CN108032698B - Magnetorheological semi-active suspension Taylor series-triple H2Time lag compensation control method - Google Patents

Magnetorheological semi-active suspension Taylor series-triple H2Time lag compensation control method Download PDF

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CN108032698B
CN108032698B CN201711097878.1A CN201711097878A CN108032698B CN 108032698 B CN108032698 B CN 108032698B CN 201711097878 A CN201711097878 A CN 201711097878A CN 108032698 B CN108032698 B CN 108032698B
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苑磊
陈士安
孙文强
王骏骋
蒋旭东
姚明
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    • B60—VEHICLES IN GENERAL
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    • B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
    • B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
    • B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
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Abstract

The invention discloses a magnetorheological semi-active suspension Taylor series-triple H2The time lag compensation control method is characterized in that time lags are written into a first-order Taylor series-time lag equation and form an augmented state equation with a suspension system state equation; for the augmented equation of state, first, H is used2Norm constraint suspension comprehensive performance index, and H reuse2The norm restrains the predictive control force at the next time lag moment; then another H is utilized for the suspension system state equation set2The controller calculates the ideal control force and designs the Taylor series-H2/H2/H2A skew compensation controller; the skew compensation controller uses the suspension state variable and the ideal H2The controller output is input, the control current signal is obtained by taking the predicted control force at the next time lag as output, and the numerical control current source is input to obtain the actual control current of the magneto-rheological shock absorber, so that the time lag compensation control of the magneto-rheological semi-active suspension is realized.

Description

Magnetorheological semi-active suspension Taylor series-triple H2Time lag compensation control method
Technical Field
The invention belongs to the field of vehicle suspension control, and particularly relates to a Taylor series-triple H for time lag compensation of a magnetorheological semi-active suspension of a vehicle2(i.e., Taylor series-H)2/H2/H2) A controller design method.
Background
The suspension is an important structural and functional component of an automobile, and has an important influence on the riding comfort and the driving safety of the automobile. The magneto-rheological semi-active suspension technology is a revolution of a vehicle suspension system, does not need an external power source, can output control force according to the change of the running condition of a vehicle, and is expected to obtain the riding comfort and the tire grounding performance close to those of the active suspension.
In the working process of the magneto-rheological semi-active suspension, a time lag phenomenon is inevitable. The sources of this skew are:
1) measuring a detection transmission time lag of a signal transmitted from the sensor to the control computer;
2) calculating a time lag caused by control output;
3) controlling a transmission time lag of an output signal transmitted from a computer to the magnetorheological damper;
4) and reaction time lag of the magneto-rheological damper.
The reaction time lag of the magnetorheological damper is the largest and is about 25 milliseconds. The time lag has great influence on the performance of the magneto-rheological semi-active suspension, and if the control is not added, the instability of the whole suspension system can be caused sometimes, and even wheel slip which is extremely unfavorable for safety can occur. The time lag of magnetorheological semi-active suspension systems seriously affects their practical use. Therefore, the skew compensation control is one of the key technologies for the magnetorheological semi-active suspension.
Common time-lag compensation control methods include a Smith predictor method, a time-lag system robust control method based on a Jenson inequality of a linear matrix inequality and a time-lag system robust control method of a free weight matrix, and although the methods obtain a certain time-lag compensation control effect, the methods cannot meet the high-performance requirement of real-time control of the magnetorheological semi-active suspension.
Disclosure of Invention
The invention aims to provide a magnetorheological semi-active suspension Taylor series-triple H aiming at the problems2Time lag compensation control method based on design Taylor series-H2/H2/H2The time lag compensation controller enables the magneto-rheological semi-active suspension to obtain the working effect close to the ideal semi-active suspension.
The technical scheme of the invention is as follows: the invention relates to a magneto-rheological semi-active suspension, wherein a wheel is composed of a wheel mass and a tire which is equivalent to a spring in the vertical direction, the wheel is positioned below a spring-loaded mass, and the spring and a magneto-rheological shock absorber are connected in parallel between the spring-loaded mass and the wheel mass; the spring-loaded mass acceleration sensor is arranged on the spring-loaded mass, the wheel mass acceleration sensor is arranged on the wheel mass, and the spring-loaded mass acceleration sensor and the wheel mass acceleration sensor are respectively connected with the magneto-rheological semi-active suspension controller through signal lines; the magneto-rheological shock absorber is connected to the numerical control current source through a wire, and the numerical control current source is connected to the magneto-rheological semi-active suspension controller through a signal wire.
The magneto-rheological semi-active suspension controller comprises a Taylor series-H2/H2/H2A time-lag compensation controller and a magneto-rheological damper input current solver.
