CN110096840A - The sliding-mode control of vehicle suspension - Google Patents
The sliding-mode control of vehicle suspension Download PDFInfo
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Abstract
The sliding-mode control of vehicle suspension, belongs to field of vehicle control.In order to solve the problems, such as existing control method to be applied to vehicle rheological suspension, that there are effectiveness in vibration suppression is undesirable.The present invention combines optimum control with sliding formwork control, form the Optimal Sliding Mode Control based on smooth performance indicator, controller can determine sliding formwork diverter surface equation according to optimal control index, move system along diverter surface, so that system obtains optimal performance and good variable working condition robustness.The suspension mass center acceleration and mass center pitching angular acceleration that the present invention also further obtains the Optimal Sliding Mode Control target multiplied by corresponding coefficient, as bottom control respectively.PSO- is finally obscured PI to be applied in the bottom control of decoupling suspension, to realize the hierarchical control of vehicle rheological suspension, the control damping force of fore suspension and rear suspension is respectively obtained by bottom control algorithm in this way, can further promote control effect.The present invention is used for the control of vehicle suspension.
Description
Technical field
The present invention relates to a kind of control methods of vehicle.Belong to field of vehicle control.
Background technique
In recent years, using control strategy as means, the damping property for studying suspension system becomes the heat of domestic and foreign scholars' research
Point problem.It is different according to the method for realizing control, by the suspension system with control function be divided into active control suspension system and
Semi- active control suspension system, to breach the damper mode of passive suspension system.Compared with full Active control suspension, half
Active control suspension does not need to be actively entered energy, it is only necessary to adjust control suspension system according to the requirement of vehicle driving-cycle
Damping or spring rate, securely and reliably, it is easy to accomplish, there is critically important application value.
Semi-active suspension system based on MR damper has excellent effectiveness in vibration suppression, effectively improves vehicle driving
Ride comfort, comfort have become the hot issue studied both at home and abroad at present.In external vehicle, Ferrari 599,
It is filled in California, 458 Italia, F12 Berlinetta, FF and low and middle-grade ATS, CTS, XTS vehicles of Cadillac
Equipped with magnetic rheology type semi-active suspension control system, with the deep and automobile test research of magnetic rheology type semi-active suspension research
The increasingly maturation of work, magneto-rheological semiactive suspension have the tendency that promoting to middle-grade vehicle, domestic vehicle be looked forward to, in order to develop
With same external rheological suspension system similar vehicle ride comfort under different driving cycles, double of active vehicle suspension
Control system is studied.Vehicle seat is the important component of vehicle vibration reduction system, it can make driver and conductor avoid height
The vibration of intensity.The working environment of especially heavy-duty car, agricultural vehicle and engineering truck is poor, load is big, driving process vibration
It is dynamic big, it is undesirable to improve its vehicle suspension effectiveness in vibration suppression, but raising seat suspension performance is convenient and easy, the period is short, quick.Cause
This, research and improvement seat dynamic property have great significance for improving vehicle riding comfort.But MR damper
Control in terms of be research and develop half active vehicle difficult point, therefore the effective control method of magneto-rheological semiactive suspension become research and development
Emphasis and difficult point.
Summary of the invention
The present invention is that applied to vehicle rheological suspension, that there are effectiveness in vibration suppression is undesirable in order to solve existing control method
The problem of.
The sliding-mode control of vehicle suspension, comprising the following steps:
Step 1 carries out dynamic analysis for half vehicle 4DOF auto model, and determines state equation:
State vector X=(x1,x2,x3,x4,x5,x6,x7,x8)T, wherein x1=z11-q1,x2=z21-q2,x3=z12-z11,
x4=z22-z21, For the first derivative of X；
Input vector U*=[F1,F2,q1,q2]T；
Output vector are as follows:
Y=(y1,y2,y3,y4,y5,y6)T
In formula:y2=z11-q1,y3=z21-z11,y4=z12-z11,y5=z22-z21,
Output equation are as follows:
Y=CX+DU*
In formula: z21、z22The vertical displacement of respectively forward and backward suspension and vehicle body tie point；l1、l2Respectively vehicle body mass center O
To the distance of forward and backward axle；θ is pitch angle；z3For the vertical deviation of vehicle body mass center；m1、m2、m3Respectively forward and backward non-spring charge material
Amount and spring carried mass；I is pitch rotation inertia of the vehicle body around mass center；z11、z12Respectively forward and backward nonspring carried mass vertical deviation；
c1、c2Not Wei forward and backward suspension Equivalent damping coefficient；k11、k21、k12、k22Respectively forward and backward tire is equivalent with forward and backward suspension
Stiffness coefficient；F1、F2Respectively forward and backward half active desired control power of suspension；F3、F4It is respectively acquired by controller forward and backward
Suspension semi- active control power；q1、q2The Excitation of Random Road Surface of respectively forward and backward axle；V is speed；f0For lower limiting frequency；n0
For reference frequency；Gn(n0) it is road roughness coefficient；W is road surface white noise signal；
Step 2, the Optimal Sliding Mode Control based on the smooth performance indicator of rheological suspension:
The suspension integrated performance index J of selection:
In formula: T is the total time of vehicle operation；T indicates time change；δ1, δ2, δ3, δ4, δ5And δθFor(z11-q1)2, (z21-q2)2,WithWeighting coefficient；
Building Optimal Sliding Mode manifold function and selection linear sliding mode tendency rate simultaneously find out ideal dominant vector are as follows:
U=- (KB1)-1(KA+ λ K) X=U1+U2
U in formula1=-(KB1)-1KAX,U2=-(KB1)-1λKX；
The control of vehicle suspension is realized according to ideal dominant vector.
