CN105159094A

CN105159094A - Design method of optimal control force of LQG controller of automobile active suspension bracket

Info

Publication number: CN105159094A
Application number: CN201510645787.1A
Authority: CN
Inventors: 周长城; 于曰伟; 赵雷雷
Original assignee: Shandong University of Technology
Current assignee: Shandong University of Technology
Priority date: 2015-10-08
Filing date: 2015-10-08
Publication date: 2015-12-16
Anticipated expiration: 2035-10-08
Also published as: CN105159094B

Abstract

The invention, which belongs to the technical field of the active suspension bracket, relates to a design method of an optimal control force of an LQG controller of an automobile active suspension bracket. On the basis of a one-quarter vehicle driving vibration model, a ride weighting coefficient optimization design simulink simulation model is constructed by using MATLAB/simulink; and optimization designing is carried out to obtain a ride weighting coefficient and an LQG optimal control force by using pavement unevenness displacement as input excitation, tyre dynamic displacement and suspension dynamic deflection as constraint conditions, and root-mean-square value minimization of vertical vibration acceleration of a vehicle body as a design target. According to examples and simulation verification, with the method, an accurate and reliable LQG optimal control force of the active suspension bracket can be obtained; and a reliable optimal control force design method can be provided for the design and control of the active suspension bracket system. Therefore, the design level and product quality of the active suspension bracket system can be improved; the vehicle riding comfort and driving safety are enhanced; and the product design and testing expenses can be reduced.

Description

Design method for optimal control force of LQG controller of automobile active suspension

Technical Field

The invention relates to an automobile active suspension, in particular to a design method of an optimal control force of an LQG controller of the automobile active suspension.

Background

The LQG control has strong applicability and is widely applied to active suspension systems, wherein the determination of the optimal control force is the key of the design of the LQG controller of the active suspension of the vehicle. However, according to the data consulted, the current design of the optimal control force of the LQG controller of the active suspension of the automobile at home and abroad is mostly based on the tendency of a designer to the performance of the suspension, the LQG control weighting coefficient is preliminarily determined according to experience, and then the weighting coefficient is gradually adjusted according to the response through a plurality of times of simulation until the satisfactory output response is obtained, so as to design the optimal control force of the LQG controller of the active suspension. Although the LQG control force obtained by the method can enable the vehicle to meet the requirements of the current running condition, the designed control force is not optimal. With the rapid development of the vehicle industry and the continuous improvement of the vehicle running speed, people put forward higher requirements on the vehicle running safety and the riding comfort, and the current method for designing the optimal control force of the LQG controller of the active suspension cannot meet the requirements of the vehicle development and the design of the controller of the active suspension. Therefore, an accurate and reliable design method for the optimal control force of the LQG controller of the automobile active suspension must be established, the requirements of vehicle development and active suspension controller design are met, the design level and the product quality of an automobile active suspension system are improved, and the riding comfort and the safety of the automobile are improved; meanwhile, the product design and test cost is reduced, and the product design period is shortened.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to provide an accurate and reliable method for designing the optimal control force of the LQG controller of the active suspension of the automobile, wherein a design flow chart is shown in figure 1; 1/4A model diagram of vibration of vehicle running is shown in FIG. 2.

In order to solve the technical problem, the method for designing the optimal control force of the LQG controller of the automobile active suspension is characterized by comprising the following design steps of:

(1) 1/4 vehicle running vibration differential equation is established:

according to unsprung mass m of a single wheel of the vehicle₁Sprung mass m₂Suspension spring rate K₂Stiffness of the tire K_tControl force U of active suspension to be designed_a(ii) a By vertical displacement z of the tyre₁Vertical displacement z of the car body₂Is a coordinate; taking the road surface unevenness displacement q as input excitation; 1/4, establishing a differential equation of the vehicle running vibration, namely:

(2) determining a state matrix A and a control matrix B of LQG control:

according to unsprung mass m of a single wheel of the vehicle₁Sprung mass m₂Suspension spring rate K₂Stiffness of the tire K_tVehicle speed v, and filtered white noise road surface spatial cut-off frequency n_0cDetermining a state matrix A and a control matrix B controlled by the LQG, wherein the state matrix A and the control matrix B are respectively as follows:

