CN116373524B - A PID and LQR composite control method for semi-active suspension - Google Patents

Abstract

The invention discloses a semi-active suspension PID and LQR composite control method, namely a PID-LQR composite control strategy is adopted, the overall vehicle running smoothness index and the vehicle body posture stability index are optimized, namely the vehicle body vertical acceleration, the suspension dynamic travel, the tire dynamic load, the pitch angle acceleration and the roll angle acceleration are optimized, and a PID-LQR controller is designed according to PID control, pre-aiming control and LQR control theory, and an actuator is four suspension actuators. A method for setting PID parameter value is provided, namely MATLAB/PIDTuner is utilized to set PID parameter, and genetic algorithm is utilized to find out optimal weight of each performance index of the system. The 7-degree-of-freedom model established by the invention can more comprehensively analyze the performance of the whole vehicle, is more similar to a real vehicle, can obtain various performance indexes of the vehicle under different test working conditions by establishing different grades of road surface models to change the experimental scene, and can more comprehensively analyze the performance of the whole vehicle.

Description

Semi-active suspension PID and LQR composite control method

Technical Field

The invention belongs to the technical field of semi-active suspension control systems, and particularly relates to a semi-active suspension PID and LQR composite control method.

Background

The suspension is a force buffer device for connecting the chassis and the vehicle body, and has the functions of reducing vibration impact transmitted to the vehicle body by road surface excitation, improving riding experience of passengers in the vehicle body and driving experience of a driver, so that the suspension plays a vital role in comfort of the vehicle body, smoothness of running, and stability of the posture and operation of the vehicle body.

The air suspension and the full-active suspension which are changeable in rigidity and damping are better in working performance than semi-active suspensions, and the comprehensive performance of a vehicle can be remarkably improved, but the air suspension is complex in structure and high in manufacturing cost, and because the air suspension uses air as a working medium, air is frequently required to be flushed and deflated in the running process of an automobile, an air valve is high in temperature and high in failure rate, the service life of an air suspension system is short, the semi-active suspension is not as good as the above two types of suspensions in working performance, but the advantages are obvious compared with the traditional passive suspension, and the semi-active suspension is simple in structure, low in cost, reliable in working and long in service life, is more suitable for middle-low end vehicles, has a great market application prospect, can be gradually popularized, becomes a main stream of markets by replacing the traditional passive suspension, and is very necessary to conduct deep research on the semi-active suspension.

The research of the semi-active suspension system mainly expands from two aspects of structure and controller design, the structure mainly researches electrorheological or magnetorheological technology of the semi-active suspension, namely, the research is conducted from a method for changing damping coefficients, the controller design mainly researches control strategies, at present, a plurality of control methods such as ceiling damping control, ground damping control, optimal control, fuzzy control, variable structure synovial membrane control and the like are put forward for the semi-active suspension controller by students, although the control methods are different in control theory, the control effect is not very different, the control effect is limited by adopting one control method, the comprehensive performance index of the whole vehicle is difficult to comprehensively optimize at the same time, and if the semi-active suspension is controlled by adopting a plurality of control theory, the control methods can complement each other, each evaluation index can be optimized to the greatest extent, and the performance of the whole vehicle is improved.

The determination of the control system parameter value by utilizing the PID control theory and the LQR control theory to design the semi-active suspension is the core work of the invention, the control parameter plays a very important role in the control effect of the control system, the control parameter can influence the stability and the sensitivity of the control system, the parameter values required to be set in the control system of the invention are P, I and D parameters and the optimal weight of each performance index, and many researchers adjust the parameters by adopting an empirical test method.

Therefore, in order to solve the above-mentioned problems, a semi-active suspension PID and LQR composite control method is proposed herein.

Disclosure of Invention

In order to solve the technical problems, the invention designs a semi-active suspension PID and LQR composite control method, and designs a semi-active suspension PID-LQR controller by adopting PID control and LQR control, and in order to continuously improve the control effect, a pre-aiming control strategy with front wheel feedback is added, pre-aiming information is provided for the rear wheel in advance, the controller sends control instructions to the rear wheel in advance, and an actuator acts in advance when the actuator is about to pass through a front road surface, and pre-control force is output.

In order to achieve the technical effects, the invention is realized by the following technical scheme that the semi-active suspension PID and LQR composite control method is characterized by comprising the following steps:

Step1, establishing a 7-degree-of-freedom vehicle dynamics model and a pre-aiming control pavement model;

Step2, designing a PID-LQR composite controller;

step3, determining the weight coefficient of each performance index of LQR control, and setting P, I, D parameters;

step4, building a simulation experiment model by using Simulink, setting experiment working conditions and running simulation.

