Hong-yan SHI, Shou-li PAN, Li-ping LIU, Chun-you ZHANG*

(1College of Mechanical Engineering, Inner Mongolia University for the Nationalities College, Tongliao 028000, China)(2No.208 Research Institute of China Ordnance, Beijing 102202, China)(3Changchun Vocational Institute of Technology, Changchun 130000, China)

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Research on active suspension control strategy based on fuzzy PID control

Hong-yan SHI1, Shou-li PAN2, Li-ping LIU3, Chun-you ZHANG1*

(1CollegeofMechanicalEngineering,InnerMongoliaUniversityfortheNationalitiesCollege,Tongliao028000,China)(2No.208ResearchInstituteofChinaOrdnance,Beijing102202,China)(3ChangchunVocationalInstituteofTechnology,Changchun130000,China)

It is inevitable for cars to vibrate because of road excitation during the movement. Regarding this problem, this paper selects the active suspension of the quarter-car as the research object and ride smoothness and handling balance as the goal. Under the condition of class B and class C road excitation, it takes tire dynamic load, body vertical acceleration and suspension dynamic travel as evaluation indicators. Meanwhile, the fuzzy inference and PID control are combined to propose a fuzzy PID control strategy which is applied in the active suspension system. Then the PID parameters can be adjusted online so that the system can adapt to the changing road conditions. The simulation and test results show that the fuzzy PID control strategy can effectively reduce the vibration amplitude and speed of the car under the typical road excitation and greatly improve ride comfort and handling stability. The fuzzy PID has a certain value in terms of practical application.

Passive suspension, Active suspension, Fuzzy control, PID control, ADAMS

1 Introduction

The suspension system is an important part of the automobile, whose dynamic performance directly determines the automobile’s ride smoothness, handling stability and ride comfort. The parameters of traditional passive suspension are fixed, which can’t automatically change with environmental changes and guarantee a good control effect [1]. By using the force generator to replace the passive suspension’s elastic and damping components, the active suspension can adjust control force in realtime based on road excitation and get the best control characteristics [2-3]. Therefore, the research on the active suspension is widely valued currently.

For research on the active suspension system, scholars at home and abroad have done a lot of work and used a variety of control techniques, such as sliding mode control [4], neural network control [5], LQG optimal control [6], etc.. Most of the methods which are based on mathematical models are applied in the simulation research for the automobile motion. In other cases, they just focus on the ride comfort, neglecting the handling stability [7]. The automobile suspension system is a multi-variable, time-varying and nonlinear complex systems and a simplified mathematical model can’t not truly reflect the real control situation [8]. According to such situation, this paper applies fuzzy reasoning to the active suspension control system of a quarter-car, and combines with PID control strategy and proposes a kind of control strategy based on fuzzy PID. Moreover, under the condition of level B and level C road excitation, tire dynamic load, body vertical acceleration and suspension dynamic travel are selected as the evaluation indicators for suspension performance. The simulation and test results verify the correctness of the model and the reliability of the control strategy.

2 Structure of suspension system and operating principle

2.1Passivesuspension

Passive suspension is composed of springs and dampers, which has a simple structure and is convenient to manufacture as shown in Fig. 1. During the movement of automobiles, the stiffness and damping coefficient of the passive suspension are fixed and only at a particular condition, they are optimal. When speed, load as well as road conditions and other factors change, handling stability and ride comfort will get worse [9-10].

2.2 Active suspension

Active suspension is made up of springs, dampers and actuators, as shown in Fig. 2. The active suspension effectively overcomes the shortcomings of the passive suspension and according to the road and the automobile condition detected, it can achieve the automatical adjustment of the suspension system’s parameters through a variety of feedback information [11-12]. When the sensor detects a change in the road surface input, the processor will send a control signal to the actuator, which generates a corresponding control force to counteract the automobile body vibration and road excitation. Thus, the active suspension is the best combination to realize the stability and the ride comfort.

Fig.1SimplifiedmodelofpassivesuspensionFig.2Simplifiedmodelofactivesuspension

3 Mathematical model

3.1Quarter-carmodel(twodegreesoffreedom)oftheactivesuspension

There are three kinds of commonly used automobile suspension system models: quarter-car model, half-car model and full vehicle model [13]. Quarter-car model is often used in the research on control strategy of the suspension system [14]. Half-car model is mainly used in the study about parameter match problem between the front and rear suspension [15]. Full vehicle model is aimed at the study on the vertical, pitch and roll movement [16]. This paper selects quarter-car model with two degrees of freedom as the research object and takes kinematic analysis for it. While modeling, make the following assumptions:

1) Ignore the impact of air power on the automobile during moving.