The invention relates to a Taylor series-H of a magneto-rheological semi-active suspension2/H2/H2The time lag compensation control method comprises the following steps:
step S1, writing a suspension motion state equation of the magneto-rheological semi-active suspension aiming at the motion of the vehicle in the vertical direction;
step S2, writing the time lag into a first-order Taylor series-time lag equation, and forming an augmented state equation with the suspension motion state equation;
step S3, utilizing H for the augmented equation of state2Norm constraint suspension comprehensive performance index by using H2The norm restrains the control force at the next time lag moment;
step S4, introduce another H2The controller calculates the ideal control force and designs the Taylor series-H2/H2/H2A skew compensation controller;
step S5, the input current solver of the magneto-rheological damper of the magneto-rheological semi-active suspension uses the predictive control force signal FpDetermining a control current signal I for the inputiAnd the control current signal I is usediA digitally controlled current source input to the suspension generates the actual control current IaActual control current IaThe time lag compensation control device acts on the magneto-rheological shock absorber to generate actual control force, so that the time lag compensation control of the magneto-rheological semi-active suspension of the vehicle is realized.
In the above scheme, the specific process of step 1 is as follows:
the suspension system state vector is x0＝(x1,x2,x3,x4)T,x1＝z1-q,x2＝z2-z1,
Figure BDA0001462642640000024
Wherein z is1For vertical displacement of the wheel mass 7, z2For vertical displacement of sprung mass 2, q is the displacement input to the suspension system by road surface irregularities, constructing an ideal suspension equation of state that does not account for time lag
Figure BDA0001462642640000022
In the formula
Figure BDA0001462642640000023
G＝[-1 0 0 0]T，u0＝[F′MR]，w＝[w]；
In the formula: a. the0Is a suspension system state vector matrix, B0Is a suspension system control vector matrix, G is a suspension system disturbance term matrix, u0Control vector of suspension system, w is disturbance term of suspension system, w is white noise signal, m1And m2Unsprung and sprung masses, respectively; k is a radical of1And k2Tire stiffness and suspension stiffness, respectively; c. CsViscous damping for the magnetorheological damper; f'MRWhen the time lag is equal to tau, the magneto-rheological damper generates Coulomb damping force at the time t, namely control force.
In the above scheme, the step 2 comprises the following specific processes:
the predicted control force F of the next time lag momentpRepresenting the desired control force F to be derived from the current state of the suspensiontiIs a first order taylor series of variables,
Figure BDA0001462642640000031
first order Taylor series-time-lag equation written in the form of a state equation
Figure BDA0001462642640000032
And forms an augmented state equation with the suspension motion state equation
Figure BDA0001462642640000033
In the formula: x is the number oftState being a state equation of a first order Taylor series-time-lag equationAnd (5) vector quantity.
In the above scheme, the step 2 is to establish the predicted control force F at the next time lagpThe invention relates to a relation between the suspension system and a suspension system so as to smoothly design a time-lag compensation controller, and the invention relates to a suspension motion state equation FtiIs transformed as followsti＝αFti+βFpAnd α + β is 1, α is equal to or more than β and more than 0, wherein the values of α and β can be arbitrarily selected under the condition that the above conditions are met, for example, α is equal to 0.99, and β is equal to 0.01, and the suspension motion augmentation state equation is converted into:
Figure BDA0001462642640000036
in the formula:
Figure BDA0001462642640000034
u1＝[Fp]
Figure BDA0001462642640000035
Bw1＝[-1 0 0 0 0]T；
in the formula: a is the state vector matrix of the augmented system, Bu1For the augmented system control vector matrix, Bw1To augment the system interference term matrix. x is the augmented system state vector, u1To augment the system control vector.
When F is presentpBy means of H2When the norm is constrained, the weighting coefficient is selected to adjust the β value, so that the transformation is not needed.
In the above scheme, the specific process of step 3 is as follows:
step 3.1, constructing the comprehensive performance indexes of the suspension:
selecting comprehensive performance indexes of suspension
Figure BDA0001462642640000041
Represented by a state vector is:
Figure BDA0001462642640000042
in the formula:1is (z)1-q)2The weighting coefficient of (a) is determined,2is (z)2-z1)2The weighting coefficient of (2);
y1＝Cy1x+Dyu1u+Dyw1w；
Figure BDA0001462642640000043
Dyw1＝[0 0 0]T；y1as a performance output, Cy1Outputting a state vector matrix for the performance; dyu1Outputting a control vector matrix for the performance; dyw1Outputting an interference vector matrix for the performance;
step 3.2, constructing Taylor series-H2A controller:
for a given scalar gamma1> 0, there is a state feedback H for the system equation and the optimal performance output equation2Control law, if and only if there are positive symmetric definite matrix X, Z and matrix W, such that
Figure BDA0001462642640000044
Figure BDA0001462642640000045
Trace(Z)＜γ1，
Thereby realizing the utilization of H2Norm constraint suspension comprehensive performance indexes;
step 3.3, with H2The norm constrains the predictive control force at the next time lag: f is introduced on the basis of the evaluation index of the comprehensive performance of the original vehicle suspensionpPerformance index, i.e.
