A PID and LQR composite control method for semi-active suspension

Abstract

The present invention discloses a semi-active suspension PID and LQR composite control method, that is, a PID-LQR composite control strategy is adopted to optimize the vehicle's ride smoothness index and vehicle body posture stability index: vehicle body vertical acceleration, suspension dynamic travel, tire dynamic load, pitch angular acceleration and roll angular acceleration. According to PID control, preview control and LQR control theory, a PID-LQR controller is designed, and the actuators are four suspension actuators. A method for adjusting PID parameter values is proposed, that is, using MATLAB / PIDTuner to adjust the PID parameters, and using a genetic algorithm to find the optimal weights of various performance indicators of the system. The 7-degree-of-freedom model established by the present invention can more comprehensively analyze the performance of the whole vehicle and is closer to the actual vehicle. By establishing road models of different levels to change the experimental scene, various performance indicators of the vehicle under different test conditions can be obtained, and the performance of the whole vehicle can be more comprehensively analyzed.

Description

Technical Field

[0001] The present invention belongs to the technical field of semi-active suspension control systems, and in particular relates to a semi-active suspension PID and LQR composite control method. Background Art

[0002] The suspension is a force buffering device connecting the chassis and the body. Its function is to reduce the vibration impact transmitted to the body by road excitation, improve the riding experience of the passengers in the body and the driving experience of the driver. Therefore, the suspension plays a vital role in the comfort of the body, the smoothness of the ride, the body posture stability and the handling stability.

[0003] Different suspension types have different working performance and vibration reduction effects. The working performance of air suspension and fully active suspension with changeable stiffness and damping is better than that of semi-active suspension, and can significantly improve the overall performance of the vehicle. However, the disadvantages are complex structure and high cost. Moreover, since air suspension uses air as the working medium, it often needs to be flushed and deflated during driving, causing the air valve to have high temperature and high failure rate, which shortens the service life of the air suspension system. Although the working performance of semi-active suspension is not as good as the above two types of suspension, its advantages over traditional passive suspension are also obvious. In addition, semi-active suspension has a simple structure, low cost, reliable operation and long service life, and is more suitable for some mid- and low-end models. Therefore, semi-active suspension has great market application prospects and will gradually become popular, replacing traditional passive suspension and becoming the mainstream of the market. Therefore, it is necessary to conduct in-depth research on semi-active suspension.

[0004] The research on semi-active suspension system mainly focuses on two aspects: structure and controller design. The structure mainly studies the electrorheological or magnetorheological technology of semi-active suspension, that is, the method of changing the damping coefficient is studied. The controller design mainly studies the control strategy. At present, scholars have proposed many control methods for semi-active suspension controllers, such as skyhook damping control, floorhook damping control, optimal control, fuzzy control, variable structure sliding film control, etc. Although these control methods have different control theories, the control effects are not much different. The control effect of using one control method is limited, and it is difficult to comprehensively optimize the comprehensive performance indicators of the whole vehicle at the same time. If multiple control theories are used to control the semi-active suspension, the control methods can complement each other, and can optimize various evaluation indicators to the greatest extent and improve the performance of the whole vehicle.

[0005] When designing a controller for a semi-active suspension using PID control theory and LQR control theory, determining the control system parameter values is the core work of the present invention. The control parameters play a very important role in the control effect of the control system. The control parameters will affect the stability and sensitivity of the control system. The parameter values that need to be adjusted in the control system of the present invention are: P, I and D parameters and the optimal weights of various performance indicators. Many researchers use the empirical trial and error method to adjust the parameters. This method is very subjective, and human factors have a great impact on the control effect. It is easily interfered with by local optimal solutions, making it difficult to find a global optimal solution.