2) The body of automobiles will not become deformed.

3) Ignore the impact of the engine vibration.

Differential equations of quarter-car model (two degrees of freedom) of the active suspension are described as follows:

(1)

Where:m1,m2respectively expresses tire mass and body mass;zs,zlrespectively expresses vertical displacement wheels and body;sexpresses road vertical excitation;k1,k2respectively expresses tire and suspension stiffness;cexpresses the damping coefficient of the shock absorber;uexpresses actuator control force.

Take tire dynamic load, by vertical acceleration and suspension dynamic performance as output of performance indicators . Then the output variables are:

The state space expression of active suspension model is written as follows:

(2)

Where:

3.2Mathematicalmodelofrandomroad

Road excitation is the most important reason for automobile vibration. Usually different levels of road are represented by road roughness. Take Random road as input. Then the model can be expressed as[18-19]:

(3)

Where,G0is road roughness coefficient;w(t) is Gaussian white noise;vis automobile speed;f0is the below cut-off frequency.

4 Study on control strategy

4.1 PID control

Conventional PID control is a kind of control mode based on proportion - integral - differential, whose expression is written as:

(4)

Where,KPis Proportional gain coefficient;TDis Differential time constant;TIis Integration time constant;e(t) is the difference between the output and the input, namely the deviation signal;u(t) is The output signal of controller.

PID structure diagram is shown in Fig.3.

Fig.3 The structure of PID controller

For the conventional PID controller, it is difficult to guarantee control precision when the load and other external conditions change because parameters can’t be adjusted online. Therefore, it has some limitations in application and only suits situations where working condition is simple and the accuracy demand is low.

4.2ActivesuspensionwithfuzzyPIDcontrol

4.2.1 Control principle

To ensure the control precision, this paper designs a fuzzy PID controller by combining fuzzy control and traditional PID control. This controller takes erroreand deviation changeecas input variables and selects ΔKp,ΔKiand ΔKdas output variables. The design not only retains the advantages of the PID control strategy, which is simple and easy to realize, but also can adjust PID parameters in real-time. Thus the controller meets different demands for PID control parameters under different working conditions and ensure the control precision. The structure is shown in Fig.4.

Fig.4 Structure of fuzzy PID controller

4.2.2 Rules of fuzzy control

The given domain of discourse for the input variables are [-8.3, 8.3] and [-0.4, 0.4] and the correspond fuzzy domain of discourse are respectively [-6,6] and [-3,3]. The domain of discourse for the output variables is [-780,780] and the correspond fuzzy domain of discourse is [-1, 1]. Fuzzy subset is {NB, NM, NS, ZE, PS, PM, PB}, which respectively expresses{negative large, negative middle, negative small, zero, positive small, positive middle, positive large}. Quantification factorke=0.75 andkec=7.5. The scale factorku=130. The trigonometric function is used as membership function.

When the controller parameters are adjusted on-line, the following principles should be considered.

1) When the deviation |e| is large, in order to improve the response speed of the system the smaller and the larger should be taken. Then take zero to reduce overshoot.

2) When the deviation |e| is moderate, take the moderate and the smaller to maintain fast response.

3) When the deviation |e| is small, sum should be increased and select properly to enhance the anti-jamming capability and improve system stability.

Based on the above principles, consider practical experience and the influence of |ec|. Then make the specific fuzzy rules of parameters. They are shown in Table 1 to Table 3.

