CN110096840B - Sliding mode control method for vehicle suspension - Google Patents
Sliding mode control method for vehicle suspension Download PDFInfo
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Abstract
A sliding mode control method of a vehicle suspension belongs to the field of vehicle control. The method aims to solve the problem that the existing control method is not ideal in vibration reduction effect when applied to the magnetorheological suspension of the vehicle. According to the method, the optimal control and the sliding mode control are combined to form the optimal sliding mode control based on the smoothness performance index, and the controller can determine the sliding mode switching surface equation according to the optimal control index to enable the system to move along the switching surface, so that the system obtains the optimal performance and good variable working condition robustness. The invention further multiplies the acceleration of the mass center of the suspension and the acceleration of the pitch angle of the mass center obtained by the optimal sliding mode control by corresponding coefficients respectively to be used as a target of bottom layer control. And finally, applying the PSO-fuzzy PI to the bottom control of the decoupling suspension, thereby realizing the layered control of the magnetorheological suspension of the vehicle, respectively obtaining the control damping force of the front suspension and the rear suspension through a bottom control algorithm, and further improving the control effect. The invention is used for controlling the vehicle suspension.
Description
Technical Field
The present invention relates to a control method of a vehicle. Belongs to the field of vehicle control.
Background
In recent years, with a control strategy as a means, research on vibration damping performance of a suspension system has become a hot issue for researchers at home and abroad. According to different control methods, a suspension system with a control function is divided into an active control suspension system and a semi-active control suspension system, so that the shock absorber mode of a passive suspension system is broken through. Compared with a full-active control suspension, the semi-active control suspension does not need active energy input, only needs to adjust and control the damping or spring stiffness of a suspension system according to the requirement of the running working condition of the vehicle, is safe and reliable, is easy to realize, and has very important popularization and application values.
The semi-active suspension system based on the magnetorheological damper has an excellent vibration reduction effect, effectively improves the running smoothness and comfort of a vehicle, and is a hot problem of domestic and foreign research at present. In foreign vehicle models, the magnetorheological semi-active suspension control systems are assembled in the Farly 599, California, 458 Italia, F12 Berlinietta, FF and Kadillack low-and-medium ATS, CTS and XTS vehicle models, along with the deepening of the research on the magnetorheological semi-active suspension and the gradual maturity of the research work on the vehicle test, the magnetorheological semi-active suspension has the tendency of being popularized to a medium-grade vehicle, and for domestic vehicle enterprises, the semi-active whole vehicle suspension control systems are researched in order to develop the vehicle smoothness similar to that of the foreign magnetorheological suspension systems under different driving conditions. Vehicle seats are an important component of vehicle vibration damping systems, which protect the occupants from high-level vibrations. Particularly, heavy-duty automobiles, agricultural vehicles and engineering vehicles have poor working environment, large load and large vibration in the driving process, the whole vehicle suspension is not ideal in vibration reduction effect, but the improvement of the seat vibration reduction performance is convenient and easy to implement, the period is short, and the effect is quick. Therefore, it is important to research and improve the dynamic performance of the seat to improve the riding comfort of the vehicle. However, the control aspect of the magnetorheological damper is a difficulty in developing a semi-active vehicle model, so that an effective control method of the magnetorheological semi-active suspension becomes a key and difficult point in research and development.
Disclosure of Invention
The invention aims to solve the problem that the existing control method is not ideal in vibration reduction effect when applied to a vehicle magneto-rheological suspension.
A sliding mode control method for a vehicle suspension comprising the steps of:
state vector X ═ X 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ) T Wherein x is 1 ＝z 11 -q 1 ,x 2 ＝z 21 -q 2 ,x 3 ＝z 12 -z 11 ,x 4 ＝z 22 -z 21 ,
Is the first derivative of X;
input vector U * ＝[F 1 ,F 2 ,q 1 ,q 2 ] T ；
The output vector is:
Y＝(y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 ) T
in the formula:
y 2 ＝z 11 -q 1 ,y 3 ＝z 21 -z 11 ,y 4 ＝z 12 -z 11 ,y 5 ＝z 22 -z 21 ,
the output equation is:
Y＝CX+DU *
in the formula: z is a radical of 21 、z 22 Vertical displacement of the connecting points of the front suspension and the rear suspension and the vehicle body is respectively realized; l. the 1 、l 2 From the centre of mass O of the vehicle body to the front and rear axles respectivelyA distance; theta is a pitch angle; z is a radical of 3 Is the vertical displacement of the center of mass of the car body; m is a unit of 1 、m 2 、m 3 Front and rear unsprung masses and sprung masses, respectively; i is the pitching moment of inertia of the vehicle body around the center of mass; z is a radical of 11 、z 12 Front and rear unsprung mass vertical displacements, respectively; c. C 1 、c 2 The equivalent damping coefficients of the front suspension and the rear suspension are respectively; k is a radical of 11 、k 21 、k 12 、k 22 Respectively the equivalent stiffness coefficients of the front and rear tires and the front and rear suspensions; f 1 、F 2 Respectively, the front suspension and the rear suspension are semi-actively expected to control force; f 3 、F 4 Respectively the front and rear suspension semi-active control forces obtained by the controller; q. q.s 1 、q 2 Respectively exciting the road surfaces of the front axle and the rear axle randomly; v is the vehicle speed; f. of 0 Is the lower cut-off frequency; n is 0 Is a reference spatial frequency; g n (n 0 ) The coefficient of road surface unevenness; w is a white noise signal of the road surface;
selected suspension combination property index J:
in the formula: t is the total time of vehicle operation; t represents a temporal change; delta 1 ，δ 2 ，δ 3 ，δ 4 ，δ 5 And delta θ Is composed of
(z 11 -q 1 ) 2 ，(z 21 -q 2 ) 2 ，
And
the weighting coefficients of (a);
constructing an optimal sliding mode manifold function, selecting a linear sliding mode approximation rate and solving an ideal control vector as follows:
U＝-(KB 1 ) -1 (KA+λK)X＝U 1 +U 2
in the formula of U 1 ＝-(KB 1 ) -1 KAX,U 2 ＝-(KB 1 ) -1 λKX；
And realizing the control of the vehicle suspension according to the ideal control vector.