Figure BDA0001462642640000046
Represented by a state vector is:
Figure BDA0001462642640000047
3is FpThe weighting coefficient of (2); by pairs3The parameters are optimized to restrain the predicted control force at the next time lag moment of the magneto-rheological semi-active suspension, y'1＝C′y1x+D′yu1u+D′yw1w, wherein: c'y1＝Cy1，
Figure BDA0001462642640000051
D′yw1＝Dyw1，y′1Is H2Norm constraint Performance output, C'y1Is H2Outputting a state vector matrix by norm constraint performance; d'yu1Is H2Outputting a control vector matrix by norm constraint performance; d'yw1Is H2Outputting an interference vector matrix by norm constraint performance;3the determination of (1) takes the index J as a final optimization index, and adopts a dichotomy to iterate the optimization index J and the index J' to obtain the final optimization index.
In the above scheme, the specific process of step 4 is as follows:
for FtiAnd FpWhen solving cyclically by Taylor series, FtiNot really ideal control force, another H2Controller for using suspension system motion state vector x and H using suspension state variable as input2The ideal control force output by the controller is input, and the control force at the next time lag moment is obtained, namely the real ideal control force. From w to y'1Closed loop transfer function of
Figure BDA0001462642640000052
H of (A) to (B)2H is utilized while comprehensive performance evaluation index of norm constraint suspension2Norm constraint predictive control force, for a given scalar γ2If more than 0, state feedback H exists for system equation and constraint output equation2Control law, if and only if there are positive symmetric definite matrices X and W, such that
minγ1，
Figure BDA0001462642640000053
Figure BDA0001462642640000054
Trace(Z)＜γ2，
Find the optimal solution X*,W*And u ═ W*X*-1x is the Taylor series-H of the next time lag acquired according to the current motion state of the suspension2/H2/H2Time-lag compensation state feedback control law, predicted control force signal F derived from the control lawp。
Compared with the prior art, the invention has the beneficial effects that: in order to improve the working effect of time lag compensation control of the magneto-rheological semi-active suspension of the vehicle, time lag is written into a first-order Taylor series-time lag equation and forms an augmented state equation with a suspension system state equation; for the augmented equation of state, first, H is used2Norm constraint suspension comprehensive performance index, and H reuse2The norm restrains the predictive control force at the next time lag moment; then another H is utilized for the suspension system state equation set2The controller calculates the ideal control force and designs the Taylor series-H2/H2/H2A skew compensation controller; the skew compensation controller uses the suspension state variable and the ideal H2The controller output is input, the control current signal is obtained by taking the predicted control force at the next time lag as output, and the numerical control current source is input to obtain the actual control current of the magneto-rheological shock absorber, so that the time lag compensation control of the magneto-rheological semi-active suspension is realized. The invention designs a Taylor series-H based on the invention2/H2/H2The time lag compensation controller can enable the magneto-rheological semi-active suspension to obtain the working effect close to the ideal semi-active suspension.
Drawings
FIG. 1 is a schematic diagram of the operation of a magnetorheological semi-active suspension for a vehicle according to an embodiment of the invention.
FIG. 2 is a schematic diagram of time lag compensation control of a magnetorheological semi-active suspension according to an embodiment of the present invention.
FIG. 3 shows a Taylor series-H with an ideal control force and time lag of 30ms in accordance with one embodiment of the present invention2/H2/H2Control force comparison graph of control.
FIG. 4 is a Taylor series-H for a passive suspension, an ideal magnetorheological semi-active suspension, with a time lag of 30ms2/H2/H2And the time lag compensation control J-t curve of the magneto-rheological semi-active suspension device.
FIG. 5 is a Taylor series-H for a passive suspension, an ideal magnetorheological semi-active suspension, with a 30ms lag2/H2/H2PSD (a) controlled by time lag compensation of magneto-rheological semi-active suspension device2) -a frequency plot.
In the figure: 1. a suspension spring; 2. a sprung mass; 3. a sprung mass acceleration sensor; 4. a magnetorheological semi-active suspension controller; 5. a wheel mass acceleration sensor; 6. a magnetorheological damper; 7. wheel mass; 8. a spring-equivalent tire; 9. and (4) a numerical control current source.
Detailed Description
The present invention will be described in further detail with reference to the following drawings and detailed description, but the scope of the present invention is not limited thereto.