[0006] Therefore, in order to solve the above problems, this paper proposes a semi-active suspension PID and LQR composite control method. Summary of the Invention

[0007] In order to solve the above technical problems, the present invention designs a semi-active suspension PID and LQR composite control method. The present invention adopts PID control and LQR control to design a semi-active suspension PID-LQR controller. In order to further improve the control effect, a preview control strategy with front wheel feedback is added to provide preview information to the rear wheels in advance. The controller sends control instructions to the rear wheels in advance, and the actuator moves in advance when it is about to pass the road ahead to output pre-control force.

[0008] In order to achieve the above technical effects, the present invention is implemented by the following technical solutions: a semi-active suspension PID and LQR composite control method, characterized by comprising the following steps:

[0009] Step 1: Establish a 7-DOF vehicle dynamics model and a preview control road surface model;

[0010] Step 2: Design a PID-LQR composite controller;

[0011] Step 3: Determine the weight coefficients of each performance index of LQR control and adjust the P, I, and D parameters;

[0012] Step 4. Use Simulink to build a simulation experiment model, set the experimental conditions, and run the simulation.

[0013] Furthermore, the specific steps in Step 1 are:

[0014] Step 1.1. Establish a 7-DOF vehicle dynamics model based on Newton's laws of motion;

[0015] Step 1.2: Determine the control strategies for the front and rear wheels based on preview control theory. For the front wheels, only feedback control is used, while for the rear wheels, feedforward plus feedback control with preview information is used.

[0016] Step 1.3: According to the front and rear wheel control strategies, establish the road surface input models at the four wheels. The front wheel uses a random road surface simulation model as input, and the rear wheel uses a road surface simulation model with front wheel preview information as input.

[0017] Furthermore, in Step 1.1, the vehicle body vertical acceleration, suspension dynamic travel, and tire dynamic displacement are used as performance indicators for evaluating vehicle ride comfort, and two evaluation indicators that affect vehicle body posture stability, namely, pitch angular acceleration and roll angular acceleration, are added;

[0018] The 7 degrees of freedom include the vertical degrees of freedom at the four axles, the vertical degrees of freedom at the four tires, the pitch and roll degrees of freedom around the X and Y axes at the center of mass of the vehicle body, and the vertical degree of freedom along the Z axis.

[0019] Furthermore, in Step 1.1, the force analysis of the 7 degrees of freedom can be performed according to Newton's laws of mechanics to list the 7-degree-of-freedom motion differential equations:

[0020] The vertical force balance equation of the Z axis at the center of mass of the vehicle body is as follows (1):

[0021]

[0022] The balance equation of the rotation moment of the vehicle body around the Y axis is as follows:

[0023]

[0024] The balance equation of the rotation moment of the vehicle body around the X-axis is as follows:

[0025]

[0026] The vertical force balance equation of the four unsprung masses along the Z axis is as follows:

[0027]

[0028] When the range of the vehicle body pitch angle and roll angle is small enough, the displacement of the end points of the suspended mass above the four wheels can be expressed as follows:

[0029] z sf1 =z s -L r θ-aφ

[0030] z sf2 =z s -L l θ-aφ

[0031] z sr1 =z s -L r θ+bφ

[0032] z sr2 =z s +L l θ+bφ (5)

[0033] In formula (1) to formula (5), z s is the vertical displacement of the vehicle's center of mass, is the body's rotation angle around the Y axis (pitch angle), θ is the body's rotation angle around the X axis (roll angle); m wf1 ,m wf2 ,m wr1 ,m wr2 Represent the unsprung masses of the right front, left front, left rear and right rear respectively; k wf1 ,k wf2 ,k wr1 ,k wr2 are the four tire stiffness coefficients respectively; k sf1 ,k sf2 ,k sr1 ,k sr2 are the four suspension stiffness coefficients respectively; c sf1 ,c sf2 ,c sr1 ,c sr2 are the four suspension damping coefficients respectively; q f1 ,q f2 ,q r1 ,q r2 are the displacements of the road surface roughness of the four wheels; z wf1 ,z wf2 ,z wr1 ,z wr2 are the vertical displacements at the four axles; z sf1 ,z sf2 ,z sr1 ,z sr2 are the vertical displacements of the suspended masses above the four wheels; a and b are the distances from the center of mass of the vehicle to the front and rear axes, respectively; L l ,L r The distances from the center of mass of the vehicle to the centerline of the left and rear wheels, m s is the vehicle mass, I sy is the pitch moment of inertia, I sx is the roll moment of inertia; G0 is the road roughness coefficient, u is the test vehicle speed, and f0 is the lower cutoff frequency.