Further, the specific steps in Step1 are as follows:

Step1.1, establishing a 7-degree-of-freedom vehicle dynamics model according to Newton's law of motion;

step1.2, determining a front wheel control strategy and a rear wheel control strategy according to a pretightening control theory, wherein only feedback control is adopted for the front wheel, and feedforward and feedback control with pretightening information is adopted for the rear wheel;

Step1.3, according to the control strategy of the front wheels and the rear wheels, building a road surface input model at four wheels, wherein the front wheels adopt a random road surface simulation model as input, and the rear wheels adopt a road surface simulation model with pre-aiming information of the front wheels as input.

Further, in step1.1, the vertical acceleration of the vehicle body, the dynamic travel of the suspension and the dynamic displacement of the tire are taken as performance indexes for evaluating the smoothness of the vehicle, and two evaluation indexes of pitch angle acceleration and roll angle acceleration, which influence the stability of the posture of the vehicle body, are added;

the 7 degrees of freedom include four degrees of vertical freedom at the axle, four degrees of vertical freedom at the tires, pitch and roll degrees of freedom at the body center of mass that rotates about the X-axis, Y-axis, and Z-axis vertical degrees of freedom.

Further, in step1.1, the force analysis of 7 degrees of freedom according to newton's law of mechanics may list a differential equation of motion of 7 degrees of freedom:

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

The torque balance equation of the rotation of the vehicle body around the Y axis is as follows (2):

The torque balance equation of the rotation of the vehicle body around the X axis is as follows (3):

The Z-axis vertical force balance equation of the 4 unsprung masses is as follows (4):

When the vehicle body pitch angle and roll angle variation ranges are sufficiently small, the displacement of the suspension mass end points above the four wheels may be represented as in formula (5):

z_sf1＝z_s-L_rθ-aφ

z_sf2＝z_s-L_lθ-aφ

z_sr1＝z_s-L_rθ+bφ

z_sr2＝z_s+L_lθ+bφ (5)

in the formulas (1) - (5), z_s is the vertical displacement of the centroid of the vehicle,The steering angle (pitch angle) of the vehicle body around the Y-axis direction is theta, the steering angle (roll angle) of the vehicle body around the X-axis direction is theta, m_wf1,m_wf2,m_wr1,m_wr2 is the non-sprung mass of the right front part, the left rear part and the right rear part respectively, k_wf1,k_wf2,k_wr1,k_wr2 is the four tire stiffness coefficients respectively, k_sf1,k_sf2,k_sr1,k_sr2 is the four suspension stiffness coefficients respectively, c_sf1,c_sf2,c_sr1,c_sr2 is the four suspension damping coefficients respectively, q_f1,q_f2,q_r1,q_r2 is the displacement of the road surface unevenness of four wheels respectively, z_wf1,z_wf2,z_wr1,z_wr2 is the vertical displacement at four axles respectively, z_sf1,z_sf2,z_sr1,z_sr2 is the vertical displacement of the suspension mass above four wheels respectively, a and b are the distances of the mass center of the vehicle from the front axis and the rear axis respectively, L_l,L_r is the distance of the mass center of the vehicle from the center line of the left wheel and the rear wheel respectively, m_s is the mass of the whole vehicle, I_sy is the pitch moment of inertia, I_sx is the roll moment of inertia, G₀ is the road surface unevenness coefficient, u is the experiment vehicle speed, and f₀ is the frequency of the cut-down.

Furthermore, in step1.3, the filtered white noise is used as the front-wheel simulation road surface input signal, and the time domain expression is as follows:

wherein w_f (t) is Gaussian white noise in the front wheel pavement input model;

the pretightening time tau is related to the vehicle speed, the speed of the vehicle influences the control effect, the pretightening time tau is equal to the wheelbase/vehicle speed, and the road surface input relation of the front wheel and the rear wheel is expressed as a Laplacian transfer function as shown in the formula (7):

To convert the frequency domain expression to a state space expression, a low order transfer function (8) is found to replace expression (7) using pade approximation

Taking pade second-order approximation, taking road surface unevenness information obtained by sensors at front and rear wheels as a state vector eta_f,η_r, and the state equation can be expressed as formula (9):

in the formula (10):

Wherein, the

The gaussian white noise w_r (t) in the rear wheel road surface input model can be expressed as formula (10):

w_r(t)＝w_f(t-τ)＝η_f(t)+w_f(t) (10)