A sliding mode control method for a vehicle suspension comprising the steps of:
state vector X ═ X 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ) T Wherein x is 1 ＝z 11 -q 1 ,x 2 ＝z 21 -q 2 ,x 3 ＝z 12 -z 11 ,x 4 ＝z 22 -z 21 ,
Is the first derivative of X;
input vector U * ＝[F 1 ,F 2 ,q 1 ,q 2 ] T ；
The output vector is:
Y＝(y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 ) T
in the formula:
y 2 ＝z 11 -q 1 ,y 3 ＝z 21 -z 11 ,y 4 ＝z 12 -z 11 ,y 5 ＝z 22 -z 21 ,
the output equation is:
Y＝CX+DU *
in the formula: z is a radical of 21 、z 22 Vertical displacement of the connecting points of the front suspension and the rear suspension and the vehicle body is respectively realized; l 1 、l 2 Respectively the distances from the barycenter O of the vehicle body to the front axle and the rear axle; theta is a pitch angle; z is a radical of 3 Is the vertical displacement of the center of mass of the car body; m is a unit of 1 、m 2 、m 3 Front and rear unsprung masses and sprung masses, respectively; i is the pitching moment of inertia of the vehicle body around the center of mass; z is a radical of 11 、z 12 Front and rear unsprung mass vertical displacements, respectively; c. C 1 、c 2 The equivalent damping coefficients of the front suspension and the rear suspension are respectively; k is a radical of 11 、k 21 、k 12 、k 22 Respectively the equivalent stiffness coefficients of the front and rear tires and the front and rear suspensions; f 1 、F 2 Respectively, the front suspension and the rear suspension are semi-actively expected to control force; f 3 、F 4 Respectively the front and rear suspension semi-active control forces obtained by the controller; q. q.s 1 、q 2 Respectively exciting the road surfaces of the front axle and the rear axle randomly; v is the vehicle speed; f. of 0 Is the lower cut-off frequency; n is 0 Is a reference spatial frequency; g n (n 0 ) The coefficient of road surface unevenness; w is a white noise signal of the road surface;
selected suspension combination property index J:
in the formula: t is the total time of vehicle operation; t represents a temporal change; delta. for the preparation of a coating 1 ，δ 2 ，δ 3 ，δ 4 ，δ 5 And delta θ Is composed of
(z 11 -q 1 ) 2 ，(z 21 -q 2 ) 2 ，
And
the weighting coefficient of (2);
constructing an optimal sliding mode manifold function, selecting a linear sliding mode approximation rate and solving an ideal control vector as follows:
U＝-(KB 1 ) -1 (KA+λK)X＝U 1 +U 2
in the formula of U 1 ＝-(KB 1 ) -1 KAX,U 2 ＝-(KB 1 ) -1 λKX；
converting a four-degree-of-freedom system of a half vehicle suspension into two-degree-of-freedom systems through conversion of a suspension kinetic equation;
after the sprung mass of the front and rear suspension systems is decomposed, the unsprung mass of the front and rear suspension systems correspondingly generates displacement deltax uf 、Δx ur If so
Respectively representing the displacement state of the unsprung mass of the front and rear suspension systems after disassembly, by x uf 、x ur Respectively representing the displacement state of the unsprung mass before disassembly
And respectively arranging the dynamic balance equations of the sprung mass and the unsprung mass of the decomposed suspension system:
in the formula, k mi And c ni Respectively representing the rigidity coefficient and the damping coefficient of the suspension; f mi Representing the output force of the semi-active actuator; k is a radical of ui Represents the tire stiffness; m is a unit of ui Represents an unsprung mass; x is the number of si Denotes road surface excitation, subscript i ═ f or r, denotes front or rear side;
adding the two formulas to obtain:
will be Δ x uf And Δ x ur The displacement variation of the unsprung mass of the suspension system can be respectively obtained by substituting the expression into the formula:
(1) suspension center of mass acceleration obtained by optimal sliding mode control
And centroid pitch angular acceleration
Multiplying the obtained data by a set coefficient respectively to serve as a target of bottom control;
(2) according to
And
is estimated to be sum
And
obtaining the decomposed estimated values of the front and rear suspension spring load mass acceleration;
(3) handle
And
establishing a two-degree-of-freedom suspension space state equation expression as a known value;
obtaining the control force F required by the two-freedom suspension according to the space state equation of the two-freedom suspension mi Then determine
And
the actual value of (d);
(4) obtained according to the process of step 3
And
actual value of (a), and
and
the actual value of (c);
(5) semi-active suspension bottom control based on PSO-fuzzy PI:
let subscript i ═ f or r denote front and rear suspensions, respectively;
first, the ratio coefficient K is compared by a trial and error method P_i And integral coefficient K I_i Coarse adjustment is carried out, and the coarse adjustment steps are as follows:
(a) coarse adjustment of proportion parameters: firstly, K is firstly P_i The value is put at a smaller position, and when the output does not oscillate, the proportionality coefficient K is increased P_i ；
(b) Coarse tuning of integration parameters: after setting the proportion parameters, reducing the proportion value (by 10-20%), and then gradually adding the integration time from large to small until a 4:1 attenuation process is obtained;
after coarse adjustment, adding a PSO algorithm into the fuzzy PI controller; the front and rear suspension has a deviation of
(i ═ f or r), the control law is input into a PSO-fuzzy PI controller, and the controller outputs a control law u fuzzy-pi-pso_i (t) according to the control law
Has the advantages that:
in order to improve the smoothness of the whole vehicle suspension, the smoothness performance index of the vehicle is reflected on the sliding mode switching surface, the optimal control and the sliding mode control are combined to form the optimal sliding mode control based on the smoothness performance index, so that the controller can determine the sliding mode switching surface equation according to the optimal control index to enable the system to move along the switching surface, the system obtains the optimal performance and good working condition changing robustness, and the vibration damping effect of the magnetorheological suspension of the vehicle can be ensured.
