) selects "Sigmoid".
The method is simplified as follows:
Hβ＝T
wherein T is an expected output matrix, β is an output weight matrix, and H is a hidden layer output matrix, as shown below:
Figure BDA0003329105830000172
s42, as shown in figure 7, a differential evolution algorithm is introduced to optimize the extreme learning machine, and the extreme learning machine outputs a weight matrix of excitation frequency, acceleration, pitch amplitude, time and speed. And (4) introducing a differential evolution algorithm to optimize the number and the parameters of the hidden layer nodes obtained in the step S41, and improving the calculation speed of the model.
(1) Population initialization: randomly select individual P (satisfying constraint) and compose size NpThe maximum evolution algebra is set to be gmax. Let i individual PiComprises the following steps:
Pi＝{Pi1，Pi2，…Pij…，PiD}j＝1，2，…D
wherein: 1, 2, … Np(ii) a D is the base factor of a single individual, PijIs the j gene, P, on the i individualij＝rand(0，1)·(Pij U-Pij L)+Pij LAnd rand (0, 1) is a random integer between (0, 1), Pij U、Pij LThe upper and lower limits of the j gene of the i individual, respectively.
(2) Mutation operation: randomly selecting three mutually unequal individuals (P) from the populationr1，g，Pr2，g，Pr3，g) Press PiAnd (3) carrying out mutation:
Figure BDA0003329105830000181
wherein: g is the current generation number, Pr1，g，Pr2，gAnd Pr3，gR1, r2 and r3 individuals of the g-th generation and r1 ≠ r2 ≠ r3 ≠ r, vr，g+1For the newly constructed next generation vector, F is the scaling factor.
(3) And (3) cross operation: new individuals obtained by mutation vr，g+1And the parent PiDiscrete interleaved updated individual ui：
Figure BDA0003329105830000182
Wherein: the cross probability CR belongs to [0, 1], rand (1, D) is a random integer between (1, D), and j represents the j gene on an individual.
(4) Selecting operation: and comparing the fitness of the new generation and the previous generation, and entering the next generation by the individuals with smaller values, otherwise, keeping:
Figure BDA0003329105830000183
wherein: f (-) is the selected fitness function.
Repeating the mutation, crossing and selection processes until the maximum iteration number gmaxAnd outputting to obtain the optimal input weight and hidden layer deviation combination of the extreme learning machine network, thereby constructing an unmodeled dynamic suspension support system dynamic model.
According to the invention, the dynamic running state working condition and the road working condition of the vehicle are considered, the suspension support control system is dynamically optimized by adopting a differential evolution algorithm and a feedforward neural network, the accuracy of the model is improved, and the stability of the suspension support control system, namely the stability of the operation of the rotor is improved.
Finally, it should be noted that: the foregoing is only a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should be considered as the protection scope of the present invention.

Claims (10)

1. A dynamic modeling method for a suspension support system under multiple working conditions is characterized by comprising the following steps:
s1, preprocessing the dynamic driving state working condition and the road working condition of the vehicle: presetting a vehicle Dynamic driving state working condition and a road working condition, leading an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM, axial permanent magnet magnetic suspension flywheel motor system) into an ADAMS (Automatic Mechanical system dynamics Analysis of Mechanical Systems), obtaining an amplitude response curve of the APM-BFM under the vehicle Dynamic driving state working condition and the road working condition in the ADAMS, and fitting an electromagnetic force response curve according to the amplitude response curve;
s2, establishing a rotor dynamics coarse model: establishing a rotor dynamics coarse model according to the electromagnetic force response curve in the step S1 and by combining a dynamic equation of the APM-BFM system; a rotor mass center dynamic offset matrix in the rotor dynamics coarse model is related to excitation frequency, acceleration, pitching amplitude, simulation time and speed;
s3, constructing a suspension support system with multiple working conditions: setting a linear quadratic controller (LQR), feeding back a rotor centroid dynamic deviation matrix of the rotor dynamics coarse model in the step S2 into the LQR as disturbance, wherein the LQR and the multi-operating-condition flywheel rotor dynamics coarse model form a multi-operating-condition suspension support system; the suspension support system under multiple working conditions outputs suspension force;
s4, dynamically optimizing the suspension support system under multiple working conditions: and calculating weights of excitation frequency, acceleration, pitching amplitude, simulation time and speed by adopting a differential evolution algorithm and an extreme learning machine, further adjusting a rotor mass center dynamic offset matrix of the rotor dynamics coarse model, realizing dynamic optimization of the rotor dynamics coarse model, controlling stable output of suspension force and improving the stability of the suspension support system under multiple working conditions.