The filtered white noise is used as the input signal of the simulation road surface of the rear wheel, and the time domain expression is as shown in the formula (11):

combining the vehicle motion differential equations (1) - (5) and combining the road surface input model to obtain a state space expression (12):

The method comprises the steps of selecting 20 variables in total of vertical displacement of a vehicle body, pitch angle of the vehicle body, roll angle of the vehicle body, dynamic displacement of 4 tires, input of 4 road surfaces, vertical speed of the vehicle body, pitch angle speed of the vehicle body, roll speed of the vehicle body, vertical speed of 4 unsprung masses (4 axles) and two state variables eta_f,η_r as state variable quantities of a system, namely:

11 quantities of vertical acceleration, pitch angle acceleration, roll angle acceleration, 4 suspension dynamic strokes and 4 tire dynamic displacements of the vehicle body are selected as output variables of the system, namely:

4 damping adjustment forces F_cuf1,F_cuf2,F_cur1,F_cur2 are selected as components of the control vector U, i.e., u= (F_cuf1,F_cuf2,F_cur1,F_cur2)^T;

The front wheel road surface input white noise W_f (t) is selected as a component of the disturbance vector W, i.e., w=w_f (t).

Further, the Step2 specifically includes the steps of:

Step2.1, designing a PID controller according to a PID control theory;

Step2.2, designing an LQR controller according to an LQR control theory;

step2.3, combining the PID controller and the LQR controller into a PID-LQR composite controller.

Further, in step2.1, the PID control is an error control, the control object is a vertical acceleration of the vehicle body at the center of mass of the vehicle, 0 is taken as a given expected value, and the PID control law is as shown in formula (13):

Further, in said Step2.2

U_LQR=-KX(t) (14)

The gain K is obtained by the equation (15):

K=R_d^-1B^TP (15)

p is determined from the following Richti equation (16):

A^TP+PA-PBR_d^-1B^TP+Q_d=0 (16)

Giving an optimal performance index function J for evaluating various output performance indexes, calculating an optimal gain K of the controller when J is minimum, and outputting four optimal actuator control forces U_LQR (t), wherein the mathematical expression of the optimal performance index function J is the integral of weighted square sums of various performance indexes, and the matrix form is shown as the formula (17):

in which Q_d＝C^TQC;N_d＝C^TQD;R_d＝R+D^T QDs

Q and R are each represented by ：Q＝diag(q₁,q₂,q₃,q₄,q₅,q₆,q₇,q₈,q₉,q₁₀,q₁₁);R＝diag(r₁,r₂,r₃,r₄)

Wherein q₁ is a vertical acceleration weight at the mass center of the vehicle body of the seven-degree-of-freedom vehicle model, q₂ is a pitch angle acceleration weight of the seven-degree-of-freedom vehicle model, q₃ is a roll angle acceleration weight of the seven-degree-of-freedom vehicle model, q₄,q₅,q₆,q₇ is a four-suspension dynamic travel weight of the seven-degree-of-freedom vehicle model, q₈,q₉,q₁₀,q₁₁ is a four-wheel dynamic displacement weight of the seven-degree-of-freedom vehicle model, and r₁,r₂,r₃,r₄ is a four-actuator control force weight of the seven-degree-of-freedom vehicle model.

Further, the Step3 specifically includes the steps of:

Step3.1, determining the optimal weight of the performance index by utilizing a genetic algorithm;

step3.2, tuning the PID parameters using MATLAB/PID Tuner.

Further, in step3.1, the key of LQR control is to select a proper weight, calculate matrices Q and R, and then calculate an optimal controller gain K;

the genetic algorithm comprises the basic steps of determining population scale, randomly assigning values to optimization variables, calculating fitness values and selecting cross mutation operation.

In step3.2, the tuning of the three parameters of PID is the key of the design of the whole controller, and the parameters of the PID controller are tuned by means of the PID Tuner tool box of MATLAB.