As shown in fig. 1: the invention applies to the magneto-rheological semi-active suspension system of 1/4 vehicle with two degrees of freedom as follows: in the vertical direction, a wheel mass 7 and a tire 8 equivalent to a spring form a wheel, the wheel is positioned below a sprung mass 2, a suspension spring 1 and a magnetorheological damper 6 are connected in parallel between the sprung mass 2 and the wheel mass 7, and uneven ground acts on the wheel through the tire 8 equivalent to the spring to enable the suspension to vibrate; the spring-loaded mass 2 is provided with a spring-loaded mass acceleration sensor 3, the wheel mass 7 is provided with a wheel mass acceleration sensor 5, and the spring-loaded mass acceleration sensor 3 and the wheel mass acceleration sensor 5 are respectively connected with the magneto-rheological semi-active suspension controller 4 through signal lines. The magneto-rheological shock absorber 6 is connected to the numerical control current source 9 through an electric wire, and the numerical control current source 9 is connected to the magneto-rheological semi-active suspension controller 4 through a signal wire.
As shown in fig. 2: the magneto-rheological semi-active suspension controller 4 consists of a Taylor series-H2/H2/H2The time-lag compensation controller and the magneto-rheological damper input current solver are formed.
Taylor series-H2/H2/H2The time lag compensation controller is responsible for solving a predicted control force signal F at the next time lag moment according to the current suspension motion statep: taylor series-H2/H2/H2Time lag compensation controller using suspension system motion state vector x and H with suspension state variable as input2The ideal control force output by the controller is input, and the predicted control force at the next time lag moment is obtained; the motion state vector x of the suspension system is obtained by taking the collected signals of the sprung mass acceleration sensor 3 and the wheel mass acceleration sensor 5 as input through a Kalman filter adopting the conventional technology.
The input current solver of the magneto-rheological shock absorber is responsible for predicting the control force signal FpConverted into a proper current value and input into the magnetorheological damper 6: using suspension system motion state vector x and H using suspension state variable as input2The ideal control force output by the controller is input, the predicted control force signal at the next time lag moment is output, and the magneto-rheological damper input current solver of the conventional technology is adopted to predict the control force signal FpDetermining a control current signal I for an inputiAnd the control current signal I is usediInput to a numerical control current source 9 to generate an actual control current IaActual control current IaThe time lag compensation control device acts on the magneto-rheological shock absorber to generate actual control force, so that the time lag compensation control of the magneto-rheological semi-active suspension of the vehicle is realized.
Step 1, writing a suspension motion state equation aiming at the motion of a vehicle in the vertical direction.
The invention aims to research the influence and the solution of time lag on the smoothness of a magneto-rheological semi-active suspension, and an 1/4 vehicle 2 degree-of-freedom magneto-rheological semi-active suspension mathematical model is used as the most basic magneto-rheological semi-active suspension model, has few parameters and a clear target, so the model is used as the mathematical model of the invention to research and simulate, and is shown in figure 1.
The differential equation of motion for the suspension is as follows:
Figure BDA0001462642640000071
in the formula: m is1And m2Unsprung and sprung masses, respectively; k is a radical of1And k is2Tire stiffness and suspension stiffness, respectively; z is a radical of1And z2Vertical displacement of the unsprung mass and vertical displacement of the sprung mass, respectively; f'MRWhen the time lag is equal to tau, the magneto-rheological shock absorber generates coulomb damping force at the time t, namely control force; q is the displacement input to the suspension system by the road surface irregularity, expressed as:
Figure BDA0001462642640000072
in the formula: n is0Is the spatial reference frequency, 0.1; w is a road white noise signal; gq(n0) Is the road surface irregularity coefficient; v is vehicle speed; f. of0Is the lower cut-off frequency, equal to 0.011 v.
Based on a two-degree-of-freedom 1/4 vehicle magneto-rheological semi-active suspension mathematical model, taking a suspension system state vector as:
Figure BDA0001462642640000073
the state equation of the suspension system is:
Figure BDA0001462642640000074
in the formula
Figure BDA0001462642640000075
G＝[-1 0 00]Tu0＝[F′MR]，w＝[w]，A0Is a suspension system state vector matrix, B0Is a suspension system control vector matrix, G is a suspension system disturbance term matrix, u0Suspension systemAnd (3) a system control vector, wherein w is a suspension system interference term quantity, and w is a unit white noise signal.
And 2, writing the time lag into a first-order Taylor series-time lag equation, and forming an augmented state equation together with the suspension motion state equation.
Without compensation for skew, H2The ideal control force signal obtained by the controller passes through the lag-containing control force F'MR：
F′MR＝Fi(t-τ) (5)
In the formula, FiIs H2And controlling the obtained ideal control force.