(3) determining a weighting matrix expression of LQG control:

according to unsprung mass m of a single wheel of the vehicle₁Sprung mass m₂Suspension spring rate K₂Stiffness of the tire K_tSuspension limit travel [ f ]_d]And the acceleration of gravity g, determining a weighting coefficient alpha for the smoothness₁、α₂、α₃State variable, controlled variable, and state variable and controlled variable cross product term weighting matrix expression Q (alpha)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) Respectively is as follows:

wherein, q₃＝1；α₁as weighting factors for the relative dynamic loads of the wheels, alpha₂Weighting coefficient of relative dynamic deflection of suspension, alpha₃Weighting coefficients of the vertical vibration relative acceleration of the vehicle body;

(4) determining active suspension LQG control force U_aExpression:

i, step: selecting an initial value of the ride-comfort weighting factor, i.e. alpha₁＝k₁、α₂＝k₂、α₃＝k₃Wherein k is₁，k₂，k₃Are all values greater than zero and less than 1, andk₁+k₂+k₃＝1.0；

II, step (2): according to the initial value alpha of the smoothness weighting coefficient selected in the step I₁＝k₁、α₂＝k₂、α₃＝k₃And the weighting matrix expression Q (alpha) determined in step (3)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) And calculating to obtain a weighting matrix Q (k)₁,k₂,k₃)、R(k₁,k₂,k₃)、N(k₁,k₂,k₃)；

Step III: according to the state matrix A and the control matrix B determined in the step (2) and the weighting matrix Q (k) determined in the step II₁,k₂,k₃)、R(k₁,k₂,k₃)、N(k₁,k₂,k₃) Calculating a control feedback gain matrix K of the active suspension LQG by using an LQR function in Matlab;

IV, step (2): according to the feedback gain matrix K determined in the step III, the vibration speed of the wheel is calculatedAnd a displacement z₁Vehicle body vibration speedAnd a displacement z₂And determining the control force U of the active suspension LQG by taking the road surface displacement q as a state variable_aThe expression, namely:

wherein,

is a matrix

The transposed matrix of (2);

(5) optimization design of the smoothness weighting coefficient:

firstly, constructing a ride comfort weighting coefficient optimization design simulation model

According to 1/4 vehicle running vibration differential equation established in step (1) and control force U obtained in step IV in step (4)_aConstructing a smoothness weighting coefficient optimization design Simulink simulation model by using Matlab/Simulink simulation software;

establishing smoothness weighting coefficient optimization design objective function

Optimally designing a Simulink simulation model according to the smoothness weighting coefficient established in the step I, and using the smoothness weighting coefficient alpha₁、α₂、α₃Simulating the running vibration of the vehicle by taking the displacement of the road surface unevenness as input excitation for designing variables, and obtaining the mean square root value of the vertical vibration acceleration of the vehicle body by utilizing the simulationOptimal design objective function J for establishing smoothness weighting coefficient_o(α₁,α₂,α₃) Namely:

establishing smoothness weighting coefficient optimization design constraint condition

According to unsprung mass m of a single wheel of the vehicle₁Sprung mass m₂Stiffness of the tire K_tAcceleration of gravity g, and suspension limit travel f_d]By vertical displacement z of the tyre₁Vertical displacement z of the car body₂The road surface irregularity displacement q, and the smoothness weighting coefficient alpha₁、α₂、α₃Establishing ride comfort weighting factor optimization design constraints, i.e.

Optimization design of smoothness weighting coefficient

Optimally designing a Simulink simulation model according to the smoothness weighting coefficient established in the step (i), and optimally designing constraint conditions according to the smoothness weighting coefficient established in the step (iii) to obtain a smoothness weighting coefficient alpha₁、α₂、α₃For design variables, the displacement of the road surface unevenness is taken as input excitation, and an optimization algorithm is utilized to solve the smoothness weighting coefficient established in the second step to optimize a design objective function J_o(α₁,α₂,α₃) The corresponding design variable is the optimal optimized design value of the smoothness weighting coefficient, namely alpha_1o、α_2o、α_3o；

(6) Optimal control force U of active suspension LQG controller_aoThe design of (2):

i, step: obtaining a smoothness weighting coefficient alpha according to the optimization design in the step (5)_1o、α_2o、α_3oAnd the weighting matrix expression Q (alpha) determined in step (3)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) And calculating to obtain a weighting matrix Q (alpha)_1o,α_2o,α_3o)、R(α_1o,α_2o,α_3o)、N(α_1o,α_2o,α_3o)；

ii, step: according to the state matrix A and the control matrix B determined in the step (2) and the weighting matrix Q (alpha) determined in the step i_1o,α_2o,α_3o)、R(α_1o,α_2o,α_3o)、N(α_1o,α_2o,α_3o) Calculating to obtain the optimal control feedback gain matrix K of the active suspension LQG by using the LQR function in Matlab_o；