The beneficial effects of the invention are as follows:

The built 7-degree-of-freedom model is closer to a real vehicle, performance analysis is more comprehensive on the 7-degree-of-freedom vehicle model, the scheme provides a semi-active suspension composite control strategy based on wheelbase pre-aiming to control the 7-degree-of-freedom semi-active suspension, a PID-LQR controller is designed by combining a PID control theory and an LQR control theory, the comprehensive performance index of the whole vehicle is optimized, the working performance of the rear part of the vehicle body is further improved, and although the pitch angle acceleration and the side inclination angle acceleration representing the stability of the vehicle body are slightly deteriorated, the running smoothness of the whole vehicle is greatly improved. Meanwhile, a new method for adjusting the PID parameters by utilizing the MATLAB/PID Tuner is provided, so that the parameter adjusting efficiency is improved, the method is more reliable and convenient, and the influence of artificial subjective factors on a control system is avoided.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a 7 degree of freedom semi-active suspension whole vehicle dynamics model;

FIG. 2 is a schematic diagram of semi-active suspension wheelbase pretightening control;

FIG. 3 is a front wheel random road surface input model;

FIG. 4 is a rear wheel random road surface input model with pre-sighting information;

FIG. 5 is a PID control model;

FIG. 6 is an LQR control model;

FIG. 7 is a PID-LQR control model;

FIG. 8 is a graph of the dynamic response characteristics of a semi-active suspension PID control system;

FIG. 9 is a graph of fitness curves and optimal variable values of a semi-active suspension PID-LQR control system based on a pre-targeting strategy;

FIG. 10 is a time domain plot of vehicle body vertical acceleration;

FIG. 11 is a vehicle body pitch angle acceleration time domain plot;

FIG. 12 is a vehicle body roll angle acceleration time domain plot;

FIG. 13 is a time domain plot of the motion travel of the front right suspension;

FIG. 14 is a time domain plot of the dynamic range of the rear right suspension;

FIG. 15 is a graph of the dynamic displacement time domain of the front right tire;

FIG. 16 is a graph of the dynamic displacement time domain of the rear right tire;

FIG. 17 is a graph of vehicle body vertical acceleration power spectral density;

FIG. 18 is a plot of vehicle body pitch angle acceleration power spectral density;

FIG. 19 is a graph of power spectral density for the dynamic range of the front right suspension;

FIG. 20 is a graph of power spectral density for the dynamic range of the rear right suspension;

FIG. 21 is a graph of power spectral density for the dynamic displacement of the front right tire;

FIG. 22 is a graph of power spectral density for dynamic displacement of a rear right tire;

FIG. 23 is a front right and rear right suspension actuator output force of the vehicle;

FIG. 24 is a front left and rear left suspension actuator output force of the vehicle;

FIG. 25 is a front right and left vehicle suspension actuator output force;

FIG. 26 is a graph showing the output force of the rear right and left suspension actuators of the vehicle.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Example 1

1. Vehicle ride comfort analysis under random road surface working condition

TABLE 1 vehicle model parameter values

2. The pre-aiming control principle is that the sensors at the front and rear of the vehicle collect the state variables of the control system of the vehicle, such as vertical displacement of the vehicle body, pitch angle of the vehicle body, vertical displacement of four axles, uneven displacement of the road surface of four wheels, etc., and then the sensors feed back the variables to the controller, and the controller gives an instruction to the front wheel suspension actuator to perform feedback control according to the feedback information of the front part of the vehicle, and gives an instruction to the rear wheel actuator to take the state variable information sent back by the rear wheel sensor into consideration, and adopts the feedback information of the front part of the vehicle according to the speed and the wheelbase to perform feedforward and feedback control, as shown in figure 2

3. And (3) designing a PID-LQR controller, determining control instructions of actuators of a front wheel and a rear wheel, wherein the front wheel adopts feedback control, the rear wheel adopts feedforward and feedback control with pre-aiming information, and the design scheme of the PID-LQR controller is shown in figures 3-5.

4. And (3) setting the PID parameters by utilizing a MATLAB/PID Tuner, and optimizing the performance index weight coefficient by utilizing a MATLAB/genetic algorithm tool box, wherein the population scale is preliminarily determined to be 100, the genetic algebra is 30 generations, the crossover probability is set to be 0.4, the mutation probability is set to be 0.2, the search range is set to be [0.11e6], and the PID setting results are shown in fig. 8 and table 2.

TABLE 2 parameter settings such as rise time, adjustment time, overshoot, etc. of a semi-active suspension PID-LQR control system based on pre-aiming

P	0	Adjusting the time	0.802s
				I	3200.0612	Maximum overshoot	4.78×107%
D	0	Peak value	0.488
				Rise time	1.04×10-7s	Steady state error	0.0012

The performance index weight optimization curve is shown in fig. 9, and after 30 generations of iterative optimization, 15 performance index weights and the optimal controller gain K are as follows:

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

q₉＝4.5784,q₁₀＝505640,q₁₁＝886550,r₁＝1.5349,r₂＝1.7254,r₃＝0.5001,r₄＝0.2147

5. And constructing a simulation experiment model by using Simulink, inputting the parameter values of the vehicle model into the model, and adding a passive suspension for comparison. Setting the speed of an automobile to be 72km/h, setting the road surface type to be a branch road, setting the value range of the road surface unevenness coefficient under the road condition to be 5 multiplied by 10^-7～3×10^-5, and taking the average value to be 5 multiplied by 10^-6. When the automobile runs, the automobile body moves from two degrees of freedom of pitching and rolling, road surface inputs at four wheels of the automobile are not related to each other, the simulation step length is set to be 0.05, and the simulation time is set to be 10s.