The sliding-mode control of vehicle suspension, comprising the following steps:
Step 1 carries out dynamic analysis for half vehicle 4DOF auto model, and determines state equation:
State vector X=(x1,x2,x3,x4,x5,x6,x7,x8)T, wherein x1=z11-q1,x2=z21-q2,x3=z12-z11,
x4=z22-z21, For the first derivative of X；
Input vector U*=[F1,F2,q1,q2]T；
Output vector are as follows:
Y=(y1,y2,y3,y4,y5,y6)T
In formula:y2=z11-q1,y3=z21-z11,y4=z12-z11,y5=z22-z21,
Output equation are as follows:
Y=CX+DU*
In formula: z21、z22The vertical displacement of respectively forward and backward suspension and vehicle body tie point；l1、l2Respectively vehicle body mass center O
To the distance of forward and backward axle；θ is pitch angle；z3For the vertical deviation of vehicle body mass center；m1、m2、m3Respectively forward and backward non-spring charge material
Amount and spring carried mass；I is pitch rotation inertia of the vehicle body around mass center；z11、z12Respectively forward and backward nonspring carried mass vertical deviation；
c1、c2Not Wei forward and backward suspension Equivalent damping coefficient；k11、k21、k12、k22Respectively forward and backward tire is equivalent with forward and backward suspension
Stiffness coefficient；F1、F2Respectively forward and backward half active desired control power of suspension；F3、F4It is respectively acquired by controller forward and backward
Suspension semi- active control power；q1、q2The Excitation of Random Road Surface of respectively forward and backward axle；V is speed；f0For lower limiting frequency；n0
For reference frequency；Gn(n0) it is road roughness coefficient；W is road surface white noise signal；
Step 2, the Optimal Sliding Mode Control based on the smooth performance indicator of rheological suspension:
The suspension integrated performance index J of selection:
In formula: T is the total time of vehicle operation；T indicates time change；δ1, δ2, δ3, δ4, δ5And δθFor(z11-q1)2, (z21-q2)2,WithWeighting coefficient；
Building Optimal Sliding Mode manifold function and selection linear sliding mode tendency rate simultaneously find out ideal dominant vector are as follows:
U=- (KB1)-1(KA+ λ K) X=U1+U2
U in formula1=-(KB1)-1KAX,U2=-(KB1)-1λKX；
Step 3 establishes dynamics hierarchical mode:
By the conversion of dynamic suspension system of vehicles equation, by half suspension four-degree-of-freedom it is system converting be two two degrees of freedom systems
System；
Currently, after rear-suspension system spring carried mass decomposes, nonspring carried mass also accordingly generates displacement xuf、ΔxurIf
With The displacement state of its nonspring carried mass after forward and backward suspension system is decomposed is respectively indicated, with xuf、xurIt respectively indicates point
The displacement state of nonspring carried mass before solution, then haveTo the suspension system after decomposition
Spring carried mass, nonspring carried mass arrange its dynamic balance equation respectively:
In formula, kmiAnd cniRespectively indicate the stiffness coefficient and damped coefficient of suspension；FmiIndicate the output of semi active actuator
Power；kuiIndicate tire stiffness；muiIndicate nonspring carried mass；xsiIndicate road excitation, subscript i=f or r, indicate front side or after
Side；
After two formulas are added in formula:
By Δ xufWith Δ xurExpression formula substitutes into the change in displacement that can acquire suspension system nonspring carried mass in above formula respectively
Amount:
Step 4, the dynamics hierarchical mode based on step 3 are outstanding to vehicle to carry out hierarchical control:
(1) the suspension mass center acceleration for obtaining Optimal Sliding Mode ControlWith mass center pitching angular accelerationRespectively multiplied by setting
Determine coefficient, the target as bottom control；
(2) basisWithDiscreet value andWithDiscreet value, the fore suspension and rear suspension spring charge material after being decomposed
Measure the discreet value of acceleration；
(3)WithAs given value, two degrees of freedom suspension state-space equation expression formula is established；
Control force F needed for obtaining two degrees of freedom suspension according to two degrees of freedom suspension state-space equationmi, then determine
WithActual value；
(4) it is obtained according to the process of step 3WithActual value, andWithActual value；
(5) the semi-active suspension bottom control of PI is obscured based on PSO-:
It sets mark i=f or r and respectively indicates forward and backward suspension；
Trial and error procedure comparative example COEFFICIENT K is used firstP_iWith integral coefficient KI_iCoarse adjustment is carried out, coarse steps are as follows:
(a) coarse adjustment scale parameter: first by KP_iValue is placed on lesser position, when exporting nonoscillatory, scaling up coefficient
KP_i；
(b) coarse adjustment integral parameter: after adjusting scale parameter, ratio value is reduced into (10~20%), when then will integrate
Between it is descending be gradually added, until obtain 4:1 attenuation process；
After coarse adjustment, PSO algorithm is added in Fuzzy PI Controller；The deviation of fore suspension and rear suspension is(i=f
Or r), it is entered into PSO- Fuzzy PI Controller, controller exports control law ufuzzy-pi-pso_i(t), control law is
The utility model has the advantages that
The present invention is to improve vehicle suspension ride comfort, and vehicle ride comfort energy index is embodied on sliding formwork diverter surface, will most
Excellent control is combined with sliding formwork control, forms the Optimal Sliding Mode Control based on smooth performance indicator, and such controller can basis
Optimal control index determines sliding formwork diverter surface equation, moves system along diverter surface, thus system obtain optimal performance with
And good variable working condition robustness, and can also ensure that vehicle rheological suspension there are effectiveness in vibration suppression.