In order to improve the control effect, at the time t, a first-order Taylor series is combined with H2Controlling the predicted control force F at the moment when t + tau is predicted in advancepSo as to compensate the system time lag, when tau is smaller, then
Figure BDA0001462642640000081
When the magneto-rheological semi-active suspension control design is carried out, an ideal control force signal F is firstly obtained by a controllertiThen, the ideal control force signal is transmitted to the magneto-rheological damper to obtain the actual control force, namely the predicted control force Fp. Taylor series-H2The control that the controller needs to find is FpBut not Fti。
Writing equation (6) as an expansion equation:
Figure BDA0001462642640000082
design H2When the controller is used, F 'in the formula (4) is set'MRBy FtiAlternatively, it is then directly combined with formula (6):
Figure BDA0001462642640000083
in the formula: x is the number oftIs a state vector of a first-order taylor series-time-lag equation state equation.
For establishing a predicted control force F for the next time lagpThe invention relates to a relation between the suspension system and a suspension system so as to smoothly design a time-lag compensation controller, and the invention relates to a suspension motion state equation FtiThe following transformations are made:
Figure BDA0001462642640000084
the α and β values may be arbitrarily selected so as to satisfy the above conditions, and for example, α -0.99 and β -0.01 are used.
The new extended state equation is as follows:
Figure BDA0001462642640000085
in the formula: u. of1＝[Fp]
Figure BDA0001462642640000091
Bw1＝[-1 0 0 0 0]TA is the state vector matrix of the augmented system, Bu1For the augmented system control vector matrix, Bw1To augment the system interference term matrix. x is the augmented system state vector, u1To augment the system control vector.
Since α > β > 0, F before conversion in equation (10)tiAnd β F after transformationti+αFpAre almost equal. When F is presentpBy means of H2When the norm is constrained, the transformation may not be required.
Step 3, aiming at the augmented state equation, H is utilized2Norm optimization of comprehensive performance index of suspension by using H2The norm constrains the predicted control force at the next time lag instant.
(1) And constructing the comprehensive performance index of the suspension.
The suspension system has a great influence on the smoothness and the steering stability of the automobile, and generally, performance evaluation indexes of the suspension system mainly include vehicle body acceleration, suspension dynamic deflection and tire dynamic load (or tire dynamic deformation). The invention constructs the comprehensive performance evaluation index of the suspension on the basis of the three evaluation indexes.
Selecting comprehensive performance indexes of suspension
Figure BDA0001462642640000092
Represented by a state vector is:
Figure BDA0001462642640000093
y1＝Cy1x+Dyu1u+Dyw1w (11)
in the formula:
Figure BDA0001462642640000094
Dyw1＝[0 0 0]T，y1as a performance output, Cy1Outputting a state vector matrix for the performance; dyu1Outputting a control vector matrix for the performance; dyw1An interference vector matrix is output for performance.
(2) Design of Taylor series-H2And a controller.
A controller is designed to ensure that the closed loop system is gradually stable and from w to y1Closed loop transfer function of
Figure BDA0001462642640000095
H of (A) to (B)2Norm as small as possible, using H2And (4) evaluating the comprehensive performance of the norm constraint suspension. This problem can be translated into making a closed loop system satisfactory
Figure BDA0001462642640000106
In all controllers of (1), look for so that γ is1Minimized controller, this problem translates into H of the system's equation of state and optimal performance output equation2The design of the controller.
For a given scalar gamma1If > 0, state feedback H exists for the system equation (10) and the performance output equation (11)2Control law, if and only if there are positive symmetric definite matrix X, Z and matricesW is added. So that
Figure BDA0001462642640000101
Figure BDA0001462642640000102
Trace(Z)＜γ1(12.c)
(3) By means of H2The norm constrains the predicted control force at the next time lag instant.
When the state estimation is carried out by the first-order Taylor series, only an approximate process is carried out, and a certain error still exists between the coefficient tau and an ideal value, which can cause the expansion H of the Taylor series2The control gain is too large. However, in the magneto-rheological semi-active suspension system with time lag, the larger the feedback gain is, the smaller the critical time lag is, and H is2Too much control gain will reduce the critical time lag, resulting in degraded suspension performance. The invention proposes to utilize H2The predictive control force for controlling and restraining the magneto-rheological semi-active suspension solves the Taylor series-H2The problem of the deterioration of the suspension performance caused by the overlarge control gain.
F is introduced on the basis of the evaluation index of the comprehensive performance of the original vehicle suspensionpPerformance index, i.e.