2. The dynamic modeling method for the multi-operating-condition suspended support system according to claim 1, characterized in that: the specific process of step S1 is as follows:
s11, presetting the dynamic driving state working condition and the road working condition of the vehicle: the dynamic running state working conditions of the vehicle comprise vehicle starting acceleration, braking deceleration, turning and climbing, and the road working conditions comprise vehicle longitudinal vibration, transverse vibration and pitching vibration caused by uneven road surface;
s12, constructing an equivalent three-dimensional model: an axial permanent magnet magnetic suspension flywheel motor system (APM-BFM) is introduced into an ADAMS to obtain an equivalent three-dimensional model, wherein the equivalent three-dimensional model comprises an equivalent installation base of the APM-BFM, an electromagnetic force application point and a sensor observation point, and the electromagnetic force application point and the sensor observation point are arranged on the equivalent installation base;
s13, obtaining an amplitude response curve of APM-BFM: setting a driving function for the equivalent three-dimensional model constructed in S12 in ADAMS, and simulating the motion conditions of APM-BFM under the preset vehicle dynamic driving state working condition and road working condition to obtain an APM-BFM amplitude response curve; the amplitude response curve is the relation between the rotor mass center amplitude and the excitation frequency, the acceleration, the pitching amplitude, the simulation time and the speed;
and S14, fitting an electromagnetic force response curve according to the amplitude response curve, wherein the electromagnetic force response curve is the relation between the electromagnetic force of the rotor mass center and the amplitude displacement of the rotor mass center relative to the balance point.
3. The method for dynamically modeling a multi-condition suspended support system according to claim 2, wherein: the electromagnetic force application point and the sensor observation point are changed along with the position change of the equivalent installation foundation, the equivalent installation foundation is used for simulating the motion condition of the flywheel supporting system foundation, and gravity and electromagnetic force constraint are added between the equivalent installation foundation and the rotor and are used for simulating electromagnetic force and rotary driving force.
4. The method for dynamically modeling a multi-condition suspended support system according to claim 2, wherein: the driving function is:
V＝90000(°/s2)×time
wherein V is the driving speed of the rotor, ° s2Is the unit of acceleration and time is the simulation time.
5. The method for dynamically modeling a multi-condition suspended support system according to claim 2, wherein: the amplitude response curve includes:
when the vehicle is in a starting acceleration state, the speed of the APM-BFM starts to increase along the X direction, different accelerations are set, the vehicle is simulated to do acceleration motion, and a response curve of the mass center amplitude and the acceleration of a rotor is obtained;
when the vehicle is in a braking and decelerating state, different acceleration and friction coefficients are set, the vehicle is simulated to do deceleration movement, and a rotor mass center amplitude and simulation time response curve is obtained;
when the vehicle is in a turning state, setting different turning radiuses and speeds, and simulating the vehicle to turn to obtain a response curve of the rotor mass center amplitude, the simulation time and the speed;
when the vehicle is in a climbing state, different climbing speeds and different slopes are set, the vehicle is simulated to do climbing motion, and a response curve of rotor mass center amplitude and simulation time in the X, Y direction is obtained;
when the vehicle vibrates longitudinally: different excitation frequencies are set in the Y direction, longitudinal vibration of the vehicle is simulated, and response curves of the mass center amplitude of the rotor, the simulation time and the excitation frequencies are obtained;
when the vehicle vibrates transversely: different excitation frequencies are set in the X direction, and the transverse vibration of the vehicle is simulated to obtain the response curve of the mass center amplitude of the rotor, the simulation time and the excitation frequency;
when the vehicle vibrates in a pitching mode: excitation frequencies are respectively given in the direction X, Y, different rotor center-of-mass pitching amplitudes are set, and the motion trail of the rotor center-of-mass is obtained, wherein the motion trail is the amplitude response curve of the rotor center-of-mass in the direction X, Y.
6. The dynamic modeling method for the multi-operating-condition suspended support system according to claim 1, characterized in that: the mathematical formula of the electromagnetic force response curve is as follows:
Figure FDA0003329105820000031
wherein the content of the first and second substances,
Figure FDA0003329105820000032
is the electromagnetic force of the mass center of the rotor,
Figure FDA0003329105820000033
is an amplitude displacement matrix of the rotor centroid relative to the balance point,
Figure FDA0003329105820000034
in order to control the current matrix,
Figure FDA0003329105820000035
Kxis a displacement stiffness matrix, kxIs the displacement stiffness coefficient, which is a constant number;
Figure FDA0003329105820000036
Kiis a current stiffness matrix, kiFor the current stiffness coefficient, constant quantities, a and B represent motor phases a and B.