[0034] Furthermore, in Step 1.3, filtered white noise is used as the front wheel simulated road input signal, and its time domain expression is as follows:

[0035]

[0036] where w f(t) is the Gaussian white noise in the front wheel road input model;

[0037] The preview time τ is related to the vehicle speed. The speed of the vehicle affects the control effect. The preview time τ is equal to the wheelbase / vehicle speed. The relationship between the road input of the front and rear wheels is expressed by the Laplace transfer function as shown in formula (7):

[0038]

[0039] In order to convert the frequency domain expression into the state space expression, the pade approximation method is used to find a low-order transfer function (8) to replace equation (7)

[0040]

[0041] Take the pade second-order approximation and use the road roughness information obtained by the sensors at the front and rear wheels as the state vector η f , η r , its state equation can be expressed as formula (9):

[0042]

[0043] In formula (10):

[0044] in,

[0045] Gaussian white noise w in the rear wheel road input model r (t) can be expressed as formula (10):

[0046] w r (t) = w f (t-τ)=η f (t)+w f (t) (10)

[0047] Filtered white noise is used as the input signal of the rear wheel simulated road surface, and its time domain expression is as shown in formula (11):

[0048]

[0049] Combining the vehicle motion differential equations (1)-(5) and the road input model, we can obtain the state space expression (12):

[0050]

[0051] Select the vehicle body vertical displacement, vehicle body pitch angle, vehicle body roll angle, four tire dynamic displacements, four road surface inputs, vehicle body vertical velocity, vehicle body pitch angle velocity, vehicle body roll velocity, four unsprung masses (four axles) vertical velocity and two state variables η f , ηr A total of 20 variables are used as the state changes of the system, namely:

[0052] A total of 11 variables, including the vehicle body vertical acceleration, vehicle body pitch angular acceleration, vehicle body roll angular acceleration, four suspension dynamic travels, and four tire dynamic displacements, are selected as the output variables of the system, namely:

[0053]

[0054] Choose from 4 damping adjustment forces F cuf1 ,F cuf2 ,F cur1 ,F cur2 As the component of the control vector U, that is: U=(F cuf1 ,F cuf2 ,F cur1 ,F cur2 ) T ;

[0055] Select the front wheel road surface input white noise w f (t) is the component of the disturbance vector W, that is: W = w f (t).

[0056] Furthermore, the specific steps in Step 2 are:

[0057] Step 2.1. Design a PID controller based on PID control theory.

[0058] Step 2.2, design the LQR controller according to the LQR control theory;

[0059] Step 2.3. Combine the PID controller and LQR controller into a PID-LQR composite controller.

[0060] Furthermore, in Step 2.1, PID control is error control, and the control object is the vertical acceleration of the vehicle body at the center of mass, with 0 as the given expected value; the PID control rule is as shown in formula (13):

[0061]

[0062] Furthermore, in Step 2.2

[0063] U LQR =-KX(t) (14)

[0064] The gain K is calculated from formula (15):

[0065] K=R d -1 B TP (15)

[0066] P is obtained from the following Riccati equation (16):

[0067] A T P+PA-PBR d -1 B T P+Q d =0 (16)

[0068] Given an optimal performance index function J for evaluating the output performance indicators, when J is minimum, calculate the optimal controller gain K and output the optimal control force U of the four actuators. LQR (t); The mathematical expression of the optimal performance index function J is the integral of the weighted square sum of each performance index, and the matrix form is as shown in formula (17):