The suspension mass center acceleration and mass center pitching angular acceleration that the present invention also further obtains Optimal Sliding Mode Control point
Target not multiplied by corresponding coefficient, as bottom control.PSO- is finally obscured into the bottom control that PI is applied to decoupling suspension
In, to realize the hierarchical control of vehicle rheological suspension, the control of fore suspension and rear suspension is respectively obtained by bottom control algorithm in this way
Damping force processed can further promote control effect, and obtaining more excellent vehicle rheological suspension, there are effectiveness in vibration suppression.The present invention
The acceleration root mean square and equivalent averages of further PSO- fuzzy PI hybrid control layering are respectively less than passive and PID layering control
System, the i.e. present invention have good effect for the comfort for improving vehicle suspension.
Detailed description of the invention
Fig. 1 is vehicle rheological suspension Optimal Sliding Mode hierarchical control schematic diagram；
Fig. 2 is the system block diagram of automobile ride analytic process；
Fig. 3 is spring carried mass force analysis figure；
Fig. 4 is simplified spring carried mass force diagram and its assumes the displacement diagram after decomposing；
Fig. 5 is the forward and backward suspension system after decomposing；
Fig. 6 is PSO- fuzzy PI hybrid control schematic diagram；
Fig. 7 is the simulation result of the vehicle body acceleration of each control method；
Fig. 8 is the simulation result of the vehicle body velocities of each control method；
Fig. 9 is equiband acceleration Power spectral density.
Specific embodiment
To improve vehicle suspension ride comfort, vehicle ride comfort energy index is embodied on sliding formwork diverter surface, by optimum control
It is combined with sliding formwork control, forms the Optimal Sliding Mode Control based on smooth performance indicator, such controller can be according to optimal control
Index processed determines sliding formwork diverter surface equation, moves system along diverter surface, so that system obtains under nominal condition most
Dominance energy and good variable working condition robustness.Then it on the basis of based on the Optimal Sliding Mode of smooth performance indicator, proposes most
Half suspension is decoupled into 1/4 fore suspension and rear suspension by theory deduction first, then by Optimal Sliding Mode Control by excellent sliding formwork hierarchical control
The obtained suspension mass center acceleration and mass center pitching angular acceleration target multiplied by corresponding coefficient, as bottom control respectively.
PSO- is finally obscured PI to be applied in the bottom control of decoupling suspension, to realize the hierarchical control system of vehicle rheological suspension
System.Vehicle magneto-rheological semiactive suspension is referred to as vehicle rheological suspension by this patent, and Fig. 1 is the optimal cunning of vehicle rheological suspension
Mould hierarchical control schematic diagram, multi-layer controller are made of top level control and bottom control, by theory deduction by half suspension
It is decoupled into 1/4 fore suspension and rear suspension, wherein top level control provides target for bottom control, makes 1/4 fore suspension and rear suspension of bottom that target be followed to transport
It is dynamic.The present invention bows suspension mass center acceleration and mass center that Optimal Sliding Mode Control obtains on the basis of the Optimal Sliding Mode of proposition
Elevation angle acceleration is applied to decoupling respectively multiplied by corresponding coefficient, as the target of bottom control, then by PSO- fuzzy PI hybrid control
In the bottom control of suspension, the control damping force of fore suspension and rear suspension is respectively obtained by bottom control algorithm, is realized to vehicle magnetic current
Become the Optimal Sliding Mode hierarchical control of suspension.
Specific embodiment 1:
The sliding-mode control of vehicle suspension described in present embodiment, comprising the following steps:
Step 1 establishes half suspension model:
The present invention uses half vehicle 4DOF auto model, sees Fig. 1, carries out dynamic analysis to auto model:
In formula: z21、z22The vertical displacement of respectively forward and backward suspension and vehicle body tie point；l1、l2Respectively vehicle body mass center O
To the distance of forward and backward axle；θ is pitch angle；z3For the vertical deviation of vehicle body mass center；m1、m2、m3Respectively forward and backward non-spring charge material
Amount and spring carried mass；I is pitch rotation inertia of the vehicle body around mass center；z11、z12Respectively forward and backward nonspring carried mass vertical deviation；
c1、c2Not Wei forward and backward suspension Equivalent damping coefficient；k11、k21、k12、k22Respectively forward and backward tire is equivalent with forward and backward suspension
Stiffness coefficient；F1、F2Respectively forward and backward half active desired control power of suspension；F3、F4It is respectively acquired by controller forward and backward
Suspension semi- active control power；q1、q2The Excitation of Random Road Surface of respectively forward and backward axle；V is speed；f0For lower limiting frequency；n0
For reference frequency；Gn(n0) it is road roughness coefficient；W is road surface white noise signal.