Figure BDA0001462642640000103
Represented by a state vector is:
Figure BDA0001462642640000104
3is FpBy a pair of3And optimizing the parameters to restrain the predictive control force of the magnetorheological semi-active suspension at the next time lag moment.
y′1＝C′y1x+D′yu1u+D′yw1w (13)
Wherein:
Figure BDA0001462642640000105
D′yw1＝Dyw1,y′1is H2The norm constrains the performance output to be,
Figure BDA0001462642640000107
is H2Outputting a state vector matrix by norm constraint performance; d'yu1Is H2Outputting a control vector matrix by norm constraint performance; d'yw1Is H2The norm constraint performance outputs a matrix of interference vectors,3the determination of (1) takes the index J as a final optimization index, and adopts a dichotomy to iterate the optimization index J and the index J' to obtain the final optimization index.
Step 4, another H is introduced2The controller calculates the ideal control force and designs the Taylor series-H2/H2/H2A skew compensation controller.
For FtiAnd FpWhen solving cyclically by Taylor series, FtiNot really ideal control force, it is proposed to introduce another H2Controller for using suspension system motion state vector x and H using suspension state variable as input2The ideal control force output by the controller is input, and the control force at the next time lag moment is obtained, namely the real ideal control force. And designing a controller to ensure that the closed loop system is gradually stable from w to y'1Closed loop transfer function of
Figure BDA0001462642640000111
H of (A) to (B)2H is utilized while comprehensive performance evaluation index of norm constraint suspension2Norm constraint predictive control force, for a given scalar γ2> 0, for system equation (10), H2Norm constrained output equation (13) presence state feedback H2Control law, if and only if there are positive symmetric definite matrices X and W, such that
minγ1
Figure BDA0001462642640000112
Figure BDA0001462642640000113
Trace(Z)＜γ2(14.c)
Find the optimal solution X*,W*And u ═ W*X*-1x is a Taylor series-H2/H2And (3) feedback control law of time lag compensation state of the magneto-rheological semi-active suspension.
Step S5, passing the Taylor series-H2/H2/H2Time-lag compensation controller for solving predicted control force signal FpThe input current solver of the magneto-rheological damper of the magneto-rheological semi-active suspension adopts the prediction control force signal FpDetermining a control current signal I for an inputiAnd the control current signal I is usediA digitally controlled current source 9 input to the suspension generates the actual control current IaActual control current IaActing on the magneto-rheological shock absorber 6 to generate actual control force so as to realize time lag compensation control of the magneto-rheological semi-active suspension of the vehicle.
The preferred embodiment:
the invention discloses a best specific implementation method which comprises the following steps:
parameters adopted in practical application: m is1＝35kg，m2＝500kg，k1＝30000N/m，k2＝50500N/m，cs3015 Ns/m, the time lag τ is 30ms considering the time lag of the magnetorheological damper is about 25-28 ms. The nominal working condition of the vehicle is that the vehicle runs on a C-level road at a vehicle speed v-20 m/s, and corresponds to the following conditions: gq(n0)＝256×10-6m2/m-1，1＝53775，2＝4108.7。
The vehicle body acceleration sensor and the tire acceleration sensor respectively measure the output vectors of the vehicle body acceleration and the tire acceleration, and the output state vector enters Taylor series-H through the Kalman filter2/H2/H2And a controller. Taylor series-H2/H2/H2The time lag compensation controller obtains a predicted control force signal F at the next time lag moment according to the current suspension motion statepAnd inputting the current into an input current solver of the magneto-rheological shock absorber; control force signal F of magnetorheological damper input current solverpConverting the control current signal IiAnd the control current signal I is usediInput to a numerical control current source 9 to generate an actual control current IaActual control current IaActing on the magnetorheological damper to generate actual control force.
As shown in FIG. 3, the ideal control force and time lag of the MR semi-active suspension is Taylor series-H when the ideal control force and time lag is 30ms2/H2/H2The predicted control force of the control is compared. The estimated time lag control force has good tracking ability on the ideal control force, and the Taylor series-H2/H2/H2The magnitude of the control force controlled is effectively limited.
As shown in FIG. 4, the Taylor series-H of the passive suspension, the ideal magneto-rheological semi-active suspension and the time lag of 30ms2/H2/H2And comparing J-t curves of time lag compensation control of the magneto-rheological semi-active suspension device. The smaller the numerical value of the secondary performance index J is, the better the control performance is, the J value of the passive suspension is 5.4165 at 10 seconds, the J value of the ideal semi-active control is 3.286 at 10 seconds, and the Taylor series-H2/H2/H2The J value is 3.5099 when the time lag compensation of the magneto-rheological semi-active suspension device is controlled at 10 seconds, and the Taylor series-H designed by the invention can be seen from the figure2/H2/H2The time lag compensation control method of the magneto-rheological semi-active suspension can effectively improve the performance of a magneto-rheological semi-active suspension system with time lag.