[0069]

[0070] Where: Q d =C T QC; N d =C T QD;R d =R+D T QD

[0071] Q and R are expressed as: Q = diag (q1, q2, q3, q4, q5, q6, q7, q8, q9, q 10 ,q 11 ); R = diag(r1,r2,r3,r4)

[0072] Among them: q1 is the vertical acceleration weight at the center of mass of the seven-degree-of-freedom vehicle model, q2 is the pitch angle acceleration weight of the seven-degree-of-freedom vehicle model, q3 is the roll angle acceleration weight of the seven-degree-of-freedom vehicle model, q4, q5, q6, q7 are the weights of the four suspension dynamic strokes of the seven-degree-of-freedom vehicle model, q8, q9, q 10 ,q 11 are the weights of the dynamic displacements of the four wheels of the seven-degree-of-freedom vehicle model, and r1, r2, r3, and r4 are the weights of the control forces of the four actuators of the seven-degree-of-freedom vehicle model.

[0073] Furthermore, the specific steps in Step 3 are:

[0074] Step 3.1, use genetic algorithm to determine the optimal weight of performance indicators;

[0075] Step 3.2. Use MATLAB / PID Tuner to adjust the PID parameters.

[0076] Furthermore, in Step 3.1, the key to LQR control is to select appropriate weights, calculate matrices Q and R, and then calculate the optimal controller gain K;

[0077] The basic steps of genetic algorithm are: determine the population size, randomly assign values to optimization variables, calculate fitness values, and select crossover and mutation operations.

[0078] In Step 3.2, the tuning of the three PID parameters is the key to the entire controller design. The parameters of the PID controller are tuned with the help of MATLAB's PIDTuner toolbox.

[0079] The beneficial effects of the present invention are:

[0080] The established 7-DOF model is closer to the actual vehicle, allowing for a more comprehensive performance analysis of the 7-DOF vehicle model. This solution provides a semi-active suspension hybrid control strategy based on wheelbase preview to control the 7-DOF semi-active suspension. A PID-LQR controller is designed by combining PID control theory with LQR control theory. This optimizes the overall vehicle performance while further improving the rear end's performance. Although the pitch and roll accelerations, representing vehicle posture stability, deteriorate slightly, the overall vehicle ride comfort is significantly improved. Furthermore, a new method for tuning PID parameters using MATLAB / PID Tuner is proposed, which improves parameter tuning efficiency, is more reliable and convenient, and avoids the influence of subjective factors on the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0082] Figure 1 It is a vehicle dynamics model with 7-DOF semi-active suspension;

[0083] Figure 2 This is the principle diagram of the semi-active suspension wheelbase preview control;

[0084] Figure 3 Input model for random road surface of front wheels;

[0085] Figure 4 Input model for random road surfaces with preview information for rear wheels;

[0086] Figure 5 is the PID control model;

[0087] Figure 6 It is the LQR control model;

[0088] Figure 7 It is the PID-LQR control model;

[0089] Figure 8 is the dynamic response characteristic curve of the semi-active suspension PID control system;

[0090] Figure 9 is the fitness curve and optimal variable value of the semi-active suspension PID-LQR control system based on the preview strategy;

[0091] Figure 10 is the time domain curve of vehicle body vertical acceleration;

[0092] Figure 11 is the time domain curve of vehicle body pitch angle acceleration;

[0093] Figure 12 is the time domain curve of vehicle body roll angle acceleration;

[0094] Figure 13 is the time domain curve of the right front suspension travel;

[0095] Figure 14 is the time domain curve of the right rear suspension travel;

[0096] Figure 15 is the time domain curve of the right front tire dynamic displacement;

[0097] Figure 16 is the time domain curve of the right rear tire displacement;

[0098] Figure 17 is the power spectrum density curve of vehicle body vertical acceleration;