Take state vector are as follows:
X=(x1,x2,x3,x4,x5,x6,x7,x8)T (6)
In formula:
x1=z11-q1,x2=z21-q2,x3=z12-z11,x4=z22-z21,
State equation are as follows:
Input vector U*=[F1,F2,q1,q2]T；
In formula:
Output vector are as follows: Y=(y1,y2,y3,y4,y5,y6)T (8)
In formula:y2=z11-q1,y3=z21-z11,y4=z12-z11,y5=z22-z21,
Output equation are as follows:
Y=CX+DU* (9)
In formula:
Step 2, the Optimal Sliding Mode Control based on the smooth performance indicator of rheological suspension:
In the design process of semi-active suspension system controller, how to guarantee that automobile has ideal traveling smooth
Property and control stability are one of Car design emphasis.And researching and analysing for road holding, Fig. 2 automobile can be passed through
The maneuvering sequence of Ride Comfort Analysis procedures system block diagram carries out.The system block diagram analysis of automobile ride analytic process according to fig. 2
It is found that automobile crosses the vibration that uneven road surface causes tire, suspension, elastic element, damping element and seat with certain speed,
Vibration passes to human body eventually by seat.The present invention is using vehicle body acceleration, tyre dynamic load lotus and pitching angular acceleration as most
The evaluation index of excellent sliding formwork.In order to carry out ride comfort evaluation to Optimal Sliding Mode, pass through the Optimal Sliding Mode algorithm of smooth performance indicator
Control obtained vehicle body accelerationTire dynamic deformation (z11-q1And z21-q2) and pitching angular accelerationRespectively with formula (10)
Seek their root mean square
In formula: X is vehicle body acceleration, tire dynamic deformation and the pitch angle emulated by semi-active suspension Optimal Sliding Mode
Acceleration, NnFor the quantity of each parameters simulation.
To sum up flexibility index is determined as vehicle body acceleration, tire dynamic deformation and pitching angular acceleration, in order to improve suspension
The suspension integrated performance index J such as formula (11) that selects of the ride comfort present invention shown in:
In formula: T is the total time of vehicle operation；T indicates time change；δ1, δ2, δ3, δ4, δ5And δθRespectively (z11-q1)2, (z21-q2)2,WithWeighting coefficient.
The suspension integrated performance index J the big, and then suspension property is poorer.The suspension system model that formula (11) indicates can pass through
Derive the standard optimum control quadratic form for being organized into state variable X and control input U:
In formula: Q=[Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8]T, U=[F1,F2]TIndicate the reason that Optimal Sliding Mode Control device is sought
Think dominant vector.
Q1=[δ3 0 0 0 0 0 0 0]T,Q2=[0 δ4 0 0 0 0 0 0]T
Consider sliding formwork control have preferable robustness, in order to by vehicle ride comfort energy index in sliding formwork diverter surface upper body
It is existing, by optimum control in conjunction with sliding formwork control, form the Optimal Sliding Mode Control based on smooth performance indicator, such controller energy
Sliding formwork diverter surface equation is determined according to optimal control index, so that system be made to move along diverter surface, obtains system in name
Optimal performance and good variable working condition robustness under operating condition.The specific configuration process of Optimal Sliding Mode Control device is expressed as follows:
Firstly, building semi-active suspension state equation as shown in formula (1) and the suspension comprehensive performance as shown in formula (11)
Index.
Secondly, building Optimal Sliding Mode manifold function is
In formula: S indicates Optimal Sliding Mode manifold function, and suspension motion state should be from two under sliding mode controller effect
Side tends to S=0.P is symmetric positive definite matrix, is obtained by solving Riccati equation, corresponding Riccati equation is as follows:
In formula:
In formula: AT1、AT2、AT3、AT4For ATMatrix in block form；QT1、QT2、QT3、QT4For QTMatrix in block form；AT1And QT1It is 6
× 6 rank matrixes；AT2And QT2For 6 × 2 rank matrixes；AT3And QT3For 2 × 6 rank matrixes；AT4And QT4For 2 × 2 rank matrixes.
Finally, in order to avoid non-linear shake occurs for control system, selection linear sliding mode tendency rate:
λ is approach rate coefficient in formula, is positive number.
Formula (15) are substituted into (13), can be obtained:
Formula should use AX+BU in (16)*SubstitutionDue toIn include road agitation vector solution,
But in practical control process, interference vector is uncertain and unknown.And one of the advantages of sliding formwork control is exactly to interfere vector
Influence caused by system can be compensated by tendency rate solution, so practical System with Sliding Mode Controller, in design Shi Bukao
Consider road agitation vector, therefore willUse AX+B1U is substituted, wherein U=[F1,F2]T。
Ideal dominant vector is found out by formula (16) are as follows:
U=- (KB1)-1(KA+ λ K) X=U1+U2 (17)
In formula
U1=-(KB1)-1KAX,U2=-(KB1)-1λKX
Ideal control amount in formula (17) contains forward and backward suspension MR damper control force.
The control of vehicle suspension is realized according to ideal dominant vector.