Table 1 Fuzzy control rule table of ΔKp

eecNBNMNSZEPSPMPBNBPBPBPMPMPSPSZENMPBPBPMPMPSZEZENSPMPMPMPSZENSNMZEPMPSPSZENSNMNMPSPSPSZENSNSNMNMPMZEZENSNMNMNMNBPBZENSNSNMNMNBPB

Table 2 Fuzzy control rule table of ΔKi

eecNBNMNSZEPSPMPBNBNBNBNBNMNMZEZENMNBNBNMNMNSZEZENSNMNMNSNSZEPSPSZENMNSNSZEPSPSPMPSNSNSZEPSPSPMPMPMZEZEPSPMPMPBPBPBZEZEPSPMPMPBPB

Table 3 Fuzzy control rule table of ΔKd

eecNBNMNSZEPSPMPBNBPSPSZEZEZEPMPBNMNSNSNSNSZENSPMNSNBNMNMNSZEPSPMZENBNMNMNSZEPSPMPSNBNMNSNSZEPSPSPMNMNSNSNSZEPSPSPBPSZEZEZEZEPBPB

According to the model rule table, adjust the PID parameters online. The formulas are written as follows:

(5)

Where:Kp0,Ki0andKd0represent the initial values of the PID parameters. Through this relationship, the fuzzy controller will be able to tune PID parameters online and make input consistent with the ideal.

5 Simulation analysis

5.1Roadexcitation

Road input is an important indicator testing the suspension performance. Real roads are often very complex and fluctuate at random. This study selects level B and leve C road as the reference input. The simulation model is set up in the Simulink section of MATLAB, as shown in Fig.5. The random signal simulation curve can be gained, as shown in Fig.6 and Fig.7.

Fig.5 Simulation model of road input

Fig.6 Excitation curve of level B

Fig. 7 Excitation curve of level C

5.2 Simulation

According to the model and the control strategy established, the fuzzy PID control system model of the active suspension is established in the Matlab/Simulink, as shown in Fig.8.

Fig.8 Fuzzy PID control system model of the active suspension

During the simulation, vehicle speedv=20 m/s, tire qualitym1=45 kg, body massm2=300 kg, damping coefficientC=3 000 N·s/m, spring stiffnessk2=3 000 N/s, simulation time is 10 s. The tire dynamic load, body vertical acceleration and suspension dynamic travel are taken as performance indicators. In order to inspect control effects, the simulation data of passive suspension are taken as a reference. The results are shown in Figs.9 to 14.

Fig.9 Tire dynamic load on level B road

Fig.10 Body vertical acceleration on level B road

Fig.11 Suspension dynamic travel on level B road

Fig.12 Tire dynamic load on level C road

Fig.13 Body vertical acceleration on level C road

Fig.14 Suspension dynamic travel on level C road

To further illustrate the differences in the dynamic characteristics between the active suspension and the passive suspension based on the fuzzy PID control, the rms of all data in simulation curves are made and compared in the list, as shown in Table 4.

Table 4 Comparison of simulation results

EvaluationindicatorPassivesuspensionActivesuspensionbasedonfuzzyPIDIncreaseamplitudeofperfor-mance/%LevelBroadTiredynamicLoad/kN0.0860.06326.7Bodyverticalacceleration/(m·s-2)0.1980.10646.5Suspensiontravel/mm5.1124.36814.6LevelCroadTiredynamicLoad/kN0.1390.08141.7Bodyverticalacceleration/(m·s-2)0.4570.23847.9SuspensionTravel/mm9.4257.92715.9

Simulation results show that compared with the passive suspension, active suspension can greatly reduce the effects of road excitation on automobile dynamic performance. Moreover, Fuzzy PID control strategy has high control accuracy and strong robustness for the active suspension. It has a certain practicality.

6 Road test

In order to verify the simulation results and the correctness of the control strategies, road tests are conducted for the real vehicle using the fuzzy PID control established. Due to limited technical conditions, only the body vertical acceleration test is done.

Road conditions: test site is the cement road which conforms with Class B road and <2% slope.

Test equipment: a homemade modified vehicle, CDSP dynamic data collection instrument, ULT24 type piezoelectric acceleration sensor, a control system platform.

Test conditions: Tests are conducted under 40 km/h and 60 km/h speed in Class B road; The vehicle is tested when passing bump under the same condition. Test results are shown in Fig.15 and 16.

From the test results, compared with the passive suspension, the magnitude of the vertical acceleration of the vehicle using fuzzy PID control under various testing conditions significantly reduces. This result indicates that using fuzzy PID control on the active suspension can effectively improve the vehicle’s ride smoothness. The test results and simulation results are consistent and verify the correctness of the findings.