[0099] Figure 18 is the power spectrum density curve of vehicle body pitch angle acceleration;

[0100] Figure 19 is the power spectrum density curve of the right front suspension dynamic stroke;

[0101] Figure 20 is the power spectrum density curve of the right rear suspension dynamic stroke;

[0102] Figure 21 is the power spectrum density curve of the right front tire dynamic displacement;

[0103] Figure 22 is the power spectrum density curve of the right rear tire displacement;

[0104] Figure 23 Output force for the right front and right rear suspension actuators of the vehicle;

[0105] Figure 24Output force for the vehicle's left front and left rear suspension actuators;

[0106] Figure 25 Output force for the right front and left front suspension actuators of the vehicle;

[0107] Figure 26 Output force for the right and left rear suspension actuators of the vehicle. DETAILED DESCRIPTION

[0108] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0109] Example 1

[0110] 1. Vehicle ride comfort analysis under random road conditions

[0111] Table 1. Vehicle model parameter values

[0112]

[0113] 2. Preview control principle: Sensors located at the front and rear of the vehicle collect state variables of the vehicle control system: vertical displacement of the vehicle body, pitch angle of the vehicle body, vertical displacement of the four axles, road surface unevenness displacement of the four wheels, etc. The sensors then feed these variables back to the controller. When the controller issues instructions to the front wheel suspension actuator, it only performs feedback control based on the feedback information from the front of the vehicle. When issuing instructions to the rear wheel actuator, it considers the state variable information sent back by the rear wheel sensor and adopts the feedback information from the front of the vehicle based on the vehicle speed and wheelbase, performing feedforward and feedback control. Figure 2 shown

[0114] 3. Design a PID-LQR controller to determine the control instructions for the front and rear wheel actuators. The front wheel adopts feedback control, and the rear wheel adopts feedforward plus feedback control with preview information. The PID-LQR controller design scheme is as follows: Figure 3-Figure 5 .

[0115] 4. Use MATLAB / PID Tuner to tune the PID parameters, and use MATLAB / Genetic Algorithm Toolbox to optimize the performance index weight coefficient. The population size is initially determined to be 100, the number of generations is 30, the crossover probability is set to 0.4, the mutation probability is set to 0.2, and the search range is set to [0.11e6]. The PID tuning results are as follows: Figure 8 and Table 2.

[0116] Table 2 Parameter setting values of rise time, adjustment time, overshoot, etc. of the semi-active suspension PID-LQR control system based on preview

[0117] P 0 Adjustment time 0.802s I 3200.0612 Maximum overshoot <![CDATA[4.78×10 7 %]]> D 0 Peak 0.488 Rise time <![CDATA[1.04×10- 7 s]]> Steady-state error 0.0012

[0118] The performance index weight optimization curve is as follows Figure 9 After 30 generations of iterative optimization, the weights of 15 performance indicators and the optimal controller gain K are as follows:

[0119] q1=0.5377, q2=811580, q3=681980, q4=422890, q5=0.3188, q6=949310, q7=648200, q8=72886,

[0120] q9=4.5784,q 10 =505640,q 11 =886550, r1=1.5349, r2=1.7254, r3=0.5001, r4=0.2147

[0121]

[0122] 5. Use Simulink to build a simulation model, input the vehicle model parameter values into the model, and add a passive suspension for comparison. Set the vehicle speed to 72km / h, the road type to branch road, and the road roughness coefficient value range under this road condition is 5×10 -7 ~3×10 -5 , take the mean value 5×10 -6 The vehicle body motions in two degrees of freedom, pitch and roll, are generated during driving, and the road inputs at the four wheels of the vehicle are independent of each other; the simulation step size is set to 0.05, and the simulation time is set to 10s.

[0123] 6. Results Analysis

[0124] 6.1 After adopting the PID-LQR-preview composite control strategy, the time domain curves and power spectrum density curves of various performance indicators are as follows: Figure 10-Figure 22 The RMS values of various performance indicators are shown in Table 2.