6. Analysis of results

6.1 After PID-LQR-pretightening composite control strategy is adopted, the time domain curve and the power spectrum density curve of each performance index are shown in figures 10-22, and the average root value of each obtained performance index is shown in table 2

Table 3, average root value of each performance index of seven-degree-of-freedom model at 72km/h speed

Table 3 shows that the vehicle smoothness index is improved comprehensively after PID-LQR-pretightening compound control is adopted, but the pitch angle acceleration and the roll angle acceleration of the vehicle body posture stability index are slightly deteriorated.

6.2 After PID-LQR-pretightening compound control is adopted, the control forces output by the four actuators are shown in figures 23-26. The maximum control force output by the four actuators is shown in table 3:

TABLE 4 seven degrees of freedom full vehicle model four suspension controller control force maximum

It can be seen from table 4 and fig. 23 to 26 that the control forces output from the four actuators are unbalanced, and the front-rear pitch moment and the left-right roll moment are not balanced, so that the pitch angle acceleration and the roll angle acceleration are deteriorated, but are also in a reasonable range, which also shows that after the active control of the suspension is adopted, the smoothness and the vehicle body stability are difficult to be simultaneously considered. The PID-LQR-pretightening composite control strategy slightly sacrifices a certain vehicle body attitude stability, but greatly improves the smoothness of the vehicle.

Example 2

As can be seen from the formula (7), the pre-aiming time has a great influence on the control effect of the system, the pre-aiming time is related to the vehicle speed, when the vehicle runs at a low speed, the rear wheels have enough time to receive the pre-aiming information from the front wheels, the rear suspension actuators have enough time to perform the execution action in advance, when the vehicle runs at a high speed, the pre-aiming time is reduced, the pre-aiming information received by the controller is delayed, the received information amount is reduced, and the control effect is deteriorated. In order to verify the conclusion, the vehicle speed is changed, and the output vehicle performance index is analyzed, and the method is specifically implemented in that the parameters of the vehicle model in the embodiment 1 are not changed, the road surface condition has no great influence on the invention, and the vehicle is not required to be verified, so that the road surface grade is not changed, the vehicle speed is divided into three steps of low speed, medium speed and high speed, the simulation experiment is carried out at the low speed of u=36 km/h, the simulation experiment is carried out at the medium speed of u=72 km/h, the simulation experiment is carried out at the high speed of u=108 km/h, and each performance index of the vehicle in the embodiment 1 is respectively output.

Table 5, root values of each performance index of the seven-degree-of-freedom model at 36km/h of vehicle speed

Table 6, root values of each performance index of the seven-degree-of-freedom model are obtained at 108km/h of vehicle speed.

As can be seen from tables 3, 5 and 6, when the vehicle speed is changed, all the root values of all the performance index sides of the whole vehicle are changed, and when the vehicle runs at a low speed, all the performance index sides of the whole vehicle are optimized by a semi-active suspension PID-LQR control mode based on a pre-aiming strategy, and the deterioration of pitching and rolling motion of the vehicle body is small. When the vehicle runs at a high speed, the dynamic displacement of the whole vehicle tire is not optimized but rather is deteriorated under the semi-active suspension PID-LQR control mode based on the pre-aiming strategy, and the pitching motion of the vehicle body is seriously deteriorated. And compared with the working conditions of low-speed, medium-speed and high-speed driving, the control effect of the pre-aiming control strategy is verified to have larger influence on the speed of the vehicle. Based on conclusion, the control method of the invention has better control effect under the low-speed running condition of the vehicle, and when the vehicle runs at high speed, the problem of delay of pre-aiming information needs to be solved.