The invention further multiplies the acceleration of the mass center of the suspension and the acceleration of the pitch angle of the mass center obtained by the optimal sliding mode control by corresponding coefficients respectively to be used as a target for bottom layer control. And finally, applying the PSO-fuzzy PI to the bottom layer control of the decoupling suspension, thereby realizing the layered control of the vehicle magneto-rheological suspension, respectively obtaining the control damping forces of the front and rear suspensions through a bottom layer control algorithm, further improving the control effect, and obtaining more excellent vibration damping effect of the vehicle magneto-rheological suspension. The weighted acceleration root mean square and the equivalent mean value of the further PSO-fuzzy PI control layering of the invention are both smaller than those of passive and PID layering control, namely the invention has good effect on improving the comfort of the vehicle suspension.
Drawings
FIG. 1 is a schematic diagram of an optimal sliding mode layered control of a magnetorheological suspension of a vehicle;
FIG. 2 is a system block diagram of a vehicle ride comfort analysis process;
FIG. 3 is a sprung mass force analysis diagram;
FIG. 4 is a simplified sprung mass diagram and its hypothetical exploded displacement diagram;
FIG. 5 is an exploded front and rear suspension system;
FIG. 6 is a PSO-fuzzy PI control schematic diagram;
FIG. 7 is a simulation result of vehicle body acceleration for each control method;
FIG. 8 is a simulation result of vehicle body speed for each control method;
FIG. 9 is a constant bandwidth acceleration self-power spectral density function.
Detailed Description
In order to improve the smoothness of the whole vehicle suspension, the smoothness performance index of the vehicle is reflected on the sliding mode switching surface, the optimal control and the sliding mode control are combined to form the optimal sliding mode control based on the smoothness performance index, so that the controller can determine the sliding mode switching surface equation according to the optimal control index to enable the system to move along the switching surface, and the system obtains the optimal performance and good variable working condition robustness under the nominal working condition. And then, on the basis of an optimal sliding mode based on a smooth performance index, providing optimal sliding mode layered control, decoupling a half vehicle suspension into 1/4 front and rear suspensions through theoretical derivation, and multiplying the suspension centroid acceleration and the centroid pitch angle acceleration obtained through the optimal sliding mode control by corresponding coefficients respectively to serve as a target of bottom layer control. And finally, applying the PSO-fuzzy PI to the bottom control of the decoupling suspension, thereby realizing the hierarchical control system of the vehicle magneto-rheological suspension. This patent is with vehicle magnetic current becomes half active suspension for short vehicle magnetic current becomes suspension, and figure 1 is vehicle magnetic current becomes optimum sliding mode layering control schematic diagram of suspension, and the layering controller comprises upper control and bottom control, through theoretical derivation with half vehicle suspension decoupling into 1/4 front and back suspensions, and wherein upper control provides the target for bottom control, makes bottom 1/4 front and back suspension follow the target motion. On the basis of the provided optimal sliding mode, the optimal sliding mode control method multiplies the acceleration of the mass center of the suspension and the acceleration of the pitch angle of the mass center of the suspension obtained by the optimal sliding mode control by corresponding coefficients respectively to serve as a target of bottom layer control, then applies PSO-fuzzy PI control to the bottom layer control of a decoupling suspension, obtains control damping forces of front and rear suspensions respectively through a bottom layer control algorithm, and achieves the optimal sliding mode layered control of the vehicle magneto-rheological suspension.
The first embodiment is as follows:
the sliding mode control method of a vehicle suspension according to the present embodiment includes the steps of:
the invention adopts a half-car 4-degree-of-freedom vehicle model, as shown in figure 1, to perform dynamic analysis on the vehicle model:
in the formula: z is a radical of 21 、z 22 Vertical displacement of the connection points of the front suspension and the rear suspension and the vehicle body respectively; l 1 、l 2 Respectively the distances from the barycenter O of the vehicle body to the front axle and the rear axle; theta is a pitch angle; z is a radical of 3 Is the vertical displacement of the center of mass of the vehicle body; m is 1 、m 2 、m 3 Front and rear unsprung masses and sprung masses, respectively; i is the pitching moment of inertia of the vehicle body around the center of mass; z is a radical of formula 11 、z 12 Front and rear unsprung mass vertical displacements, respectively; c. C 1 、c 2 The equivalent damping coefficients of the front suspension and the rear suspension are respectively; k is a radical of formula 11 、k 21 、k 12 、k 22 Respectively the equivalent stiffness coefficients of the front and rear tires and the front and rear suspensions; f 1 、F 2 Respectively, the front suspension and the rear suspension are semi-actively expected to control force; f 3 、F 4 Respectively obtaining front and rear suspension semi-active control forces through a controller; q. q.s 1 、q 2 Respectively exciting the road surfaces of the front axle and the rear axle randomly; v is the vehicle speed; f. of 0 Is the lower cut-off frequency; n is a radical of an alkyl radical 0 Is a reference spatial frequency; g n (n 0 ) The coefficient of road surface unevenness; and w is a white noise signal of the road surface.