Specific embodiment 2:
The sliding-mode control of vehicle suspension described in present embodiment is also wrapped on the basis of specific embodiment one
It includes and establishes dynamics hierarchical mode, realize the process of hierarchical control, detailed process is as follows:
Step 3 establishes dynamics hierarchical mode:
Vehicle body stress is analyzed below, the bottom active force of front suspension system and rear-suspension system in Fig. 1 (including
Spring force, damping force, semi active actuator power output) respectively see a concentrated force, i.e. F asfAnd Fr, as shown in Figure 3.According to matter
Heart movement theorem and the moment of momentum theorem of opposite mass center have:
In formula, mcFor spring carried mass, unit kg；IcFor the rotary inertia of spring carried mass, unit kgm2；It is outstanding
Displacement acceleration at frame mass center, unit m/s2；For the pitching angular acceleration at suspension mass center, unit rad/s2。
It can be obtained by formula (18) and formula (19):
By forward and backward suspension displacement xcf、xcrWith displacement x at suspension mass centercRelationship xc=xcf+lfθc=xcr-lrθc, respectively
It substitutes into upper two formula and obtains:
Formula (22) is added and can be obtained with formula (23):
By formula (22) multiplied by lr/ l subtracts formula (23) multiplied by lf/ l is obtained:
In formula: mcf=mclr/ l, mcr=mclf/ l, in formula l be front and back wheel center away from.
Formula (24), (25) show: spring carried mass can simplify the lumped mass m for a massless and both ends connectioncfWith
mcrRigid rod, as shown in figure 4, wherein formula (24) can regard power dynamic balance equation as, it is dynamic flat that formula (25) is considered as torque
Weigh equation, while from formula (24) as long as it can be seen that lf=lr, then mcf=mcr, can be free by one 4 according to mass distribution coefficient
Degree suspension regards the combination of former and later two 2DOF suspensions as.But practical lf≠lr, therefore formula (24) and formula (25) solve this
One problem.
Formula (24) and formula (25) are availableWith
For front suspension system, if there is no the constraint of rear-suspension system, then lumped mass mcfIt is moved to from point F
Point F1, enable Δ xfFor point F to point F1Displacement, have Δ xf=xcf-xf, while in point F1Locate dynamic equilibrium equation:
Similarly, for rear-suspension system, Δ x is enabledrFor point R to point R1Displacement, have Δ xr=xr-xcr, while in R1Place has
Dynamic balance equation:
Above-mentioned relation is substituted into formula (24), in (25) respectively, obtained:
It is available by formula (30) and formula (31)With
By the conversion of above-mentioned dynamic suspension system of vehicles equation, the half suspension four-degree-of-freedom can system converting be two two from
By degree system, as shown in Figure 5.
Currently, after rear-suspension system spring carried mass decomposes, nonspring carried mass also accordingly generates displacement xuf、ΔxurIf
With The displacement state of its nonspring carried mass after forward and backward suspension system is decomposed is respectively indicated, with xuf、xurIt respectively indicates point
The displacement state of nonspring carried mass before solution, then haveTo the suspension system after decomposition
Spring carried mass, nonspring carried mass arrange its dynamic balance equation respectively:
In formula, kmiAnd cniThe stiffness coefficient and damped coefficient of suspension are respectively indicated, their unit is respectively N/m, N
s/m；FmiIndicate the power output of semi active actuator, unit N；kuiIndicate tire stiffness, unit N/m；muiIndicate non-
Spring carried mass, unit kg；xsiIndicate road excitation, unit m, subscript i=f or r indicate front side or rear side.
Formula (34) obtains after being added with formula (35):
By Δ xufWith Δ xurExpression formula substitutes into the displacement change that can acquire suspension system nonspring carried mass in formula (36) respectively
Change amount:
Step 4, the dynamics hierarchical mode (decoupling) based on step 3 are outstanding to vehicle to carry out hierarchical control:
(1) the suspension mass center acceleration for obtaining Optimal Sliding Mode ControlWith mass center pitching angular accelerationRespectively multiplied by
Set coefficient, the target as bottom control.
(2) it is obtained respectively by formula (20), (21), (24), (25)WithDiscreet value, obtained by formula (30), (31)WithDiscreet value, the discreet value of the fore suspension and rear suspension spring carried mass acceleration after then being decomposed:
(3)WithAs given value, Fig. 5 two degrees of freedom suspension state-space equation expression formula is established, if
System state variables are Xi, then:
In formula, subscript i takes f or r；They respectively indicate forward and backward suspension system, and output state variable is Yi
State-space expression are as follows:
Yi=CiXi (44)
In formula
Control force F needed for the available two degrees of freedom suspension of control algolithm (47) for combining design according to state equationmi,
Then available by formula (34) and formula (35)WithActual value；
(4) available according to formula (18), (19), (28) and (29)WithActual value
It can be obtained by (32) and (33) againWithTo obtainWithActual value.
(5) the semi-active suspension bottom control of PI is obscured based on PSO-
Since the control method of PI, Proportional coefficient K is applied aloneP_iWith integral coefficient KI_iBad adjusting, and effect is bad,
Therefore the present invention is added PSO and fuzzy method, makes Proportional coefficient K on the basis of PI coarse adjustment parameterP_iWith integral coefficient KI_i
With the operation of emulation, real-time update, subscript i=f or r respectively indicate forward and backward suspension.