[0125] Table 3, RMS values of various performance indicators of the seven-degree-of-freedom model at a speed of 72 km / h

[0126]

[0127]

[0128] Table 3 shows that after adopting the PID-LQR-preview composite control, the vehicle smoothness indicators have been comprehensively improved, but the body posture stability indicators pitch angle acceleration and roll angle acceleration have slightly deteriorated.

[0129] 6.2 After adopting PID-LQR-preview compound control, the control force output by the four actuators is as follows Figure 23-26 The maximum control force output by the four actuators is shown in Table 3:

[0130] Table 4. Maximum control forces of the four suspension controllers for the seven-degree-of-freedom vehicle model

[0131]

[0132] From Table 4 and Figure 23-26 The control forces output by the four actuators are uneven, resulting in a mismatch between the front and rear pitch moments and the left and right roll moments. This results in a slight deterioration in pitch and roll acceleration, but it remains within a reasonable range. This also illustrates the difficulty in balancing ride comfort and vehicle stability when using active control suspension. The PID-LQR-preview composite control strategy slightly sacrifices some vehicle posture stability, but significantly improves ride comfort.

[0133] Example 2

[0134] As can be seen from equation (7), the preview time has a significant impact on the control effect of the system. The preview time is related to the vehicle speed. When the vehicle is traveling at a low speed, the rear wheels have enough time to receive the preview information from the front wheels, and the rear suspension actuator has sufficient time to execute the action in advance. When the vehicle is traveling at a high speed, the preview time becomes shorter, and the preview information received by the controller will be delayed. The amount of information received will decrease, resulting in a poor control effect. To verify this conclusion, the vehicle speed is changed and the output vehicle performance indicators are analyzed. The specific implementation is as follows: In Example 1, the vehicle model parameters are unchanged. The road conditions have no significant impact on the present invention and do not need to be verified. Therefore, the road grade is unchanged. The vehicle speed is divided into three levels: low speed, medium speed, and high speed. The simulation experiment is carried out at low speed u = 36 km / h, medium speed u = 72 km / h, and high speed u = 108 km / h. The various vehicle performance indicators in Example 1 are output respectively.

[0135] Table 5, RMS values of various performance indicators of the seven-degree-of-freedom model at a speed of 36 km / h

[0136]

[0137] Table 6. RMS values of various performance indicators of the seven-degree-of-freedom model at a vehicle speed of 108 km / h.

[0138]

[0139] It can be seen from Table 3, Table 5 and Table 6 that when the vehicle speed changes, the root mean square values of various performance indicators of the whole vehicle are changed. When the vehicle is traveling at a low speed, the semi-active suspension PID-LQR control method based on the preview strategy optimizes various performance indicators of the whole vehicle, and the body pitch and roll motion deteriorate less. When the vehicle is traveling at a high speed, under the semi-active suspension PID-LQR control method based on the preview strategy, the dynamic displacement of the tires of the whole vehicle is not optimized but deteriorated, and the body pitch motion deteriorates more seriously. Comparing the low-speed, medium-speed and high-speed driving conditions, it is verified that the vehicle speed has a great influence on the control effect of the preview control strategy. Based on the conclusion, it can be seen that the control method of the present invention has a better control effect under the vehicle low-speed driving condition. When the vehicle is traveling at a high speed, the delay problem of the preview information needs to be solved.

Claims

1. A semi-active suspension PID and LQR composite control method, characterized in that: The following steps are involved: Step 1: Establish a 7-DOF vehicle dynamics model and a preview control road model, as follows: Step 1.