Taking the state vector as:
X＝(x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ) T (6)
in the formula:
x 1 ＝z 11 -q 1 ,x 2 ＝z 21 -q 2 ,x 3 ＝z 12 -z 11 ,x 4 ＝z 22 -z 21 ,
the state equation is:
input vector U * ＝[F 1 ,F 2 ,q 1 ,q 2 ] T ；
In the formula:
the output vector is: y ═ Y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 ) T (8)
In the formula:
y 2 ＝z 11 -q 1 ,y 3 ＝z 21 -z 11 ,y 4 ＝z 12 -z 11 ,y 5 ＝z 22 -z 21 ,
the output equation is:
Y＝CX+DU * (9)
in the formula:
in the design process of a semi-active suspension system controller, the vehicle is provided with the function of ensuring that the automobile has ideal running smoothness and operation stabilityOne of the points of focus. The research and analysis of the vehicle running performance can be carried out through the operation steps of the system block diagram of the automobile ride comfort analysis process shown in FIG. 2. According to the analysis of the system block diagram of the automobile ride comfort analysis process in fig. 2, when the automobile drives on an uneven road surface at a certain speed, the vibration of tires, a suspension, an elastic element, a damping element and a seat is caused, and the vibration is finally transmitted to a human body through the seat. The invention takes the acceleration of the vehicle body, the dynamic load of the tire and the acceleration of the pitch angle as the evaluation indexes of the optimal sliding mode. In order to carry out smoothness evaluation on the optimal sliding mode, the vehicle body acceleration obtained through the optimal sliding mode algorithm control of the smoothness performance index
Dynamic deformation of tyre (z) 11 -q 1 And z 21 -q 2 ) And pitch angular acceleration
The root mean square of them is determined by the equation (10)
In the formula: x is vehicle body acceleration, tire dynamic deformation and pitch angle acceleration obtained through semi-active suspension optimal sliding mode simulation, and N is n The number of simulations for each parameter.
In conclusion, the smoothness index is determined as the vehicle body acceleration, the tire dynamic deformation and the pitch angle acceleration, and the comprehensive performance index J of the suspension selected by the invention for improving the smoothness of the suspension is shown as the formula (11):
in the formula: t is the total time of vehicle operation; t represents a temporal change; delta. for the preparation of a coating 1 ，δ 2 ，δ 3 ，δ 4 ，δ 5 And delta θ Are respectively as
(z 11 -q 1 ) 2 ，(z 21 -q 2 ) 2 ，
And
the weighting coefficient of (2).
The greater the suspension overall performance index J, the worse the suspension performance. The suspension system model represented by equation (11) can be organized into a standard optimal control quadratic form of the state variables X and the control inputs U by derivation:
in the formula: q ═ Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8 ] T ，U＝[F 1 ,F 2 ] T Representing the ideal control vector that the optimal sliding mode controller finds.
Q 1 ＝[δ 3 0 0 0 0 0 0 0] T ,Q 2 ＝[0 δ 4 0 0 0 0 0 0] T
Considering that the sliding mode control has better robustness, in order to reflect the smoothness performance index of the vehicle on the sliding mode switching surface, the optimal control is combined with the sliding mode control to form the optimal sliding mode control based on the smoothness performance index, so that the controller can determine the sliding mode switching surface equation according to the optimal control index, the system moves along the switching surface, and the system obtains the optimal performance and good variable working condition robustness under the nominal working condition. The specific construction process of the optimal sliding mode controller is expressed as follows:
firstly, a semi-active suspension state equation shown in a formula (1) and a suspension comprehensive performance index shown in a formula (11) are constructed.
Secondly, constructing an optimal sliding mode manifold function as
In the formula: and S represents an optimal sliding mode manifold function, and the motion state of the suspension system is required to be changed from two sides to 0 under the action of a sliding mode controller. P is a symmetric positive definite matrix, and is obtained by solving the Riccati equation, and the corresponding Riccati equation is as follows:
in the formula:
in the formula: a. the T1 、A T2 、A T3 、A T4 Is A T The block matrix of (2); q T1 、Q T2 、Q T3 、Q T4 Is Q T The block matrix of (2); a. the T1 And Q T1 Is a 6 x 6 order matrix; a. the T2 And Q T2 Is a 6 x 2 order matrix; a. the T3 And Q T3 Is a 2 x 6 order matrix; a. the T4 And Q T4 Is a 2 x 2 order matrix.
Finally, in order to avoid the nonlinear jitter of the control system, a linear sliding mode approach rate is selected:
in the formula, λ is an approach rate coefficient and is a positive number.
Substituting formula (15) into (13) yields:
AX + BU should be used in formula (16) * Substitution
Due to the fact that
The solution of the road surface disturbance vector is included, but in the actual control process, the disturbance vector is uncertain and unknown. One of the advantages of sliding mode control is that the influence of interference vectors on the system can be compensated by an approach rate solution, so that the road surface interference vectors are not considered in the design of the actual sliding mode control system, and therefore, the actual sliding mode control system can be used for solving the problem of the influence of the interference vectors on the system
With AX + B 1 U is substituted, wherein U ═ F 1 ,F 2 ] T 。
The ideal control vector is found from equation (16) as:
U＝-(KB 1 ) -1 (KA+λK)X＝U 1 +U 2 (17)
in the formula
U 1 ＝-(KB 1 ) -1 KAX,U 2 ＝-(KB 1 ) -1 λKX
The ideal control quantity in equation (17) includes the front and rear suspension magnetorheological damper control forces.