Trial and error procedure comparative example COEFFICIENT K is used firstP_iWith integral coefficient KI_iCoarse adjustment is carried out, coarse steps are as follows:
(a) coarse adjustment scale parameter: first by KP_iValue is placed on lesser position, when exporting nonoscillatory, scaling up coefficient
KP_i。
(b) coarse adjustment integral parameter: after adjusting scale parameter, ratio value is reduced into (10~20%), when then will integrate
Between it is descending be gradually added, until obtain 4:1 attenuation process.
After coarse adjustment, PSO algorithm is added in Fuzzy PI Controller.The deviation of fore suspension and rear suspension is(i=f
Or r), it is entered into PSO- Fuzzy PI Controller, controller exports control law ufuzzy-pi-pso_i(t), control law is such as
Shown in formula (47).
Embodiment
It is controlled in the way of specific embodiment one and specific embodiment two.
Wherein in specific embodiment two, can be decoupled one and half suspensions by tetrameric analysis is two 1/
The combination of 4 suspensions, the specific design process of the muti-layer control tactics of Optimal Sliding Mode are as follows:
(1) the suspension mass center acceleration that the present invention obtains Optimal Sliding Mode ControlWith mass center pitching angular accelerationRespectively
Target multiplied by 0.6, as bottom control.
(2) it is obtained respectively by formula (20), (21), (24), (25)WithDiscreet value, obtained by formula (30), (31)WithDiscreet value, the discreet value of the fore suspension and rear suspension spring carried mass acceleration after then being decomposed:
(3)WithAs given value, Fig. 5 two degrees of freedom suspension state-space equation expression formula is established, if
System state variables are Xi, then:
In formula, subscript i takes f or r；They respectively indicate forward and backward suspension system, and output state variable is Yi
State-space expression are as follows:
Yi=CiXi (44)
In formula
Control force F needed for the available two degrees of freedom suspension of control algolithm (47) for combining design according to state equationmi,
Then available by formula (34) and formula (35)WithActual value；
(4) available according to formula (18), (19), (28) and (29)WithActual value
It can be obtained by (32) and (33) againWithTo obtainWithActual value.
(5) the semi-active suspension bottom control of PI is obscured based on PSO-
Since the control method of PI, Proportional coefficient K is applied aloneP_iWith integral coefficient KI_iBad adjusting, and effect is bad,
Therefore the present invention is added PSO and fuzzy method, makes Proportional coefficient K on the basis of PI coarse adjustment parameterP_iWith integral coefficient KI_i
With the operation of emulation, real-time update, subscript i=f or r respectively indicate forward and backward suspension.
Trial and error procedure comparative example COEFFICIENT K is used firstP_iWith integral coefficient KI_iCoarse adjustment is carried out, coarse steps are as follows:
(1) coarse adjustment scale parameter: first by KP_iValue is placed on lesser position, when exporting nonoscillatory, scaling up coefficient
KP_i。
(2) coarse adjustment integral parameter: after adjusting scale parameter, ratio value is reduced into (10~20%), when then will integrate
Between it is descending be gradually added, until obtain 4:1 attenuation process.
After coarse adjustment, PSO algorithm is added in Fuzzy PI Controller.The deviation of fore suspension and rear suspension is(i=f
Or r), it is entered into PSO- Fuzzy PI Controller, controller exports control law ufuzzy-pi-pso_i(t), control law is such as
Shown in formula (47).
Fig. 6 is PSO- fuzzy PI hybrid control schematic diagram.The fuzzy PI rule that the present invention designs is as shown in table 1 and table 1.
1 K of tablefuzzy_PFuzzy reasoning table
2 K of tablefuzzy_IFuzzy reasoning table
With the operation of the emulation Proportional coefficient K of the method real-time update PI of PSOP_iWith integral coefficient KI_i, the present invention
Parameter update is carried out with nonlinear least square method, nonlinear least square method is updated according to the smallest criterion of sum of square of deviations
KP_iAnd KI_i, determine that objective function is formula (48).To KP_iAnd KI_iReal-time update, it is assumed that when emulation experiment, obtain the experiment of n group
Data ei1,ei2…ein, subscript i=f or r respectively indicate forward and backward suspension, and the principle of fitting is to seek undetermined parameter to make following formula most
It is small.
In formula, θ1For parameter K undeterminedP_iAnd KI_iThe vector of composition.
To sum up, the expectation damping force based on PSO- fuzzy PI hybrid control is
In formula, subscript i=f or r respectively indicate forward and backward suspension.It is as shown in table 3 in the parameter of Simulink emulation.
The model parameter of 3 bottom control of table
4 vehicle ride comfort of table analyzes the subjective feeling of each controlling party legal person
Fig. 7,8,9 are respectively the simulation result of each control method vehicle body acceleration, speed, power spectral density function, by scheming
Know that PSO- obscures the result that PI hierarchical control method obtains and is better than passive option and PID hierarchical control.Table 1 is vehicle ride comfort
The subjective feeling of each controlling party legal person is analyzed, the acceleration root mean square and equivalent averages of PSO- fuzzy PI hybrid control layering are small
In passive and PID hierarchical control, wherein passive suspension feels very uncomfortable to people, the master of the suspension of PID hierarchical control to people
Sight be felt as it is quite uncomfortable, and PSO- obscure PI hierarchical control suspension to people subjective feeling be it is uncomfortable, to illustrate
PSO- fuzzy PI hybrid control hierarchical control method has good effect for the comfort for improving vehicle suspension.