Claims (8)

Translated fromChinese

1.一种半主动悬架PID与LQR复合控制方法，其特征在于，包括以下步骤：1. A semi-active suspension PID and LQR composite control method, characterized by comprising the following steps:Step1、建立7自由度车辆动力学模型和预瞄控制路面模型，具体如下：Step 1: Establish a 7-DOF vehicle dynamics model and a preview control road model, as follows:Step1.1、根据牛顿运动定律建立7自由度车辆动力学模型；Step 1.1. Establish a 7-DOF vehicle dynamics model based on Newton's laws of motion;Step1.2、根据预瞄控制理论，确定前轮和后轮控制策略，对前轮仅采用反馈控制，对后轮采用带有预瞄信息的前馈加反馈控制；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.Step1.3、根据前后轮控制策略，建立四个车轮处路面输入模型，前轮采用随机路面仿真模型作为输入，后轮采用带有前轮预瞄信息的路面仿真模型作为输入；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.Step2、设计PID-LQR复合控制器；Step 2: Design a PID-LQR composite controller;Step3、确定LQR控制各性能指标权重系数，整定P、I、D参数，具体如下：Step 3. Determine the weight coefficients of each performance index of LQR control and adjust the P, I, and D parameters as follows:Step3.1、利用遗传算法确定性能指标最优权重；Step 3.1, use genetic algorithm to determine the optimal weight of performance indicators;Step3.2、利用MATLAB/PID Tuner整定PID参数；Step 3.2, use MATLAB/PID Tuner to adjust PID parameters;Step4、利用Simulink搭建仿真实验模型，设置实验工况，运行仿真。Step 4. Use Simulink to build a simulation experiment model, set the experimental conditions, and run the simulation.2.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于：所述Step1.1中，以车身垂直加速度、悬架动行程和轮胎动位移作为评价车辆平顺性的性能指标，加入俯仰角加速度、侧倾角加速度两个影响车身姿态稳定性的评价指标；2. The PID and LQR composite control method for a semi-active suspension according to claim 1, characterized in that: in Step 1.1, vehicle body vertical acceleration, suspension dynamic travel, and tire dynamic displacement are used as performance indicators for evaluating vehicle ride comfort, and pitch angular acceleration and roll angular acceleration, two evaluation indicators that affect vehicle posture stability, are added;7自由度包括四个车轴处垂直自由度、四个轮胎处垂直自由度、车身质心处绕X轴、Y轴旋转的俯仰和侧倾自由度，以及Z轴垂直自由度。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.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于：所述Step1.1中，根据牛顿力学定律对7个自由度进行受力分析可列出7自由度运动微分方程：3. The PID and LQR composite control method for a semi-active suspension according to claim 1, characterized in that: in Step 1.1, a force analysis of the seven degrees of freedom is performed according to Newton's laws of mechanics to formulate the following seven-degree-of-freedom motion differential equation:车身质心处Z轴垂向力平衡方程如式(1)：The vertical force balance equation of the Z axis at the center of mass of the vehicle body is as follows (1):车身绕Y轴旋转力矩平衡方程如式(2)：The balance equation of the rotation moment of the vehicle body around the Y axis is as follows:车身绕X轴旋转力矩平衡方程如式(3)：The balance equation of the rotation moment of the vehicle body around the X-axis is as follows:4个非簧载质量Z轴垂向力平衡方程如式(4)：The vertical force balance equation of the four unsprung masses along the Z axis is as follows:当车身俯仰角和侧倾角变化范围足够小时，四个车轮上方悬挂质量端点的位移可以表示如式(5)：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:z_sf1＝z_s-L_rθ-aφz_sf1 = z_s -L_r θ-aφz_sf2＝z_s-L_lθ-aφz_sf2 = z_s -L_l θ-aφz_sr1＝z_s-L_rθ+bφ_zsr1 ＝_zs -_Lrθ +bφz_sr2＝z_s+L_lθ+bφ (5)_zsr2 ＝_zs +_Llθ +bφ (5)式(1)-式(5)中，z_s为车辆质心的垂直位移,为车身绕着Y轴方向的转角(俯仰角)，θ为车身绕着X轴方向的转角(侧倾角)；m_wf1,m_wf2,m_wr1,m_wr2分别表示右前部、左前部、左后部、右后部非簧载质量；k_wf1,k_wf2,k_wr1,k_wr2分别为四个轮胎刚度系数；k_sf1,k_sf2,k_sr1,k_sr2分别为四个悬架刚度系数；c_sf1,c_sf2,c_sr1,c_sr2分别为四个悬架阻尼系数；q_f1,q_f2,q_r1,q_r2分别为四个车轮路面不平度的位移；z_wf1,z_wf2,z_wr1,z_wr2分别为四个车轴处垂直位移；z_sf1,z_sf2,z_sr1,z_sr2分别为四个车轮上方悬挂质量的垂直位移；a,b分别为汽车质心距离前、后轴线的距离；L_l,L_r分别为车辆质心距离左轮和后轮中心线的距离,m_s为整车质量，I_sy为俯仰转动惯量，I_sx为侧倾转动惯量；G₀为路面不平度系数，u为实验车速，f₀为下截至频率。