Fig.15 Test results of the vehicle in Class B road

Fig.16 Test results of the vehicle when passing bump

7 Conclusions

Dynamic characteristic of the suspension system is an important measure of car performance. Also, it is a key factor affecting ride comfort and handling stability of the automobiles. For the problems of the passive suspension, this paper has studied the control strategy of the active suspension and draws the following conclusions:

1)A model of the active suspension is established for the quarter-car and dynamic analysis is done to identify factors that affect the dynamic characteristics of the automobile. Meanwhile, according to the evaluation conditions and standards of the ride comfort and handling stability, tire dynamic load, body vertical acceleration and suspension dynamic travel are selected as the evaluation measure for suspension performance.

2) The model is applied to the PID control to establish the fuzzy PID control strategies. Then suspension parameters can be adjusted online so that the actual output is always consistent with the ideal value of the system to adapt to changing external conditions. The simulation results show that the strategy can make the system response fast and anti-interference capacity strong.

3) Compared with passive suspension, the active suspension using the fuzzy PID control strategy can effectively overcome road excitation. Take level C road as an example. Tire dynamic load decreases 41.7%. Body vertical acceleration decreases 47.9%. Suspension dynamic travel reduces 15.9%. The results show that ride comfort and handling stability of the car have been improved a lot.

4) Compared with the half-car model (four degrees of freedom) and full vehicle model (seven degrees of freedom) of the active suspension, the quarter-car model (two degrees of freedom) is simple and can make research on control strategy come true. The simulation and test results verify that the model is correct.

Acknowledgement

This paper is supported by National Natural Science Foundation of China (No.6144041).

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摘要：針對直齒錐齒輪加工方法間歇分度、生產(chǎn)效率低的問題，基于直齒錐齒輪擺線旋分加工方法，采用空間曲線逼近直線的數(shù)學(xué)方法解釋直齒錐齒輪旋分加工原理。在此基礎(chǔ)之上，給出擺線旋分加工數(shù)學(xué)模型，即切削點軌跡的數(shù)學(xué)模型，并分析影響參數(shù)，確定各參數(shù)范圍及影響規(guī)律，進(jìn)而獲得符合加工要求的切削點軌跡。

關(guān)鍵詞：直齒錐齒輪；擺線旋分加工；切削點軌跡

10.3969/j.issn.1001-3881.2015.24.013 Document code: A

U270.35

基于模糊PID的汽車主動懸架控制策略研究

侍紅巖1，潘守禮2，劉麗萍3，張春友1*

1.內(nèi)蒙古民族大學(xué)機械工程學(xué)院， 內(nèi)蒙古 通遼028000 2.中國兵器工業(yè)第208研究所， 北京102202 3.長春職業(yè)技術(shù)學(xué)院， 長春130000

汽車在行駛過程中不可避免會受到路面激勵而產(chǎn)生振動，針對這一問題，以行駛平順性和操作平衡性為目標(biāo)，以1/4車主動懸架為研究對象，在B級、C級路面激勵條件下，把輪胎動載荷、車身垂直加速度、懸架動行程作為評價指標(biāo)進(jìn)行研究；同時，把模糊推理與PID控制相結(jié)合，提出一種模糊PID控制策略應(yīng)用于主動懸架系統(tǒng)中，對PID參數(shù)進(jìn)行實時在線整定，使之適應(yīng)實際路面環(huán)境的不斷變化；ADAMS與MATLAB聯(lián)合仿真結(jié)果表明：應(yīng)用模糊PID控制策略可有效減小典型路面激勵條件下汽車的振動幅度和速度，大幅改善乘坐舒適性和操縱穩(wěn)定性，具有一定應(yīng)用價值。

被動懸架；主動懸架；模糊控制；PID控制；ADAMS

直齒錐齒輪擺線旋分加工數(shù)學(xué)模型及參數(shù)優(yōu)化

趙桂芝，吳曉強，單曉敏，張春友*

內(nèi)蒙古民族大學(xué) 機械工程學(xué)院， 內(nèi)蒙古 通遼028000

15 Feburary 2015; revised 23 May 2015;

Chun-you ZHANG, Lecturer,

E-mail: wangzai8402@163.com

accepted 7 September 2015

Hong-yan SHI, Lecturer, E-mail: shan_xiaomin@163.com

Hydromechatronics Engineering

http://jdy.qks.cqut.edu.cn

E-mail: jdygcyw@126.com