CN116373524A - Semi-active suspension PID and LQR composite control method - Google Patents
Semi-active suspension PID and LQR composite control method Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60G—VEHICLE SUSPENSION ARRANGEMENTS
- B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
- B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
- B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60G—VEHICLE SUSPENSION ARRANGEMENTS
- B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
- B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
- B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
- B60G17/0182—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method involving parameter estimation, e.g. observer, Kalman filter
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60G—VEHICLE SUSPENSION ARRANGEMENTS
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- B60G—VEHICLE SUSPENSION ARRANGEMENTS
- B60G2600/00—Indexing codes relating to particular elements, systems or processes used on suspension systems or suspension control systems
- B60G2600/18—Automatic control means
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60G—VEHICLE SUSPENSION ARRANGEMENTS
- B60G2600/00—Indexing codes relating to particular elements, systems or processes used on suspension systems or suspension control systems
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Abstract
The invention discloses a semi-active suspension PID and LQR composite control method, namely a PID-LQR composite control strategy is adopted, and the overall vehicle running smoothness index and the vehicle body posture stability index are adopted: and (3) optimizing the vertical acceleration, the suspension dynamic travel, the tire dynamic load, the pitch angle acceleration and the roll angle acceleration of the vehicle body, designing a PID-LQR controller according to PID control, pre-aiming control and LQR control theory, and arranging four suspension actuators as 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
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, and the parameter value to be set in the control system is as follows: p, I and D parameters and optimal weight of each performance index, and many researchers adjust the parameters by adopting an empirical test method, wherein the method has great subjectivity, and human factors have great interference on control effects, are easily interfered by local optimal solutions, and are difficult to find global optimal solutions.
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: the semi-active suspension PID and LQR composite control method is characterized by comprising the following steps of:
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 r θ-aφ
z sf2 ＝z s -L l θ-aφ
z sr1 ＝z s -L r θ+bφ
z sr2 ＝z s +L l θ+bφ (5)
in the formulae (1) - (5), z s For a vertical displacement of the center of mass of the vehicle,
the angle of rotation (pitch angle) of the vehicle body around the Y-axis direction, and the angle of rotation (roll angle) of the vehicle body around the X-axis direction; m is m wf1 ,m wf2 ,m wr1 ,m wr2 Respectively representing right front, left rear, right rear unsprung mass; k (k) wf1 ,k wf2 ,k wr1 ,k wr2 Four tire stiffness coefficients respectively; k (k) sf1 ,k sf2 ,k sr1 ,k sr2 Four suspension stiffness coefficients respectively; c sf1 ,c sf2 ,c sr1 ,c sr2 Four suspension damping coefficients respectively; q f1 ,q f2 ,q r1 ,q r2 Respectively the displacement of the road surface unevenness of four wheels; z wf1 ,z wf2 ,z wr1 ,z wr2 The four axles are respectively vertically displaced; z sf1 ,z sf2 ,z sr1 ,z sr2 Vertical displacement of the suspended mass above the four wheels respectively; a, b are the distances from the center of mass of the automobile to the front and rear axes respectively; l (L) l ,L r The distances between the center of mass of the vehicle and the center lines of the left wheel and the rear wheel are respectively m s For the whole car quality, I sy For moment of inertia of pitch, I sx Is the roll moment of inertia; g 0 Is the road surface unevenness coefficient, u is the experimental vehicle speed, f 0 Is the bottom cut frequency.
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 is f (t) gaussian white noise in the front wheel road surface 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 into a state space expression, a low order transfer function (8) is found to replace expression (7) using the pad approximation
Taking the second-order approximation of the pad and taking the road surface unevenness information obtained by the sensors at the front wheel and the rear wheel as a state vector eta f ，η r The state equation thereof can be expressed as formula (9):
in the formula (10):
wherein,,
gaussian white noise w in rear wheel road surface input model r (t) can be represented by 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):
selecting a vehicle vertical displacement, a vehicle pitch angle, a vehicle roll angle, 4 tire movements, 4 road inputs, a vehicle vertical speed, a vehicle pitch angle speed, a vehicle roll speed, 4 unsprung mass (4 axles) vertical speeds and two state variables eta f ，η r A total of 20 variables are used as state variables of the 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:
select 4 damping adjustment forces F cuf1 ,F cuf2 ,F cur1 ,F cur2 As a component of the control vector U, i.e., u= (F cuf1 ,F cuf2 ,F cur1 ,F cur2 ) T ；
Selecting the white noise w of the front wheel pavement f (t) 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, PID control is error control, and the control object is the vertical acceleration of the vehicle body at the center of mass of the vehicle, and 0 is taken as a given expected value; 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 -1 B T P (15)
p is determined from the following Richti equation (16):
A T P+PA-PBR d -1 B T P+Q d ＝0 (16)
giving an optimal performance index function J for evaluating various performance indexes of the output, calculating the optimal gain K of the controller when the J is minimum, and outputting the optimal control force U of four actuators LQR (t); the mathematical expression of the optimal performance index function J is the integral of the weighted square sum of all performance indexes, and the matrix form is shown as the formula (17):
in which Q is d ＝C T QC；N d ＝C T QD；R d ＝R+D T QD
Q and R are each represented by: q=diag (Q 1 ,q 2 ,q 3 ,q 4 ,q 5 ,q 6 ,q 7 ,q 8 ,q 9 ,q 10 ,q 11 )；R＝diag(r 1 ,r 2 ,r 3 ,r 4 )
Wherein: q 1 Is the weight value, q of the vertical acceleration at the mass center of the vehicle body of the seven-degree-of-freedom vehicle model 2 The pitch angle acceleration weight value q of the seven-degree-of-freedom vehicle model 3 Is the roll angle acceleration weight value, q of the seven-degree-of-freedom vehicle model 4 ,q 5 ,q 6 ,q 7 Four suspension dynamic range weights, q, of a seven-degree-of-freedom vehicle model respectively 8 ,q 9 ,q 10 ,q 11 Four wheel dynamic displacement weights, r of seven-degree-of-freedom vehicle model 1 ,r 2 ,r 3 ,r 4 And controlling force weights of four actuators of the seven-degree-of-freedom vehicle model respectively.