And iii, step (ii): according to the optimal feedback gain matrix K determined in the step ii_oAt the wheel vibration speedAnd a displacement z₁Vehicle body vibration speedAnd a displacement z₂And determining the optimal control force U of the active suspension LQG controller by taking the road surface displacement q as a state variable_aoNamely:

compared with the prior art, the invention has the advantages that:

the LQG control has strong applicability and is widely applied to active suspension systems, wherein the determination of the optimal control force is the key of the design of the LQG controller of the active suspension of the vehicle. However, according to the data consulted, the current design of the optimal control force of the LQG controller of the active suspension of the automobile at home and abroad is mostly based on the tendency of a designer to the performance of the suspension, the LQG control weighting coefficient is preliminarily determined according to experience, and then the weighting coefficient is gradually adjusted according to the response through a plurality of times of simulation until the satisfactory output response is obtained, so as to design the optimal control force of the LQG controller of the active suspension. Although the LQG control force obtained by the method can enable the vehicle to meet the requirements of the current running condition, the designed control force is not optimal. With the rapid development of the vehicle industry and the continuous improvement of the vehicle running speed, people put forward higher requirements on the vehicle running safety and the riding comfort, and the current method for designing the optimal control force of the LQG controller of the active suspension cannot meet the requirements of the vehicle development and the design of the controller of the active suspension.

According to 1/4 vehicle running vibration model and active suspension control force, MATLAB/Simulink is utilized to construct a smoothness weighting coefficient optimization design Simulink simulation model, the road surface unevenness displacement is used as input excitation, the tire dynamic displacement and the suspension dynamic deflection are used as constraint conditions, the minimum mean square root value of the vehicle body vertical vibration acceleration is used as a design target, the smoothness weighting coefficient is obtained through optimization design, and then the active suspension LQG optimal control force is obtained through design. According to the design example and simulation comparison verification, the method can obtain the accurate and reliable optimal control force value of the active suspension LQG, and provides a reliable design method for the design of the optimal control force value of the automobile active suspension LQG. By using the method, the design level and the product quality of the automobile active suspension system can be improved, and the riding comfort and the safety of the automobile are improved; meanwhile, the product design and test cost is reduced, and the product design period is shortened.

Drawings

For a better understanding of the invention, reference is made to the following further description taken in conjunction with the accompanying drawings.

FIG. 1 is a design flow chart of an optimal control force design method for an active suspension LQG controller of an automobile;

FIG. 2 is a model diagram of 1/4 vibration of vehicle;

FIG. 3 is a smoothness weighting factor optimization design Simulink simulation model of an embodiment;

FIG. 4 is a simulation comparison curve of a time domain signal of the vertical vibration acceleration of the vehicle body of the embodiment;

FIG. 5 is a simulated contrast curve of the power spectral density of the vertical vibration acceleration of the vehicle body of the embodiment.

Detailed description of the preferred embodiments

The present invention will be described in further detail below with reference to an example.

Unsprung mass m of single wheel of certain vehicle₁40kg, sprung mass m₂320kg, suspension spring rate K₂20000N/m, tire stiffness K_t200000N/m, suspension limit travel [ f_d]100mm, and the gravity acceleration g 9.8m/s²Spatial cut-off frequency n of filtering white noise road surface_0c＝0.011m^-1The LQG control force of the active suspension to be designed is U_a. The vehicle running speed v required by the design of the vehicle active suspension is 72km/h, and the control force of the vehicle active suspension LQG controller is designed.

The design flow chart of the method for designing the optimal control force of the LQG controller of the active suspension of the automobile provided by the embodiment of the invention is shown in figure 1, the 1/4 vehicle running vibration model chart is shown in figure 2, and the specific steps are as follows:

(1) 1/4 vehicle running vibration differential equation is established:

according to unsprung mass m of a single wheel of the vehicle₁40kg, sprung mass m₂320kg, suspension spring rate K₂20000N/m, tire stiffness K_t200000N/m, active suspension control force U to be designed_a(ii) a By vertical displacement z of the tyre₁Vertical displacement z of the car body₂Is a coordinate; taking the road surface unevenness displacement q as input excitation; 1/4, establishing a differential equation of the vehicle running vibration, namely:

(2) determining a state matrix A and a control matrix B of LQG control:

according to unsprung mass m of a single wheel of the vehicle₁40kg, sprung mass m₂320kg, suspension spring rate K₂20000N/m, tire stiffness K_t200000N/m, vehicle running speed v 72km/h, and spatial cut-off frequency N of filtered white noise road surface_0c＝0.011m^-1Determining a state matrix A and a control matrix B controlled by the LQG, wherein the state matrix A and the control matrix B are respectively as follows:

A = [\begin{matrix} 0 & 0 & - 62.5 & 62.5 & 0 \\ 0 & 0 & 500 & - 5500 & 5000 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & - 1.4 \end{matrix}], B = [\begin{matrix} 0.0031 \\ - 0.025 \\ 0 \\ 0 \\ 0 \end{matrix}];

(3) determining a weighting matrix expression of LQG control:

according to unsprung mass m of a single wheel of the vehicle₁40kg, sprung mass m₂320kg suspension spring steelDegree K₂20000N/m, tire stiffness K_t200000N/m, suspension limit travel [ f_d]100mm and g 9.8m/s²Determining a weighting factor alpha for the smoothness₁、α₂、α₃State variable, controlled variable, and state variable and controlled variable cross product term weighting matrix expression Q (alpha)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) Respectively is as follows:

(4) determining active suspension LQG control force U_aExpression:

i, step: selecting an initial value of a smoothness weighting coefficient; this example selects k₁＝0.1，k₂＝0.2，k₃0.7, wherein k₁+k₂+k₃1.0, i.e. selecting the initial value alpha of the ride-comfort weighting factor₁＝0.1，α₂＝0.2，α₃＝0.7；

II, step (2): according to the initial value alpha of the smoothness weighting coefficient selected in the step I₁＝0.1、α₂＝0.2、α₃0.7, and the weighting matrix expression Q (α) determined in step (3)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) The weighting matrices Q (0.1,0.2,0.7), R (0.1,0.2,0.7), N (0.1,0.2,0.7) are calculated, i.e.:

Q (0.1, 0.2, 0.7) = [\begin{matrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 4211.1 & - 4211.1 & 0 \\ 0 & 0 & - 4211.1 & 48302.8 & - 44091.7 \\ 0 & 0 & 0 & - 44091.7 & 44091.7 \end{matrix}],

R(0.1,0.2,0.7)＝9.766×10^-6，

N (0.1, 0.2, 0.7) = [\begin{matrix} 0 \\ 0 \\ - 0.195 \\ 0.195 \\ 0 \end{matrix}];

step III: calculating to obtain the active suspension by utilizing the LQR function in Matlab according to the state matrix A and the control matrix B determined in the step (2) and the weighting matrix Q (0.1,0.2,0.7), R (0.1,0.2,0.7) and N (0.1,0.2,0.7) determined in the step (II)

The control feedback gain matrix K of LQG is:

K＝[1941.2-925.1-14412.513653.011560.0]；

wherein,

is a matrix

The transposed matrix of (2);

(5) optimization design of the smoothness weighting coefficient:

According to 1/4 vehicle running vibration differential equation established in step (1) and control force U obtained in step IV in step (4)_aConstructing a smoothness weighting coefficient optimization design Simulink simulation model by using Matlab/Simulink simulation software, as shown in FIG. 3;

According to unsprung mass m of a single wheel of the vehicle₁40kg, sprung mass m₂320kg, tire stiffness K_t200000N/m, and g 9.8m/s²And suspension limit travel [ f_d]100mm, using vertical displacement z of the tyre₁Vertical displacement z of the car body₂The road surface irregularity displacement q, and the smoothness weighting coefficient alpha₁、α₂、α₃Establishing ride comfort weighting factor optimization design constraints, i.e.