As shown in FIG. 5, the Taylor series-H of the passive suspension, the ideal magneto-rheological semi-active suspension, with a time lag of 30ms2/H2/H2PSD (a) controlled by time lag compensation of magneto-rheological semi-active suspension device2) -frequency curve comparison. a is2Representing sprung mass acceleration, which is often used to evaluate ride comfort, is a primary evaluation index for ride comfort. In practical use, PSD (a)2) Smaller means better ride comfort. The Taylor series-H designed by the invention can be seen from the figure2/H2/H2Magneto-rheological semi-active suspensionThe device time lag compensation control method can effectively improve the riding comfort of the magneto-rheological semi-active suspension system with time lag.
In summary, the following steps: the invention discloses a method based on Taylor series-H2/H2/H2The invention discloses a time lag compensation controller of a magneto-rheological semi-active suspension device, which is based on a two-degree-of-freedom 1/4 vehicle model and provides an application of Taylor series to H2The controller performs time lag compensation and adopts H for the Taylor series to predict the control force amplification phenomenon2The controller performs the constraint according to the Taylor series-H2/H2/H2And the output feedback controller obtains the control force of the suspension system. Taylor series-H designed by using the invention2/H2/H2The controller can effectively improve the time lag problem of the magnetorheological semi-active suspension control system of the vehicle. The invention provides a new idea for improving the time lag problem of the magnetorheological semi-active suspension control system of the vehicle.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.

Claims (3)

1. Magnetorheological semi-active suspension Taylor series-triple/H2The time lag compensation control method is characterized by comprising the following steps of:
step S1, writing a suspension motion state equation of the magneto-rheological semi-active suspension aiming at the motion of the vehicle in the vertical direction;
the specific process of step S1 is as follows:
the suspension system state vector is x0＝(x1,x2,x3,x4)T,x1＝z1-q,x2＝z2-z1,
Figure FDA0002437034260000011
Wherein z is1Is a vertical displacement of the wheel mass (7), z2Is a springThe vertical displacement of the load mass (2), q is the displacement input of the road surface unevenness to the suspension system, and an ideal suspension state equation without time lag is constructed
Figure FDA0002437034260000012
In the formula
Figure FDA0002437034260000013
G＝[-1 0 0 0]T，u0＝[F′MR]，w＝[w]；A0Is a suspension system state vector matrix, B0Is a suspension system control vector matrix, G is a suspension system disturbance vector matrix, u0Control vector of suspension system, w is disturbance vector of suspension system, w is white noise signal unit, m1And m2Unsprung and sprung masses, respectively; k is a radical of1And k2Tire stiffness and suspension stiffness, respectively; c. CsViscous damping for the magnetorheological damper; f'MRWhen the time lag is equal to tau, the magneto-rheological shock absorber generates coulomb damping force at the time t, namely control force;
step S2, writing the time lag into a first-order Taylor series-time lag equation, and forming an augmented state equation with the suspension motion state equation;
the specific process of step S2 is as follows:
the predicted control force F of the next time lag momentpRepresenting the desired control force F to be derived from the current state of the suspensiontiIs a first order taylor series of variables,
Figure FDA0002437034260000014
first order Taylor series-time-lag equation written in the form of a state equation
Figure FDA0002437034260000015
And forms an augmented state equation with the suspension motion state equation
Figure FDA0002437034260000016
In the formula: x is the number oftIs a Taylor series-time-lag equationA state vector of a state equation;
in the step S2, the predicted control force F for the next time lag is establishedpRelation to suspension system, equation of state of motion for suspension FtiIs transformed as followsti＝αFti+βFpAnd the conditions that α + β is 1 and α is more than or equal to β and more than 0 are met, and the suspension motion augmentation state equation is converted into:
Figure FDA0002437034260000021
in the formula:
Figure FDA0002437034260000022
u1＝[Fp]
Figure FDA0002437034260000023
Bw1＝[-1 0 0 0 0]Ta is the state vector matrix of the augmented system, Bu1For the augmented system control vector matrix, Bw1For the augmented system interference vector matrix, x is the augmented system state vector, u1Control vectors for the augmented system;
step S3, utilizing H for the augmented equation of state2Norm constraint suspension comprehensive performance index by using H2The norm restrains the control force at the next time lag moment;
the specific process of step S3 is as follows:
step 3.1, constructing the comprehensive performance indexes of the suspension:
selecting comprehensive performance indexes of suspension
Figure FDA0002437034260000024
Represented by a state vector is:
Figure FDA0002437034260000025
in the formula:1is (z)1-q)2The weighting coefficient of (a) is determined,2is (z)2-z1)2The weighting coefficient of (2);
the optimal performance output equation for the comprehensive performance evaluation of the suspension is as follows:
y1＝Cy1x+Dyu1u+Dyw1w；
Figure FDA0002437034260000026
Dyw1＝[0 0 0]T；y1as a performance output, Cy1Outputting a state vector matrix for the performance; dyu1Outputting a control vector matrix for the performance; dyw1Outputting an interference vector matrix for the performance;
step 3.2, constructing Taylor series-H2A controller:
for a given scalar gamma1Greater than 0, there is a state feedback H for the augmented state equation and the optimal performance output equation2Control law, if and only if there are positive symmetric definite matrix X, Z and matrix W, such that
Figure FDA0002437034260000031
Figure FDA0002437034260000032
Trace(Z)＜γ1，
Thereby realizing the utilization of H2Norm constraint suspension comprehensive performance indexes;
step 3.3, with H2The norm constrains the predictive control force at the next time lag: f is introduced on the basis of the evaluation index of the comprehensive performance of the original vehicle suspensionpPerformance index, i.e.