In equations (1) to (5),_zs is the vertical displacement of the vehicle's center of mass, is the rotation angle (pitch angle) of the vehicle body around the Y axis, θ is the rotation angle (roll angle) of the vehicle body around the X axis; 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 four wheels due to road roughness respectively; z_wf1 , z_wf2 , z_wr1 , z_wr2 are the vertical displacements at the four axles respectively; z_sf1 , z_sf2 , z_sr1 , z_sr2 are the vertical displacements of the suspended masses above the four wheels respectively; a and b are the distances from the center of mass of the vehicle to the front and rear axles respectively; L_l and L_r are the distances from the center of mass of the vehicle to the center lines of the left and rear wheels respectively;_ms is the vehicle mass, I_sy is the pitch moment of inertia, and I_sx is the roll moment of inertia; G₀ is the road roughness coefficient, u is the experimental vehicle speed, and f₀ is the lower cutoff frequency.4.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于：所述Step1.3中，采用滤波白噪声作为前轮仿真路面输入信号，其时域表达式如式为:4. The PID and LQR composite control method for a semi-active suspension according to claim 1, wherein in Step 1.3, filtered white noise is used as the front wheel simulated road surface input signal, and its time domain expression is as follows:其中w_f(t)为前轮路面输入模型中的高斯白噪声；Where w_f (t) is the Gaussian white noise in the front wheel road input model;预瞄时间τ和车速有关，车速的快慢影响着控制效果，预瞄时间τ等于轴距/车速，前后轮的路面输入关系用拉普拉斯传递函数表示如式(7)：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):为了将频域表达式转换为状态空间表达式，利用pade近似法，寻找一个低阶传递函数(8)代替式(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)取pade二阶近似，以前后轮处传感器获得的路面不平度信息作为状态向量η_f，η_r，其状态方程可表示为式(9)：Taking the second-order approximation of pade, the road roughness information obtained by the sensors at the front and rear wheels is used as the state vector η_f , η_r , and its state equation can be expressed as formula (9):式(10)中：In formula (10):其中，in,后轮路面输入模型中的高斯白噪声w_r(t)可表示为式(10)：The Gaussian white noise w_r (t) in the rear wheel road input model can be expressed as formula (10):w_r(t)＝w_f(t-τ)＝η_f(t)+w_f(t) (10)w_r (t)=w_f (t-τ)=η_f (t)+w_f (t) (10)采用滤波白噪声作为后轮仿真路面输入信号，其时域表达式如式(11)：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):联合车辆运动微分方程(1)-(5)，结合路面输入模型得到状态空间表达式(12)：Combining the vehicle motion differential equations (1)-(5) and the road input model, we can obtain the state space expression (12):选择车身垂向位移、车身俯仰角、车身侧倾角、4个轮胎动位移、4个路面输入、车身垂向速度、车身俯仰角速度、车身侧倾速度、4个非簧载质量(4个车轴)垂直速度和两个状态变量η_f，η_r共20个变量作为系统的状态变化量，即: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 and η_r , a total of 20 variables, are selected as the state variation of the system, namely:选择车身垂向加速度、车身俯仰角加速度、车身侧倾角加速度、4个悬架动行程、4个轮胎动位移共11个量作为系统的输出变量，即: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:选择4个阻尼调节力F_cuf1,F_cuf2,F_cur1,F_cur2作为控制向量U的分量，即:U＝(F_cuf1,F_cuf2,F_cur1,F_cur2)^T；Select four damping adjustment forces F_cuf1 , F_cuf2 , F_cur1 , F_cur2 as components of the control vector U, that is: U = ( F_cuf1 , F_cuf2 , F_cur1 , F_cur2 )^T ;选择前轮路面输入白噪声w_f(t)作为扰动向量W的分量，即:W＝w_f(t)。The front wheel road surface input white noise w_f (t) is selected as the component of the disturbance vector W, that is: W = w_f (t).5.