And controlling the vehicle suspension according to the ideal control vector.
The second embodiment is as follows:
the sliding-mode control method for the vehicle suspension according to the embodiment further includes a process of establishing a dynamic hierarchical model and realizing hierarchical control on the basis of the first specific embodiment, where the specific process is as follows:
the body forces are analyzed below, and the bottom acting forces (including spring force, damping force, and semi-active actuator output force) of the front suspension system and the rear suspension system in fig. 1 are respectively regarded as a concentrated force, i.e., F f And F r As shown in fig. 3. The theorem of moment of momentum according to the theorem of centroid motion and the theorem of relative centroid has:
in the formula, m c Is the spring load mass in kg; i is c Is the moment of inertia of the sprung mass in kg m 2 ；
Is the displacement acceleration at the center of mass of the suspension with the unit of m/s 2 ；
Is the acceleration of the pitch angle at the center of mass of the suspension in rad/s 2 。
From formulas (18) and (19):
displacing the front and rear suspensions by x cf 、x cr Displacement x from the suspension center of mass c Relation x of c ＝x cf +l f θ c ＝x cr -l r θ c Respectively substituting the two formulas to obtain:
the formula (22) and the formula (23) are added to obtain:
multiplying equation (22) by l r L minus the product of equation (23) multiplied by l f L to obtain:
in the formula: m is cf ＝m c l r /l，m cr ＝m c l f And l is the center distance of the front wheel and the rear wheel.
Formulas (24), (25) indicate: the sprung mass can be simplified into a concentrated mass m without mass and with two connected ends cf And m cr The rigid rod of (1), as shown in fig. 4, wherein the formula (24) can be regarded as a dynamic equilibrium equation of force, the formula (25) can be regarded as a dynamic equilibrium equation of moment, and the formula (24) can also be regarded as a dynamic equilibrium equation of moment, as long as l f ＝l r Then m is cf ＝m cr A 4-degree-of-freedom suspension can be regarded as a combination of front and rear 2-degree-of-freedom suspensions according to the mass distribution coefficient. But in fact f ≠l r Therefore, equations (24) and (25) solve this problem.
The formulae (24) and (25) can be obtained
And
for a front suspension system, mass m is concentrated if there are no constraints of the rear suspension system cf Moving from point F to point F 1 Let Δ x f From point F to point F 1 Has a displacement of Δ x f ＝x cf -x f At the same time at point F 1 The dynamic equilibrium equation is shown as follows:
similarly, for the rear suspension system, let Δ x r From point R to point R 1 Has a displacement of Δ x r ＝x r -x cr While at R 1 There is a dynamic balance equation:
the above relationships are substituted in the formulae (24) and (25), respectively, to obtain:
from the formulae (30) and (31)
And
through the conversion of the suspension kinetic equation, the half-vehicle suspension can be systematically converted into a two-degree-of-freedom system in four degrees of freedom, as shown in fig. 5.
When the sprung mass of the front and rear suspension systems is decomposed, the unsprung mass of the front and rear suspension systems correspondingly generates a displacement delta x uf 、Δx ur If so
Respectively representing the displacement state of the unsprung mass of the front and rear suspension systems after disassembly, by x uf 、x ur Respectively representing the displacement state of the unsprung mass before disassembly
And respectively arranging the dynamic balance equations of the sprung mass and the unsprung mass of the decomposed suspension system:
in the formula, k mi And c ni Respectively representing the rigidity coefficient and the damping coefficient of the suspension, and the units of the rigidity coefficient and the damping coefficient are N/m and N & s/m respectively; f mi Represents the output force of the semi-active actuator, and the unit of the output force is N; k is a radical of ui Representing the stiffness of the tire in units of N/m; m is a unit of ui Represents unsprung mass in kg; x is a radical of a fluorine atom si Which represents road surface excitation, in units of m, with the index i ═ f or r, representing the front or rear side.
Equation (34) and equation (35) are added to obtain:
will be Δ x uf And Δ x ur The expression is substituted into an expression (36) to respectively obtain the displacement variation of the unsprung mass of the suspension system:
(1) suspension centroid acceleration obtained by optimal sliding mode control
And centroid pitch angular acceleration
And multiplying the data by set coefficients respectively to be used as the target of the bottom control.
(2) Respectively obtained from the formulae (20), (21), (24) and (25)
And
the estimated value of (2) is obtained from the equations (30) and (31)
And
then, the decomposed estimated values of the front and rear suspension sprung mass acceleration are obtained:
(3) handle
And
as known values, the two-degree-of-freedom suspension of FIG. 5 is establishedThe expression of the frame space state equation is set as X i And then:
in the formula, subscript i is f or r; they represent the front and rear suspension systems, respectively, with an output state variable of Y i
The state space expression is:
Y i ＝C i X i (44)
in the formula
The control force F required by the suspension with two degrees of freedom can be obtained according to the state equation and the designed control algorithm (47) mi Then, the compounds can be obtained by the following formulae (34) and (35)
And
the actual value of (c);
(4) according to the formulae (18), (19), (28) and (29), the compounds
And
actual value of
And further by (32) and (33) can obtain
And
thereby obtaining
And
the actual value of (c).
(5) Semi-active suspension bottom control based on PSO-fuzzy PI
Due to the control method of PI alone, the proportionality coefficient K P_i And integral coefficient K I_i The method is not good in setting and effect, so that the method adds a PSO and fuzzy method on the basis of PI coarse adjustment parameters to ensure that the proportionality coefficient K is poor P_i And integral coefficient K I_i The index i ═ f or r denotes the front and rear suspensions, respectively, as the simulation runs, updating in real time.