Claims (10)
1. the sliding-mode control of vehicle suspension, which comprises the following steps:
Step 1 carries out dynamic analysis for half vehicle 4DOF auto model, and determines state equation:
State vector X=(x1,x2,x3,x4,x5,x6,x7,x8)T, wherein x1=z11-q1,x2=z21-q2,x3=z12-z11,x4=
z22-z21, For the first derivative of X；
Input vector U*=[F1,F2,q1,q2]T；
Output vector are as follows:
Y=(y1,y2,y3,y4,y5,y6)T
In formula:y2=z11-q1,y3=z21-z11,y4=z12-z11,y5=z22-z21,
Output equation are as follows:
Y=CX+DU*
In formula: z21、z22The vertical displacement of respectively forward and backward suspension and vehicle body tie point；l1、l2Respectively vehicle body mass center O to it is preceding,
The distance of back axle；θ is pitch angle；z3For the vertical deviation of vehicle body mass center；m1、m2、m3Respectively forward and backward nonspring carried mass with
Spring carried mass；I is pitch rotation inertia of the vehicle body around mass center；z11、z12Respectively forward and backward nonspring carried mass vertical deviation；c1、c2
Not Wei forward and backward suspension Equivalent damping coefficient；k11、k21、k12、k22The equivalent stiffness of respectively forward and backward tire and forward and backward suspension
Coefficient；F1、F2Respectively forward and backward half active desired control power of suspension；F3、F4The forward and backward suspension respectively acquired by controller
Semi- active control power；q1、q2The Excitation of Random Road Surface of respectively forward and backward axle；V is speed；f0For lower limiting frequency；n0For ginseng
Examine spatial frequency；Gn(n0) it is road roughness coefficient；W is road surface white noise signal；
Step 2, the Optimal Sliding Mode Control based on the smooth performance indicator of rheological suspension:
The suspension integrated performance index J of selection:
In formula: T is the total time of vehicle operation；T indicates time change；δ1, δ2, δ3, δ4, δ5And δθFor
(z11-q1)2, (z21-q2)2,WithWeighting coefficient；
Building Optimal Sliding Mode manifold function and selection linear sliding mode tendency rate simultaneously find out ideal dominant vector are as follows:
U=- (KB1)-1(KA+ λ K) X=U1+U2
U in formula1=-(KB1)-1KAX,U2=-(KB1)-1λKX；
The control of vehicle suspension is realized according to ideal dominant vector.
2. the sliding-mode control of vehicle suspension according to claim 1, which is characterized in that be directed to half vehicle 4 described in step 1
Freedom degree auto model carries out dynamic analysis and determines that the process of state equation is as follows:
Dynamic analysis is carried out to auto model:
Take state vector are as follows:
X=(x1,x2,x3,x4,x5,x6,x7,x8)T (6)
In formula:
x1=z11-q1,x2=z21-q2,x3=z12-z11,x4=z22-z21,
State equation are as follows:
In formula:
3. the sliding-mode control of vehicle suspension according to claim 1, which is characterized in that the building Optimal Sliding Mode stream
Shape function and selection linear sliding mode tendency rate and the process for finding out ideal dominant vector is as follows:
Constructing Optimal Sliding Mode manifold function isIn formula: S indicates Optimal Sliding Mode manifold
Function；P is symmetric positive definite matrix；
Selection linear sliding mode tendency rate:λ is approach rate coefficient in formula；
It can obtain:
It willUse AX+B1U is substituted, wherein U=[F1,F2]T；
Ideal dominant vector is found out by above formula are as follows:
U=- (KB1)-1(KA+ λ K) X=U1+U2
U in formula1=-(KB1)-1KAX,U2=-(KB1)-1λKX。
4. the sliding-mode control of vehicle suspension according to claim 3, which is characterized in that the P is symmetric positive definite matrix
It is obtained by Riccati equation, corresponding Riccati equation is as follows:
In formula:
In formula: AT1、AT2、AT3、AT4For ATMatrix in block form；QT1、QT2、QT3、QT4For QTMatrix in block form；AT1And QT1For 6 × 6 ranks
Matrix；AT2And QT2For 6 × 2 rank matrixes；AT3And QT3For 2 × 6 rank matrixes；AT4And QT4For 2 × 2 rank matrixes.
5. according to claim 1 to the sliding-mode control of vehicle suspension described in one of 4, which is characterized in that further include establishing
Dynamics hierarchical mode and the process for realizing hierarchical control, detailed process is as follows:
Step 3 establishes dynamics hierarchical mode:
By the conversion of dynamic suspension system of vehicles equation, by half suspension four-degree-of-freedom it is system converting be two coupled systems；
Currently, after rear-suspension system spring carried mass decomposes, nonspring carried mass also accordingly generates displacement xuf、ΔxurIf with The displacement state of its nonspring carried mass after forward and backward suspension system is decomposed is respectively indicated, with xuf、xurRespectively indicate decomposition
The displacement state of preceding nonspring carried mass, then haveTo the suspension system after decomposition
Spring carried mass, nonspring carried mass arrange its dynamic balance equation respectively:
In formula, kmiAnd cniRespectively indicate the stiffness coefficient and damped coefficient of suspension；FmiIndicate the power output of semi active actuator；
kuiIndicate tire stiffness；muiIndicate nonspring carried mass；xsiIndicate road excitation, subscript i=f or r indicate front side or rear side；
After two formulas are added in formula:
By Δ xufWith Δ xurExpression formula substitutes into the displacement variable that can acquire suspension system nonspring carried mass in above formula respectively:
Step 4, the dynamics hierarchical mode based on step 3 are outstanding to vehicle to carry out hierarchical control:
(1) the suspension mass center acceleration for obtaining Optimal Sliding Mode ControlWith mass center pitching angular accelerationIt is multiplied by setting respectively
Number, the target as bottom control；
(2) basisWithDiscreet value andWithDiscreet value, fore suspension and rear suspension spring carried mass after being decomposed accelerates
The discreet value of degree；
(3)WithAs given value, two degrees of freedom suspension state-space equation expression formula is established；
Control force F needed for obtaining two degrees of freedom suspension according to two degrees of freedom suspension state-space equationmi, then determineWith
Actual value；
(4) it is obtained according to the process of step 3WithActual value, andWithActual value；
(5) the semi-active suspension bottom control of PI is obscured based on PSO-.