Optimization design of smoothness weighting coefficient

Optimally designing a Simulink simulation model according to the smoothness weighting coefficient established in the step (i), and optimally designing constraint conditions according to the smoothness weighting coefficient established in the step (iii) to obtain a smoothness weighting coefficient alpha₁、α₂、α₃For design variables, the displacement of the road surface unevenness is taken as input excitation, and an optimization algorithm is utilized to solve the smoothness weighting coefficient established in the second step to optimize a design objective function J_o(α₁,α₂,α₃) To find the optimum design value of the ride comfort weighting coefficient, i.e. alpha_1o＝0.0108、α_2o＝0.0506、α_3o＝0.9386；

i, step: obtaining a smoothness weighting coefficient alpha according to the optimization design in the step (5)_1o＝0.0108、α_2o＝0.0506、α_3o0.9386, and the weighting matrix expression Q (α) determined in step (3)₁,α₂,α₃)、R(α₁,α₂,α₃)、N(α₁,α₂,α₃) The weighting matrices Q (0.0108,0.0506,0.9386), R (0.0108,0.0506,0.9386), N (0.0108,0.0506,0.9386) are calculated as:

Q (0.0108, 0.0506, 0.9386) = [\begin{matrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 3964.2 & - 3.9642 & 0 \\ 0 & 0 & - 3.9642 & 7515.3 & - 3551.0 \\ 0 & 0 & 0 & - 3551.0 & 3551.0 \end{matrix}],

R(0.0108,0.0506,0.9386)＝9.766×10^-6，

N (0.0108, 0.0506, 0.9386) = [\begin{matrix} 0 \\ 0 \\ - 0.195 \\ 0.195 \\ 0 \end{matrix}];

ii, step: calculating and obtaining an optimal control feedback gain matrix K of the active suspension LQG by using the LQR function in Matlab according to the state matrix A and the control matrix B determined in the step (2) and the weighting matrixes Q (0.0108,0.0506,0.9386), R (0.0108,0.0506,0.9386) and N (0.0108,0.0506,0.9386) determined in the step i_oNamely:

K_o＝[1247.4-270.4-1756318032.3347.5]；

under the same vehicle structure parameters and driving conditions, wherein the driving road condition of the vehicle is a B-level road surface, the driving speed v of the vehicle is 72km/h, model simulation is respectively carried out on the LQG control which determines the optimal control force by using the traditional empirical method and determines the optimal control force by using the optimal design method, wherein the optimal control force determined by using the traditional empirical method is

The comparison curves of the vehicle body vertical vibration acceleration time domain signal and the vehicle body vertical vibration acceleration power spectral density of the two control methods obtained through simulation are respectively shown in fig. 4 and fig. 5, and it can be known that the active suspension LQG controller designed by the optimization design method remarkably reduces the vehicle body vertical vibration acceleration, compared with the traditional empirical design method, the mean square root value of the vehicle body vertical vibration acceleration is reduced by 53.0%, which indicates that the established design method of the optimal control force of the vehicle active suspension LQG controller is correct.

Claims

1. The design method of the optimal control force of the automobile active suspension LQG controller comprises the following specific design steps:

(1) 1/4 vehicle running vibration differential equation is established:

according to unsprung mass m of a single wheel of the vehicle₁Sprung mass m₂Suspension spring rate K₂Stiffness of the tire K_tControl force U of active suspension to be designed_a(ii) a By vertical displacement z of the tyre₁Vertical displacement z of the car body₂Is a coordinate; taking the road surface unevenness displacement q as input excitation; 1/4 method for creating micro-vibration of vehicleThe equation, namely:

(2) determining a state matrix A and a control matrix B of LQG control:

(3) determining a weighting matrix expression of LQG control:

(4) determining active suspension LQG control force U_aExpression:

i, step: selecting an initial value of the ride-comfort weighting factor, i.e. alpha₁＝k₁、α₂＝k₂、α₃＝k₃Wherein k is₁，k₂，k₃Are all values greater than zero and less than 1, and k₁+k₂+k₃＝1.0；

wherein,

is a matrix

The transposed matrix of (2);

(5) optimization design of the smoothness weighting coefficient:

Optimally designing a Simulink simulation model according to the smoothness weighting coefficient established in the step I, and using the smoothness weighting coefficient alpha₁、α₂、α₃For design variables, with road surfacesThe unevenness displacement is used as input excitation to simulate the vehicle running vibration condition, and the mean square root value of the vertical vibration acceleration of the vehicle body obtained by simulation is utilizedOptimal design objective function J for establishing smoothness weighting coefficient_o(α₁,α₂,α₃) Namely:

Optimization design of smoothness weighting coefficient

ii, step: according to the stepsThe state matrix A and the control matrix B determined in step (2), and the weighting matrix Q (alpha) determined in step i_1o,α_2o,α_3o)、R(α_1o,α_2o,α_3o)、N(α_1o,α_2o,α_3o) Calculating to obtain the optimal control feedback gain matrix K of the active suspension LQG by using the LQR function in Matlab_o；