First, the ratio coefficient K is compared by a trial and error method P_i And integral coefficient K I_i Coarse adjustment is carried out, and the coarse adjustment steps are as follows:
(a) coarse adjustment of proportion parameters: firstly, K is firstly P_i The value is put at a smaller position, and when the output does not oscillate, the proportionality coefficient K is increased P_i 。
(b) Coarse tuning of integration parameters: after setting the proportion parameters, reducing the proportion value (10-20%), and then gradually adding the integration time from large to small until a 4:1 attenuation process is obtained.
After the coarse tuning, the PSO algorithm is added to the fuzzy PI controller. The front and rear suspension has a deviation of
(i ═ f or r), input to a PSO-fuzzy PI controller, which outputs a control law u fuzzy-pi-pso_i And (t), the control rule is shown as the formula (47).
Examples
The control is performed in the manner of the first embodiment and the second embodiment.
In the second specific embodiment, one half vehicle suspension can be decoupled into a combination of two 1/4 suspensions through four-part analysis, and the specific design process of the hierarchical control strategy of the optimal sliding mode is as follows:
(1) the invention obtains the suspension frame mass center acceleration by the optimal sliding mode control
And centroid pitch angular acceleration
And multiplying by 0.6 respectively to be used as the target of the bottom layer control.
(2) Respectively obtained from the formulae (20), (21), (24) and (25)
And
the estimated value of (2) is obtained from the equations (30), (31)
And
then, the decomposed estimated values of the front and rear suspension sprung mass acceleration are obtained:
(3) handle
And
as a known value, establishing a two-degree-of-freedom suspension space state equation expression in the figure 5, and setting a system state variable as X i And then:
in the formula, subscript i is f or r; they represent the front and rear suspension systems, respectively, with an output state variable of Y i
The state space expression is:
Y i ＝C i X i (44)
in the formula
The control force F required by the suspension with two degrees of freedom can be obtained according to the state equation and the designed control algorithm (47) mi Then, the compounds can be obtained by the following formulae (34) and (35)
And
the actual value of (c);
(4) according to the formulae (18), (19), (28) and (29), the compounds
And
actual value of
Further pass through (32) and (33) can obtain
And
thereby obtaining
And
the actual value of (c).
(5) Semi-active suspension bottom control based on PSO-fuzzy PI
Due to the control method of PI alone, the proportionality coefficient K P_i And integral coefficient K I_i The method is not good in setting and effect, so that the method adds a PSO and fuzzy method on the basis of PI coarse adjustment parameters to ensure that the proportionality coefficient K is poor P_i And integral coefficient K I_i The subscript i ═ f or r denotes the front and rear suspensions, respectively, updated in real time as the simulation runs.
First, the coefficient K is compared by trial and error P_i And integral coefficient K I_i Coarse adjustment is carried out, and the coarse adjustment steps are as follows:
(1) coarse adjustment of proportion parameters: firstly, K is firstly P_i The value is put at a smaller position, and when the output does not oscillate, the proportionality coefficient K is increased P_i 。
(2) Coarse tuning of integration parameters: after setting the proportion parameters, reducing the proportion value (by 10-20%), and then gradually adding the integration time from large to small until a 4:1 attenuation process is obtained.
After the coarse tuning, the PSO algorithm is added to the fuzzy PI controller. The front and rear suspension has a deviation of
(i ═ f or r), input to a PSO-fuzzy PI controller, which outputs a control law u fuzzy-pi-pso_i And (t), the control rule is shown as the formula (47).
FIG. 6 is a PSO-fuzzy PI control schematic diagram. The fuzzy PI rule designed by the invention is shown in the table 1 and the table 1.
TABLE 1K fuzzy_P Fuzzy rule table of
TABLE 2K fuzzy_I Fuzzy rule table of
Updating the proportionality coefficient K of PI in real time by PSO method along with simulation operation P_i And integral coefficient K I_i The invention uses nonlinear least square method to update parameters, and the nonlinear least square method updates K according to the criterion of minimum deviation square sum P_i And K I_i The objective function is determined as equation (48). To K P_i And K I_i Updating in real time, and acquiring n groups of experimental data e when a simulation experiment is assumed i1 ,e i2 …e in The subscript i ═ f or r, which indicates the front and rear suspensions, respectively, and the principle of fitting is to find the parameters to be determined so as to minimize the following equation.
In the formula, theta 1 For a parameter K to be determined P_i And K I_i The constructed vector.
In summary, the desired damping force based on PSO-fuzzy PI control is
In the formula, the subscript i ═ f or r indicates front and rear suspensions, respectively. The parameters simulated in Simulink are shown in table 3.
TABLE 3 model parameters for bottom layer control
TABLE 4 analysis of vehicle ride comfort subjective perceptions by various control methods
Fig. 7, 8 and 9 are simulation results of functions of acceleration, speed and power spectral density of the vehicle body in each control method respectively, and it can be known from the graphs that the results obtained by the PSO-fuzzy PI hierarchical control method are better than those obtained by passive component selection and PID hierarchical control. Table 1 shows that the subjective feelings of each control method person are analyzed for vehicle ride comfort, the weighted acceleration root mean square and the equivalent mean value of the PSO-fuzzy PI control hierarchy are both smaller than those of the passive and PID hierarchical controls, wherein the feeling of the passive suspension is very uncomfortable, the subjective feelings of the suspension controlled by the PID hierarchy are rather uncomfortable, and the subjective feelings of the suspension controlled by the PSO-fuzzy PI hierarchy are uncomfortable, so that the PSO-fuzzy PI control hierarchy control method has a good effect of improving the comfort of the vehicle suspension.