7. The dynamic modeling method for the multi-operating-condition suspended support system according to claim 1, characterized in that: the dynamic equation of the APM-BFM system in step S2 is:
Figure FDA0003329105820000037
wherein: m is the mass of the rotor in APM-BFM; x and y are centroidsThe translational displacement of the rotor in the direction of the x-axis and the direction of the y-axis under the coordinate, alpha and beta are the rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor,
Figure FDA0003329105820000038
Figure FDA0003329105820000039
respectively, its second derivative; j. the design is a squarex、JyRespectively, moment of inertia, Jx＝Jy＝0.0005kg·m2，，Jzω is angular momentum, H ═ Jzω, ω is the rotor rotation angular velocity, JzIs moment of inertia, Jz＝0.001kg·m2，faxAnd fbxElectromagnetic force in the x-axis direction under the coordinate system of the motor A phase and the motor B phase, respectively, fayAnd fbyElectromagnetic force in the y-axis direction under the coordinate system of the phase A and the phase B of the motor respectively; lsaAnd lsbThe distances from the a phase shift sensor and the B phase shift sensor to the centroid point O, respectively.
8. The method for dynamically modeling a multi-condition suspended support system according to claim 7, wherein: the coarse rotor dynamics model in step S2 is:
Figure FDA0003329105820000041
wherein Kxx＝LfKxLf TThe matrix is a negative stiffness matrix of the bearing,
Figure FDA0003329105820000042
Kxis a displacement stiffness matrix, kxFor the displacement stiffness coefficient, the rotor mass matrix is
Figure FDA0003329105820000043
m is the mass of the rotor, Jx、JyRespectively, moment of inertia, Jx＝Jy＝0.0005kg·m2Coordinate vector of rotor centroid
Figure FDA0003329105820000044
x and y are translational displacement of the rotor in the x-axis direction and the y-axis direction under the coordinate of the mass center, alpha and beta are rotation angles of the rotor around the x-axis and the y-axis without considering the bending deformation of the rotor, and the screw matrix
Figure FDA0003329105820000045
H is angular momentum, H ═ Jzω, ω is the rotor rotation angular velocity, JzIs moment of inertia, Jz＝0.001kg·m2Matrix of moment arm coefficients of rotor
Figure FDA0003329105820000046
lsaAnd lsbThe distances from the A phase shift sensor and the B phase shift sensor to the centroid point O respectively,
Figure FDA0003329105820000051
to control the current matrix, iax、ibx、iay、ibyThe control currents of the phase A and the phase B in the x direction and the y direction are respectively.
9. The dynamic modeling method for the multi-operating-condition suspended support system according to claim 1, characterized in that: in the step S3, the state equation of the linear quadratic controller (LQR) is:
Figure FDA0003329105820000052
x(t0)＝x0
y(t)＝C(t)x(t)
the performance indexes of the LQR are as follows:
Figure FDA0003329105820000053
wherein, a (t) is an LQR system matrix, b (t) is a control input matrix, c (t) is an output matrix, u (t) is an optimal control input vector, i.e., a reference displacement of a centroid, x (t) is a state vector, and y (t) is an output vector, i.e., an actual displacement of the centroid; f (t) is the perturbation input vector, x0、x(t0) Are all initial state vectors, tfAt the intermediate moment, J is the moment of inertia, the weighting matrix Q is a semi-positive definite matrix of dimension n multiplied by n, and R is a positive definite matrix of dimension R multiplied by R; the first integral term represents the integral of the weighted average sum of the dynamic tracking errors of the LQR system; the second integral term represents the total control energy consumption of the LQR system; the LQR is used for solving a gain K of state feedback control, and the gain K is determined by a weighting matrix Q and a positive definite matrix R;
and the weighting matrix Q and the positive definite matrix R are corrected through a fuzzy PID algorithm, and the weighting matrix Q and the positive definite matrix R are corrected through adjusting PID control parameter values in the fuzzy PID algorithm, so that the gain K of the feedback control of the LQR state is adjusted.
10. The dynamic modeling method for the multi-operating-condition suspended support system according to claim 1, characterized in that: the method for calculating the weights of the excitation frequency, the acceleration, the pitching amplitude, the simulation time and the speed by adopting the differential evolution algorithm and the extreme learning machine specifically comprises the following steps:
s41, in the extreme learning machine, selecting excitation frequency, acceleration, pitching amplitude, time and speed as input, selecting suspension force as output, and setting the number and parameters of hidden layer nodes of the extreme learning machine;
and S42, introducing a differential evolution algorithm to optimize the extreme learning machine, and outputting a weight matrix of excitation frequency, acceleration, pitching amplitude, time and speed by the extreme learning machine.
CN202111279623.3A 2021-10-29 2021-10-29 Multi-working-condition suspension support system dynamic modeling method Pending CN114002963A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114738386A (en) * 2022-04-28 2022-07-12 珠海格力电器股份有限公司 Magnetic suspension bearing control method and device, storage medium and bearing controller

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114738386A (en) * 2022-04-28 2022-07-12 珠海格力电器股份有限公司 Magnetic suspension bearing control method and device, storage medium and bearing controller

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