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 following basic steps: 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. Pre-aiming control principle: sensors located at the front and rear of the vehicle collect control system state variables for the vehicle: the vertical displacement of the vehicle body, the pitch angle of the vehicle body, the vertical displacement of four axles, the uneven pavement displacement of four wheels and the like, and then the variables are fed back to the controller by the sensor, the controller only carries out feedback control according to the feedback information of the front part of the vehicle when giving an instruction to the front wheel suspension actuator, and carries out feedforward and feedback control according to the speed and the wheelbase of the vehicle while considering the state variable information sent back by the rear wheel sensor when giving the instruction to the rear wheel actuator and adopting the feedback information of the front part of the vehicle according to the speed and the wheelbase, 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
| |
0 | Adjusting the time | 0.802s |
| I | 3200.0612 | Maximum overshoot | 4.78×10 7 |
| D | |||
| 0 | Peak value | 0.488 | |
| Rise time | 1.04×10- 7 s | 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:
q 1 ＝0.5377,q 2 ＝811580,q 3 ＝681980,q 4 ＝422890,q 5 ＝0.3188,q 6 ＝949310,q 7 ＝648200,q 8 ＝72886,
q 9 ＝4.5784,q 10 ＝505640,q 11 ＝886550，r 1 ＝1.5349,r 2 ＝1.7254,r 3 ＝0.5001,r 4 ＝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 the automobile to 72km/h, setting the road surface type to be a branch road, and setting the value range of the road surface unevenness coefficient under the road condition to be 5 multiplied by 10 -7 ～3×10 -5 Taking the average value of 5 multiplied by 10 -6 . When running, the vehicle body motion from two degrees of freedom of pitching and rolling can be generated, and road surface inputs at four wheels of the vehicle are not related to each other; the simulation step size was set to 0.05 and the simulation time was set to 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. To verify the conclusion, the vehicle speed is changed, and the output performance index of the whole vehicle is analyzed, and the method is specifically implemented as follows: in the embodiment 1, the parameters of the whole vehicle model are not changed, the road surface condition has no great influence on the invention, and the road surface condition can not be verified, so that the road surface grade is not changed, the vehicle speed is divided into three gears of low speed, medium speed and high speed, the simulation experiment is carried out at the low speed by u=36 km/h, the simulation experiment is carried out at the medium speed by u=72 km/h, the simulation experiment is carried out at the high speed by u=108 km/h, and each performance index of the whole 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 (10)
1. The semi-active suspension PID and LQR composite control method is characterized by comprising the following steps of:
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.
2. The semi-active suspension PID and LQR composite control method according to claim 1, wherein 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.
3. The semi-active suspension PID and LQR composite control method according to claim 2, wherein: in the 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.