1. Establish a 7-DOF vehicle dynamics model based on Newton's laws of motion; Step 1.2: Determine the control strategies for the front and rear wheels based on preview control theory. For the front wheels, only feedback control is used, while for the rear wheels, feedforward plus feedback control with preview information is used. Step 1.3: Based on the front and rear wheel control strategies, establish the road surface input models for the four wheels. The front wheel uses a random road surface simulation model as input, while the rear wheel uses a road surface simulation model with front wheel preview information as input. Step 2: Design a PID-LQR composite controller; Step 3. Determine the weight coefficients of each performance index of LQR control and adjust the P, I, and D parameters as follows: Step 3.1, use genetic algorithm to determine the optimal weight of performance indicators; Step 3.2, use MATLAB / PID Tuner to adjust PID parameters; Step 4. Use Simulink to build a simulation experiment model, set the experimental conditions, and run the simulation.

2. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: In Step 1.1, the vehicle body vertical acceleration, suspension dynamic travel, and tire dynamic displacement are used as performance indicators for evaluating vehicle ride comfort, and the pitch angular acceleration and roll angular acceleration are added as two evaluation indicators that affect vehicle posture stability; The 7 degrees of freedom include the vertical degrees of freedom at the four axles, the vertical degrees of freedom at the four tires, the pitch and roll degrees of freedom around the X and Y axes at the center of mass of the vehicle body, and the vertical degree of freedom along the Z axis.

3. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: In Step 1.1, the force analysis of the 7 degrees of freedom can be performed according to Newton's laws of mechanics to list the 7-degree-of-freedom motion differential equations: The vertical force balance equation of the Z axis at the center of mass of the vehicle body is as follows (1): The balance equation of the rotation moment of the vehicle body around the Y axis is as follows: The balance equation of the rotation moment of the vehicle body around the X-axis is as follows: The vertical force balance equation of the four unsprung masses along the Z axis is as follows: When the range of the vehicle body pitch angle and roll angle is small enough, the displacement of the end points of the suspended mass above the four wheels can be expressed as follows: from sf1 =from s -L r θ-aφ from sf2 =from s -L l θ-aφ With sr1 =z s -L r θ+bφ With sr2 =z s +L l θ+bφ (5) In formula (1) to formula (5), z s is the vertical displacement of the vehicle's center of mass, is the body's rotation angle around the Y axis (pitch angle), θ is the body's rotation angle around the X axis (roll angle); m wf1 ,m wf2 ,m wr1 ,m wr2 Represent the unsprung masses of the right front, left front, left rear and right rear respectively; k wf1 ,k wf2 ,k wr1 ,k wr2 are the four tire stiffness coefficients respectively; k sf1 ,k sf2 ,k sr1 ,k sr2 are the four suspension stiffness coefficients respectively; c sf1 ,c sf2 ,c sr1 ,c sr2 are the four suspension damping coefficients respectively; q f1 ,q f2 ,q r1 ,q r2 are the displacements of the road surface roughness of the four wheels; z wf1 ,z wf2 ,z wr1 ,z wr2 are the vertical displacements at the four axles; z sf1 ,z sf2 ,z sr1 ,z sr2 are the vertical displacements of the suspended masses above the four wheels; a and b are the distances from the center of mass of the vehicle to the front and rear axes, respectively; L l ,L r The distances from the center of mass of the vehicle to the centerline of the left and rear wheels, m s is the vehicle mass, I sy is the pitch moment of inertia, I sx is the roll moment of inertia; G0 is the road roughness coefficient, u is the test vehicle speed, and f0 is the lower cutoff frequency.

4. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: In Step 1.3, filtered white noise is used as the front wheel simulated road input signal, and its time domain expression is as follows: where w f (t) is the Gaussian white noise in the front wheel road input model; The preview time τ is related to the vehicle speed. The speed of the vehicle affects the control effect. The preview time τ is equal to the wheelbase / vehicle speed. The relationship between the road input of the front and rear wheels is expressed by the Laplace transfer function as shown in formula (7): In order to convert the frequency domain expression into the state space expression, the pade approximation method is used to find a low-order transfer function (8) to replace equation (7) Take the pade second-order approximation and use the road roughness information obtained by the sensors at the front and rear wheels as the state vector η f , η r , its state equation can be expressed as formula (9): In formula (10): in, Gaussian white noise w in the rear wheel road input model r (t) can be expressed as formula (10): w r (t)=w f (t-τ)=η f (t)+w f (t) (10) Filtered white noise is used as the input signal of the rear wheel simulated road surface, and its time domain expression is as shown in formula (11): Combining the vehicle motion differential equations (1)-(5) and the road input model, we can obtain the state space expression (12): Select the vehicle body vertical displacement, vehicle body pitch angle, vehicle body roll angle, four tire dynamic displacements, four road surface inputs, vehicle body vertical velocity, vehicle body pitch angle velocity, vehicle body roll velocity, four unsprung masses (four axles) vertical velocity and two state variables η f , η r A total of 20 variables are used as the state changes of the system, namely: A total of 11 variables, including the vehicle body vertical acceleration, vehicle body pitch angular acceleration, vehicle body roll angular acceleration, four suspension dynamic travels, and four tire dynamic displacements, are selected as the output variables of the system, namely: Choose from 4 damping adjustment forces F cuf1 ,F cuf2 ,F cur1 ,F cur2 As the component of the control vector U, that is: U=(F cuf1 ,F cuf2 ,F cur1 ,F cur2 ) T ; Select the front wheel road surface input white noise w f (t) is the component of the disturbance vector W, that is: W = w f (t).

5. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: The specific steps in Step 2 are: Step 2.

1. Design a PID controller based on PID control theory. Step 2.2, design the LQR controller according to the LQR control theory; Step 2.

3. Combine the PID controller and LQR controller into a PID-LQR composite controller.

6. The semi-active suspension PID and LQR composite control method according to claim 5, characterized in that: In Step 2.1, PID control is error control, and the control object is the vertical acceleration of the vehicle body at the center of mass, with 0 as the given expected value; the PID control rule is as shown in formula (13): 。 7. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: In Step 2.2 U LQR ＝- KX (t) (14) The gain K is calculated from formula (15): K=R d -1 B T P (15) P is obtained from the following Riccati equation (16): A T P+PA-PBR d -1 B T P+Q d =0 (16) Given an optimal performance index function J for evaluating the output performance indicators, when J is minimum, calculate the optimal controller gain K and output the optimal control force U of the four actuators. LQR (t); The mathematical expression of the optimal performance index function J is the integral of the weighted square sum of each performance index, and the matrix form is as shown in formula (17): Where: Q d = C T QC; N d = C T QD; R d = R + D T QD Q and R are expressed as: Q = diag (q1, q2, q3, q4, q5, q6, q7, q8, q9, q 10 ,q 11 ); R = diag(r1,r2,r3,r4) Among them: q1 is the vertical acceleration weight at the center of mass of the seven-degree-of-freedom vehicle model, q2 is the pitch angle acceleration weight of the seven-degree-of-freedom vehicle model, q3 is the roll angle acceleration weight of the seven-degree-of-freedom vehicle model, q4, q5, q6, q7 are the weights of the four suspension dynamic strokes of the seven-degree-of-freedom vehicle model, q8, q9, q 10 ,q 11 are the weights of the dynamic displacements of the four wheels of the seven-degree-of-freedom vehicle model, and r1, r2, r3, and r4 are the weights of the control forces of the four actuators of the seven-degree-of-freedom vehicle model.

8. The semi-active suspension PID and LQR composite control method according to claim 1, characterized in that: In Step 3.1, the key to LQR control is to select appropriate weights, calculate matrices Q and R, and then calculate the optimal controller gain K; The basic steps of genetic algorithm are: determine the population size, randomly assign values to optimization variables, calculate fitness values, and select crossover and mutation operations; In Step 3.2, the tuning of the three PID parameters is the key to the entire controller design. The parameters of the PID controller are tuned with the help of MATLAB's PIDTuner toolbox.

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