Claims (9)
1. A sliding mode control method for a vehicle suspension, comprising the steps of:
step 1, performing dynamic analysis on a 4-degree-of-freedom vehicle model of a half vehicle, and determining a state equation:
state vector X ═ X 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ) T Wherein x is 1 ＝z 11 -q 1 ,x 2 ＝z 21 -q 2 ,x 3 ＝z 12 -z 11 ,x 4 ＝z 22 -z 21 ,
Is the first derivative of X;
input vector U * ＝[F 1 ,F 2 ,q 1 ,q 2 ] T ；
The output vector is:
Y＝(y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 ) T
in the formula:
y 2 ＝z 11 -q 1 ,y 3 ＝z 21 -z 11 ,y 4 ＝z 12 -z 11 ,y 5 ＝z 22 -z 21 ,
the output equation is:
Y＝CX+DU *
in the formula: z is a radical of formula 21 、z 22 Vertical displacement of the connection points of the front suspension and the rear suspension and the vehicle body respectively; l 1 、l 2 Respectively the distances from the barycenter O of the vehicle body to the front axle and the rear axle; theta is a pitch angle; z is a radical of formula 3 Is the vertical displacement of the center of mass of the car body; m is a unit of 1 、m 2 、m 3 Front and rear unsprung masses and sprung masses, respectively; i is the pitching moment of inertia of the vehicle body around the center of mass; z is a radical of formula 11 、z 12 Front and rear unsprung mass vertical displacements, respectively; c. C 1 、c 2 The equivalent damping coefficients of the front suspension and the rear suspension are respectively; k is a radical of 11 、k 21 、k 12 、k 22 Respectively the equivalent stiffness coefficients of the front and rear tires and the front and rear suspensions; f 1 、F 2 Respectively, the front suspension and the rear suspension are semi-actively expected to control force; f 3 、F 4 Are respectively provided withThe semi-active control force of the front suspension and the rear suspension obtained by the controller; q. q.s 1 、q 2 Respectively exciting the road surfaces of the front axle and the rear axle randomly; v is the vehicle speed; f. of 0 Is the lower cut-off frequency; n is a radical of an alkyl radical 0 Is a reference spatial frequency; g n (n 0 ) The coefficient of road surface unevenness; w is a white noise signal of the road surface;
step 2, optimal sliding mode control based on the smooth performance index of the magneto-rheological suspension:
selected suspension combination property index J:
in the formula: t is the total time of vehicle operation; t represents a temporal change; delta 1 ，δ 2 ，δ 3 ，δ 4 ，δ 5 And delta θ Is composed of
(z 11 -q 1 ) 2 ，(z 21 -q 2 ) 2 ，
And
the weighting coefficients of (a);
constructing an optimal sliding mode manifold function, selecting a linear sliding mode approximation rate and solving an ideal control vector as follows:
U＝-(KB 1 ) -1 (KA+λK)X＝U 1 +U 2
in the formula of U 1 ＝-(KB 1 ) -1 KAX,U 2 ＝-(KB 1 ) -1 λKX；
The control of the vehicle suspension is realized according to the ideal control vector, the control is carried out in a layered control mode, and the process of the layered control comprises the following steps:
step 3, establishing a dynamic layering model:
converting a four-degree-of-freedom system of a half vehicle suspension into two-degree-of-freedom systems through conversion of a suspension kinetic equation;
when the sprung mass of the front and rear suspension systems is decomposed, the unsprung mass of the front and rear suspension systems correspondingly generates a displacement delta x uf 、Δx ur If so
Respectively representing the displacement state of the unsprung mass of the front and rear suspension systems after disassembly, by x uf 、x ur Respectively representing the displacement state of the unsprung mass before disassembly, including
And respectively arranging the dynamic balance equations of the sprung mass and the unsprung mass of the decomposed suspension system:
in the formula, k mi And c ni Respectively representing the rigidity coefficient and the damping coefficient of the suspension; f mi Representing the output force of the semi-active actuator; k is a radical of ui Represents the tire stiffness; m is ui Represents an unsprung mass; x is the number of si Denotes road surface excitation, subscript i ═ f or r, denotes front or rear side;
adding the two formulas to obtain:
will be Δ x uf And Δ x ur The displacement variation of the unsprung mass of the suspension system can be respectively obtained by substituting the expression into the formula:
step 4, carrying out layered control on the vehicle suspension based on the dynamic layered model in the step 3:
(1) suspension center of mass acceleration obtained by optimal sliding mode control
And centroid pitch angular acceleration
Multiplying the obtained data by a set coefficient respectively to serve as a target of bottom control;
(2) according to
And
is estimated to be sum
And
obtaining the decomposed estimated values of the front and rear suspension spring load mass acceleration;
(3) handle
And
establishing a two-degree-of-freedom suspension space state equation expression as a known value;
obtaining the control force F required by the two-freedom suspension according to the space state equation of the two-freedom suspension mi Then determine
And
the actual value of (c);
(4) obtained according to the procedure of step 3
And
actual value of, and
and
the actual value of (c);
(5) semi-active suspension under-layer control based on PSO-fuzzy PI.