4. The semi-active suspension PID and LQR composite control method according to claim 2, wherein: in step1.1, the force analysis of 7 degrees of freedom according to newton's law of mechanics can list the 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 r θ-aφ
z sf2 ＝z s -L l θ-aφ
z sr1 ＝z s -L r θ+bφ
z sr2 ＝z s +L l θ+bφ (5)
in the formulae (1) - (5), z s For a vertical displacement of the center of mass of the vehicle,
the angle of rotation (pitch angle) of the vehicle body around the Y-axis direction, and the angle of rotation (roll angle) of the vehicle body around the X-axis direction; m is m wf1 ,m wf2 ,m wr1 ,m wr2 Respectively representing right front, left rear, right rear unsprung mass; k (k) wf1 ,k wf2 ,k wr1 ,k wr2 Four tire stiffness coefficients respectively; k (k) sf1 ,k sf2 ,k sr1 ,k sr2 Four suspension stiffness coefficients respectively; c sf1 ,c sf2 ,c sr1 ,c sr2 Four suspension damping coefficients respectively; q f1 ,q f2 ,q r1 ,q r2 Respectively the displacement of the road surface unevenness of four wheels; z wf1 ,z wf2 ,z wr1 ,z wr2 The four axles are respectively vertically displaced; z sf1 ,z sf2 ,z sr1 ,z sr2 Vertical displacement of the suspended mass above the four wheels respectively; a, b are the distances from the center of mass of the automobile to the front and rear axes respectively; l (L) l ,L r The distances between the center of mass of the vehicle and the center lines of the left wheel and the rear wheel are respectively m s For the whole car quality, I sy For moment of inertia of pitch, I sx Is the roll moment of inertia; g 0 Is uneven road surfaceThe degree coefficient, u is the experimental vehicle speed, f 0 Is the bottom cut frequency.
5. The semi-active suspension PID and LQR composite control method according to claim 1, wherein: in step1.3, the filtered white noise is used as the front-wheel simulation pavement input signal, and the time domain expression is as follows:
wherein w is f (t) gaussian white noise in the front wheel road surface 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 into a state space expression, a low order transfer function (8) is found to replace expression (7) using the pad approximation
Taking the second-order approximation of the pad and taking the road surface unevenness information obtained by the sensors at the front wheel and the rear wheel as a state vector eta f ，η r The state equation thereof can be expressed as formula (9):
in the formula (10):
wherein,,
gaussian white noise w in rear wheel road surface input model r (t) can be represented by 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):
Y＝CX+DU (12)
selecting a vehicle vertical displacement, a vehicle pitch angle, a vehicle roll angle, 4 tire movements, 4 road inputs, a vehicle vertical speed, a vehicle pitch angle speed, a vehicle roll speed, 4 unsprung mass (4 axles) vertical speeds and two state variables eta f ，η r A total of 20 variables are used as state variables of the 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:
select 4 damping adjustment forces F cuf1 ,F cuf2 ,F cur1 ,F cur2 As a component of the control vector U, i.e., u= (F cuf1 ,F cuf2 ,F cur1 ,F cur2 ) T ；
Selecting the white noise w of the front wheel pavement f (t) as a component of the disturbance vector W, i.e. w=w f (t)。
6. The semi-active suspension PID and LQR composite control method according to claim 1, wherein the Step2 specifically comprises 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.
7. The semi-active suspension PID and LQR composite control method according to claim 6, wherein: in step2.1, PID control is error control, and the control object is vehicle body vertical acceleration at the center of mass of the vehicle, taking 0 as a given expected value; the PID control law is as shown in formula (13):
8. the semi-active suspension PID and LQR composite control method according to claim 1, wherein: in said Step2.2
U LQR ＝-KX(t) (14)
The gain K is obtained by the equation (15):
K＝R d -1 B T P (15)
p is determined from the following Richti equation (16):
A T P+PA-PBR d -1 B T P+Q d ＝0 (16)
giving an optimal performance index function J for evaluating various performance indexes of the output, calculating the optimal gain K of the controller when the J is minimum, and outputting the optimal control force U of four actuators LQR (t); the mathematical expression of the optimal performance index function J is the integral of the weighted square sum of all performance indexes, and the matrix form is shown as the formula (17):
in which Q is d ＝C T QC；N d ＝C T QD；R d ＝R+D T QD
Q and R are each represented by: q=diag (Q 1 ,q 2 ,q 3 ,q 4 ,q 5 ,q 6 ,q 7 ,q 8 ,q 9 ,q 10 ,q 11 )；R＝diag(r 1 ,r 2 ,r 3 ,r 4 )
Wherein: q 1 Is the weight value, q of the vertical acceleration at the mass center of the vehicle body of the seven-degree-of-freedom vehicle model 2 The pitch angle acceleration weight value q of the seven-degree-of-freedom vehicle model 3 Is the roll angle acceleration weight value, q of the seven-degree-of-freedom vehicle model 4 ,q 5 ,q 6 ,q 7 Four suspension dynamic range weights, q, of a seven-degree-of-freedom vehicle model respectively 8 ,q 9 ,q 10 ,q 11 Four wheel dynamic displacement weights, r of seven-degree-of-freedom vehicle model 1 ,r 2 ,r 3 ,r 4 And controlling force weights of four actuators of the seven-degree-of-freedom vehicle model respectively.
9. The semi-active suspension PID and LQR composite control method according to claim 1, wherein the Step3 specifically comprises 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.
10. The semi-active suspension PID and LQR composite control method of claim 1, wherein in said step3.1, the key of LQR control is to select proper weights, calculate matrices Q and R, and then calculate optimal controller gain K;
the genetic algorithm comprises the following basic steps: 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.
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