Figure FDA0002437034260000033
Represented by a state vector is:
Figure FDA0002437034260000034
3is FpBy a pair of3Optimizing the parameters to restrain the predictive control force of the magnetorheological semi-active suspension at the next time lag moment to obtain a constraint performance output equation: y'1＝C′y1x+D′yu1u+D′yw1w, wherein:
Figure FDA0002437034260000035
D′yw1＝Dyw1，y′1is H2Norm constraint Performance output, C'y1Is H2Outputting a state vector matrix by norm constraint performance; d'yu1Is H2Outputting a control vector matrix by norm constraint performance; d'yw1Is H2Outputting an interference vector matrix by norm constraint performance;3determining the target J by taking the target J as a final optimization target and adopting a dichotomy to iteratively optimize the target J and the target J';
step S4, introduce another H2The controller calculates the ideal control force and designs the Taylor series-H2/H2/H2A skew compensation controller; the specific process of step S4 is as follows:
for FtiAnd FpWhen solving cyclically by Taylor series, FtiNot really ideal control force, another H2Controller for using suspension system motion state vector x and H using suspension state variable as input2The ideal control force output by the controller is input, and the control force at the next time lag moment is obtained, namely the real ideal control force. From w to y'1Closed loop transfer function of
Figure FDA0002437034260000036
H of (A) to (B)2H is utilized while comprehensive performance evaluation index of norm constraint suspension2Norm constraint predictive control force, for a given scalar γ2If more than 0, state feedback H exists for the augmented state equation and the constraint performance output equation2Control law, if and only if there are positive symmetric definite matrices X and W, such that
minγ1，
Figure FDA0002437034260000041
Figure FDA0002437034260000042
Trace(Z)＜γ2，
Find the optimal solution X*,W*And u ═ W*X*-1x is the Taylor series-H of the next time lag acquired according to the current motion state of the suspension2/H2/H2A time-lag compensation state feedback control law;
step S5, passing the Taylor series-H2/H2/H2Time-lag compensation controller for solving predicted control force signal FpThe input current solver of the magneto-rheological damper of the magneto-rheological semi-active suspension adopts the prediction control force signal FpDetermining a control current signal I for an inputiAnd the control current signal I is usediA digitally controlled current source (9) input to the suspension generates an actual control current IaActual control current IaActing on the magneto-rheological shock absorber (6) to generate actual control force, thereby realizing time lag compensation control of the magneto-rheological semi-active suspension of the vehicle.
2. The taylor series-triple H of the magnetorheological semi-active suspension of claim 12The time lag compensation control method is characterized in that a wheel mass (7) of the magneto-rheological semi-active suspension in the vertical direction and a tire (8) equivalent to a spring form a wheel, the wheel is positioned below a sprung mass (2), and the spring (1) and the magneto-rheological shock absorber (6) are connected in parallel between the sprung mass (2) and the wheel mass (7); a spring-loaded mass acceleration sensor (3) is arranged on the spring-loaded mass (2), a wheel mass acceleration sensor (5) is arranged on the wheel mass (7), and the spring-loaded mass acceleration sensor (3) and the wheel mass acceleration sensor (5) are respectively connected to a magneto-rheological semi-active suspension controller (4) through signal lines; the magneto-rheological damper (6) is connected with the magnetic flow damper through an electric wireThe magnetorheological semi-active suspension controller is connected with a numerical control current source (9), and the numerical control current source (9) is connected with the magnetorheological semi-active suspension controller (4) through a signal wire.
3. The taylor series-triple H of the magnetorheological semi-active suspension of claim 22The time lag compensation control method is characterized in that the magneto-rheological semi-active suspension controller (4) comprises a Taylor series-H2/H2/H2A time-lag compensation controller and a magneto-rheological damper input current solver.
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