2. The sliding mode control method for the vehicle suspension according to claim 1, wherein the process of performing dynamic analysis and determining the state equation for the 4-degree-of-freedom vehicle model of the semi-vehicle in step 1 is as follows:
and (3) carrying out dynamic analysis on the vehicle model:
taking the state vector as:
X＝(x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ,x 7 ,x 8 ) T (6)
in the formula:
x 1 ＝z 11 -q 1 ,x 2 ＝z 21 -q 2 ,x 3 ＝z 12 -z 11 ,x 4 ＝z 22 -z 21 ,
the state equation is:
in the formula:
3. the sliding-mode control method for the vehicle suspension according to claim 1, characterized in that the process of constructing an optimal sliding-mode manifold function and selecting a linear sliding-mode approach rate and solving an ideal control vector is as follows:
constructing an optimal sliding mode manifold function as
In the formula: s represents an optimal sliding mode manifold function; p is a symmetrical positive definite array;
linear sliding mode approach rate was chosen:
wherein λ is the coefficient of approach rate;
the following can be obtained:
will be provided with
With AX + B 1 U is substituted, wherein U ═ F 1 ,F 2 ] T ；
The ideal control vector is found by the above equation:
U＝-(KB 1 ) -1 (KA+λK)X＝U 1 +U 2
in the formula of U 1 ＝-(KB 1 ) -1 KAX,U 2 ＝-(KB 1 ) -1 λKX。
4. The sliding-mode control method for a vehicle suspension according to claim 3, wherein the P is a symmetric positive definite matrix obtained by the Riccati equation, and the corresponding Riccati equation is as follows:
in the formula:
in the formula: a. the T1 、A T2 、A T3 、A T4 Is A T The block matrix of (2); q T1 、Q T2 、Q T3 、Q T4 Is Q T The block matrix of (2); a. the T1 And Q T1 Is a 6 x 6 order matrix; a. the T2 And Q T2 Is a 6 x 2 order matrix; a. the T3 And Q T3 Is a 2 x 6 order matrix; a. the T4 And Q T4 Is a 2 x 2 order matrix.
5. The sliding mode control method for the vehicle suspension according to claim 1, wherein the procedure of the PSO-fuzzy PI based semi-active suspension bottom layer control of step (5) is as follows:
let subscript i ═ f or r denote front and rear suspensions, respectively;
first, the coefficient K is compared by trial and error P_i And integral coefficient K I_i Coarse adjustment is carried out, and the coarse adjustment steps are as follows:
(a) coarse adjustment of proportion parameters: firstly, K is firstly P_i The value is put at a smaller position, and when the output does not oscillate, the proportionality coefficient K is increased P_i ；
(b) Coarse tuning of the integration parameters: after setting the proportional parameters, reducing the proportional value by 10-20%, and then gradually adding the integration time from large to small until a 4:1 attenuation process is obtained;
after coarse adjustment, adding a PSO algorithm into the fuzzy PI controller; the front and rear suspension has a deviation of
(i ═ f or r), input to a PSO-fuzzy PI controller, which outputs a control law u fuzzy-pi-pso_i (t) according to the control law
6. The sliding-mode control method for the vehicle suspension according to claim 1, wherein the step 3 of converting the half-vehicle suspension four-degree-of-freedom system into the two-degree-of-freedom system through the conversion of the suspension kinetic equation is as follows:
according to the theorem of centroid motion and the theorem of moment of momentum of relative centroid, and the displacement x of front and rear suspensions cf 、x cr Displacement x from the suspension center of mass c Determines the relationship of:
in the formula, m c Is the spring load mass in kg; I.C. A c Is the moment of inertia of the sprung mass in kg m 2 ；
Is the displacement acceleration at the center of mass of the suspension with the unit of m/s 2 ；
Is the pitch angle acceleration at the suspension centroid;
adding the two above equations to obtain:
will be provided with
Multiplied by l r L minus formula
Multiplied by l f L to obtain:
in the formula: m is cf ＝m c l r /l，m cr ＝m c l f L is the center distance of the front wheel and the rear wheel;
according to the formula
And formula
To obtain
And
for a front suspension system, mass m is concentrated if there are no constraints of the rear suspension system cf Moving from point F to point F 1 Let Δ x f From point F to point F 1 Has a displacement of Δ x f ＝x cf -x f At the same time at point F 1 The dynamic equilibrium equation is shown as follows:
similarly, for the rear suspension system, let Δ x r From point R to point R 1 Has a displacement of Δ x r ＝x r -x cr While at R 1 There is a dynamic balance equation:
substituting the above relations into the formulas
In the method, the following steps are obtained:
can be obtained by the above two formulas
And
through the conversion of the suspension kinetic equation, the half-vehicle suspension four-degree-of-freedom system is converted into two-degree-of-freedom systems.
7. The sliding mode control method for vehicle suspensions according to claim 6, characterized by the theorem of motion of the center of mass and the theorem of moment of momentum relative to the center of mass, and the front and rear suspension displacements x cf 、x cr Displacement x from the center of mass of the suspension c Determination of the relationship of
And
the process of (2) is as follows:
the theorem of motion of the center of mass and the theorem of moment of momentum of the relative center of mass have the followings:
in the formula, m c Is the spring load mass in kg; i is c Is the moment of inertia of the sprung mass in kg m 2 ；
Is the displacement acceleration at the center of mass of the suspension with the unit of m/s 2 ；
Is the pitch angle acceleration at the suspension centroid;
the following two formulas can be obtained:
displacing the front and rear suspensions by x cf 、x cr Displacement x from the center of mass of the suspension c Relation x of c ＝x cf +l f θ c ＝x cr -l r θ c Respectively substituting the two formulas to obtain:
8. the sliding-mode control method for a vehicle suspension according to claim 1, wherein the step (2) obtains the decomposed estimated values of front and rear suspension sprung mass accelerations as follows:
9. the sliding mode control method for a vehicle suspension according to claim 8,characterized in that the step (3) is
And
as a known value, the process of establishing the expression of the two-degree-of-freedom suspension space state equation is as follows:
setting the system state variable of two-freedom suspension space as X i And then:
in the formula, subscript i is f or r; they represent the front and rear suspension systems, respectively, with an output state variable of Y i
The state space expression is:
Y i ＝C i X i
in the formula
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