6. the sliding-mode control of vehicle suspension according to claim 5, which is characterized in that step (5) is described to be based on
The process that PSO- obscures the semi-active suspension bottom control of PI is as follows:
It sets mark i=f or r and respectively indicates forward and backward suspension；
Trial and error procedure comparative example COEFFICIENT K is used firstP_iWith integral coefficient KI_iCoarse adjustment is carried out, coarse steps are as follows:
(a) coarse adjustment scale parameter: first by KP_iValue is placed on lesser position, when exporting nonoscillatory, scaling up COEFFICIENT KP_i；
(b) coarse adjustment integral parameter: after adjusting scale parameter, by ratio value reduce (10~20%), then by the time of integration by
Arrive greatly it is small be gradually added, until obtain 4:1 attenuation process；
After coarse adjustment, PSO algorithm is added in Fuzzy PI Controller；The deviation of fore suspension and rear suspension is
It is entered into PSO- Fuzzy PI Controller, controller exports control law ufuzzy-pi-pso_i(t), control law is
7. the sliding-mode control of vehicle suspension according to claim 5, which is characterized in that by outstanding described in step 3
The conversion of frame kinetics equation, by half suspension four-degree-of-freedom it is system converting be two coupled systems process it is as follows:
According to the moment of momentum theorem and forward and backward suspension displacement x of center of mass motion theorem and opposite mass centercf、xcrAt suspension mass center
Displacement xcRelationship determine:
In formula, mcFor spring carried mass, unit kg；IcFor the rotary inertia of spring carried mass, unit kgm2；For suspension matter
Displacement acceleration at the heart, unit m/s2；For the pitching angular acceleration at suspension mass center；
Upper two formula is added:
It willMultiplied by lr/ l subtracts formulaMultiplied by lf/ l is obtained:
In formula: mcf=mclr/ l, mcr=mclf/ l, in formula l be front and back wheel center away from；
According to formulaAnd formulaIt obtainsWith
For front suspension system, if there is no the constraint of rear-suspension system, then lumped mass mcfIt is moved to a little from point F
F1, enable Δ xfFor point F to point F1Displacement, have Δ xf=xcf-xf, while in point F1Locate dynamic equilibrium equation:
Similarly, for rear-suspension system, Δ x is enabledrFor point R to point R1Displacement, have Δ xr=xr-xcr, while in R1Place has flat
Weigh equation:
Above-mentioned relation is substituted into formula respectively
In, it obtains:
It can be obtained by upper two formulaWith
By the conversion of above-mentioned dynamic suspension system of vehicles equation, the system converting half suspension four-degree-of-freedom is two two degrees of freedom systems
System.
8. the sliding-mode control of vehicle suspension according to claim 7, which is characterized in that according to center of mass motion theorem and
The moment of momentum theorem of opposite mass center and forward and backward suspension displacement xcf、xcrWith displacement x at suspension mass centercRelationship determineWithProcess it is as follows:
Had according to the moment of momentum theorem of center of mass motion theorem and opposite mass center:
In formula, mcFor spring carried mass, unit kg；IcFor the rotary inertia of spring carried mass, unit kgm2；For suspension mass center
The displacement acceleration at place, unit m/s2；For the pitching angular acceleration at suspension mass center；
It can be obtained by upper two formula:
By forward and backward suspension displacement xcf、xcrWith displacement x at suspension mass centercRelationship xc=xcf+lfθc=xcr-lrθc, substitute into respectively
In upper two formula:
9. the sliding-mode control of vehicle suspension according to claim 5, which is characterized in that after step (2) obtains decomposition
Fore suspension and rear suspension spring carried mass acceleration discreet value it is as follows:
10. the sliding-mode control of vehicle suspension according to claim 9, which is characterized in that step (3)WithAs given value, the process for establishing two degrees of freedom suspension state-space equation expression formula is as follows:
If the system state variables in two degrees of freedom suspension space are Xi, then:
In formula, subscript i takes f or r；They respectively indicate forward and backward suspension system, and output state variable is Yi
State-space expression are as follows:
Yi=CiXi
In formula
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| CN114611219A (en) * | 2022-03-28 | 2022-06-10 | 扬州东升汽车零部件股份有限公司 | Optimal selection method for stiffness and damping coefficient of passive vehicle suspension system |
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