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于，所述Step2中具体步骤为：5. The semi-active suspension PID and LQR composite control method according to claim 1, wherein the specific steps in Step 2 are:Step2.1、根据PID控制理论设计PID控制器；Step 2.1. Design a PID controller based on PID control theory.Step2.2、根据LQR控制理论设计LQR控制器；Step 2.2, design the LQR controller according to the LQR control theory;Step2.3、将PID控制器和LQR控制器结合为PID-LQR复合控制器。Step 2.3. Combine the PID controller and LQR controller into a PID-LQR composite controller.6.根据权利要求5所述的一种半主动悬架PID与LQR复合控制方法，其特征在于：所述Step2.1中，PID控制为误差控制，控制对象为车辆质心处车身垂直加速度，以0作为给定期望值；PID控制规律如式(13)：6. A PID and LQR composite control method for a semi-active suspension according to claim 5, characterized in that: in Step 2.1, the PID control is error control, the control object is the vertical acceleration of the vehicle body at the center of mass, and 0 is used as the given expected value; the PID control rule is as shown in Formula (13):。 .7.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于：所述Step2.2中7. A semi-active suspension PID and LQR composite control method according to claim 1, characterized in that:^U_LQR＝-^KX(t) (14)^U_LQR ＝-^KX (t) (14)增益K由式(15)求出：The gain K is calculated from formula (15):K＝R_d^-1B^TP (15)K＝R_d^-1 B^T P (15)P由如下里卡提方程(16)求出：P is obtained from the following Riccati equation (16):A^TP+PA-PBR_d^-1B^TP+Q_d＝0 (16)A^T P+PA-PBR_d^-1 B^T P+Q_d ＝0 (16)给定一个用以评价输出的各项性能指标最优性能指标函数J，当J最小时，计算出控制器最优增益K，输出四个作动器最佳控制力U_LQR(t)；最优性能指标函数J的数学表达式为各项性能指标加权平方和的积分,矩阵形式如式(17)：Given an optimal performance index function J for evaluating various output performance indicators, when J is minimum, the optimal controller gain K is calculated and the optimal control force U_LQR (t) of the four actuators is output. The mathematical expression of the optimal performance index function J is the integral of the weighted square sum of various performance indicators, and its matrix form is as shown in Equation (17):式中:Q_d＝C^TQC；N_d＝C^TQD；R_d＝R+D^TQDIn the formula: Q_d =C^T QC; N_d =C^T QD; R_d =R+D^T QDQ和R分别表示为：Q＝diag(q₁,q₂,q₃,q₄,q₅,q₆,q₇,q₈,q₉,q₁₀,q₁₁)；R＝diag(r₁,r₂,r₃,r₄)Q and R are expressed as: Q = diag(q₁ ,q₂ ,q₃ ,q₄ ,q₅ ,q₆ ,q₇ ,q₈ ,q₉ ,q₁₀ ,q₁₁ ); R = diag(r₁ ,r₂ ,r₃ ,r₄ )其中：q₁为七自由度车辆模型车身质心处垂向加速度权值,q₂为七自由度车辆模型俯仰角加速度权值，q₃为七自由度车辆模型侧倾角加速度权值，q₄,q₅,q₆,q₇分别为七自由度车辆模型四个悬架动行程权值，q₈,q₉,q₁₀,q₁₁分别为七自由度车辆模型四个车轮动位移权值，r₁,r₂,r₃,r₄分别为七自由度车辆模型四个作动器控制力权值。Among them:_q1 is the weight of the vertical acceleration at the center of mass of the seven-degree-of-freedom vehicle model,_q2 is the weight of the pitch angular acceleration of the seven-degree-of-freedom vehicle model,_q3 is the weight of the roll angular acceleration 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 ,_q10 ,_q11 are the weights of the four wheel dynamic displacements of the seven-degree-of-freedom vehicle model,_r1 ,_r2 ,_r3 ,_r4 are the weights of the four actuator control forces of the seven-degree-of-freedom vehicle model.8.根据权利要求1所述的一种半主动悬架PID与LQR复合控制方法，其特征在于，所述Step3.1中，LQR控制的关键在于选择合适的权值，计算出矩阵Q和R,然后计算出最优控制器增益K；8. The PID and LQR composite control method for a semi-active suspension according to claim 1, wherein the key to LQR control in Step 3.1 is to select appropriate weights, calculate matrices Q and R, and then calculate the optimal controller gain K;遗传算法基本步骤为：确定种群规模、随机赋值给优化变量、计算适应度值、选择交叉变异操作；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;所述Step3.2中，PID三个参数的整定是整个控制器设计的关键，借助MATLAB的PIDTuner工具箱整定PID控制器的参数。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.