An Integrated Design of Recirculating-ball EPS Based on LMS and Simulink

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1 An Integrated Design of Recirculating-all EPS Based on LMS and Simulink Muyi LIN *1,2, Mingyuan LIU 1, Liang TONG 1,2, Bin MA 1,2, Zhongjie YU 1 1. School of Mechanical and Electronic Engineering, Beijing University of Information Science and Technology, Beijing , China 2. Collaorative Innovation Center for Electric Vehicles, Beijing , China Astract An integrated design ased on LMS and Simulink is proposed to solve the prolem of separate design etween control system and steering in the design of recirculating-all EPS.The method uses LMS to uild the three-dimensional dynamic simulation model of steering and uses MATLAB/Simulink to uild the simulation model of EPS control system; The co-simulation model were designed ased on association of parameter etween dynamic model and control system model. Simulation and experimental results verified the accuracy and effectiveness of the co-simulation model and design method. Research and analysis can e progressed more accurately in terms of EPS for steering performance and overall performance etween steering and control system.the aove achievement give a feasile method for integrated design of recirculating-all EPS. Keywords - integration design; recirculating-all EPS; LMS; Simulink; co-simulation I. PREFACE With the development of the integrated design tends to e high accurate analysis and comprehensive research, the traditional design method of recirculating-all EPS,which ased on MATLAB or Laview software to estalish simulation model and conducts associated simulation and experimental analysis, has een replaced y a design method ased on Joint application etween the multi-ody dynamics software and simulink application and experimental validation [1-6]. This new design method overcomes the prolem that accuracy is not high when only one application software eing used for mechanical system modeling and simulation of EPS [7]. Nowadays, the domestic and overseas research results ased on co-simulation for integrated design of recirculatingall EPS are mainly to simulation y jointing control system model and vehicle model or y jointing EPS and vehicle model, which focuses on the research of control strategy [8-11]. The research results haven t taken the effects of the ehavior of mechanical system on EPS into consideration, however, we can gain a more accurate comprehensive research and analysis on the integrated design ased steering performance and control system for overall performance etween steering and control system. In this paper, LMS and MATLAB will e used to estalish steering dynamic simulation model and control system simulation model respectively. And, the model cosimulation and experimental analysis are ased on the parametric interaction of each model which is implemented y software interfaces. The paper strives to give a feasile method for the integrated design of EPS mechanical and control system. II. THE COMPOSITION AND WORKING PRINCIPLE OF EPS The structure of recirculating-all EPS is shown in Fig.1, which consists of two parts. On the one hand, it s the control system including ECU, motor, sensors and so on. On the other hand, it s the steering mechanism. The working principle of EPS system as follows. When the driver is handling the steering wheel, according to the steering wheel torque, vehicle speed and other signals detected y sensors, ECU gives instructions to control the motor running and makes the motor output corresponding size and direction of steering power-assisted torque. Thus, the motor generates auxiliary power. When the car isn t steering, ECU doesn t issue instructions to the motor and the motor doesn t work. Fig. 1 The Structure of Recirculating-all EPS DOI /IJSSST.a ISSN: x online, print

2 III. THE ESTABLISHMENT OF THREE- DIMENSIONAL DYNAMIC MODEL OF STEERING Taking a recirculating-all steering of a light truck as a prototype, a steering parametric model is uilt in CATIA y omitting the steering wheel, steering rod wheels and other parts in the case of meeting the demand of actual research. The parametric design of steering components implement is achieved y using a way that the key parameter drive model update automatically[12]. According to structural relationship, steering parts are assemled in CATIA. Through the constraint of assemly and correction of design parameters, we ensure that the various parts work well and haven t interference, and verify accuracy of the model generated through the parameterized design. The main parameters of recirculating-all steering are shown in Tale1. TABLE I. THE MAIN PARAMETERS OF RECIRCULATING-BALL STEERING (1-1) Tooth Rocker shaft Ball center distance fan modulus diameter /mm /mm Data (1-2) Ball diameter Working turns Pitch/mm /mm numer /mm Data (1-3) Circumfluence rows Numer of teeth of tooth fan Numer of teeth of Full circle Data (1-4) Pressure Angle of tooth fan Cutting angle Gear width/mm Data Fig. 2 MOTION Steering Dynamics Model Using the coherent and accurate characteristics of data conversion etween LMS Virtual.La Motion and CATIA, the truck EPS steering model is imported to the MOTION module of LMS Virtual.La. Besides, the constraint type of model is defined and parameters are set. According to the characteristic of steering dynamic, motion pair are added to moving link. Then, the estalishment of MOTION steering dynamics model is completed, which is shown in Fig.2. IV. THE ESTABLISHMENT OF EPS CONTROL SYSTEM SIMULATION MODEL The working principle of control system as follows. According to the steering wheel torque, car speed, actual power-assisted current of motor and other signals detected y sensors, ECU outputs power-assisted signals to the motor after processing data ased on the control strategy. And, the motor is connected to the steering reduction mechanism, thus they making power-assisted steering implement[13]. Control system simulation model consists of power-assisted motor model and control strategy model which includes powerassisted characteristic curve model and incremental PID control model. The diagram of control system is shown in Fig.3. Torque sensor signal Speed sensor signal Interface Circuit Actual power-assisted Motor current ECU (power-assisted characteristic curve, PID Module,etc) Current Sensor Fig. 3 The Diagram of Control System PWM driving power-assisted motor power-assisted torque steering mechanism A. The Estalishment of Control Strategy Model Power-assisted control uses the control method of motor armature current. Specifically, according to the torque signal from torque sensor and speed signal, it will determine the power-assisted target current through power-assisted characteristic curve. In order to make actual current track down target current quickly, incremental PID control algorithm will e used for closed-loop control of motor current when power-assisted control is running. The control algorithm is as follows: uk ( ) Aek ( ) Bek ( 1) Cek ( 2) (1) u k u k 1 u k (2) e k Im k I k (3) T T D A Kp 1 Tt T (4) T B K 1 2 D p T (5) TD C Kp T (6) DOI /IJSSST.a ISSN: x online, print

3 Where, k -- Sampling numer, k 0,1, 2 ; --Increment of motor armature voltage at the first u k K sampling times; I k --Motor actual current; k --Target current; Im e k--the deviation etween I k and Im k at the first K sampling times. EPS control strategy model ased on formula (1-7) is shown in Fig.4. Fig. 4 The Diagram of Control System B. The Estalishment of Electric Motor Model Motor used in this paper is DC permanent magnet motor. Given its motor inductance is relatively small, it can e ignored. The relational equation amongu, R, K and I is as follows: d m U RI K (7) dt U -- Motor terminal voltage; R -- Armature resistance; K -- EMF coefficient. The relational equation among Ta andt m is as follows: Ta Tm T K I (8) Gm, m a T --power-assisted torque; a T --Electromagnetic torque generated from motor; m K --Motor torque constant; a G --The drive ratio from motor to steering shaft. m Power-assisted motor model (simulink) ased on formula (8) is as in Fig.5.Input signal of motor model are motor terminal voltage and rotating speed of worm shaft connected with motor. C. The Estalishment of Control System Model For convenience of analysis, the former wheels and Steering linkage mechanism can e simplified to steering shaft. And torque value from torque sensor existed etween steering wheel and steering input shaft can e regarded as driver s input torque. Therefore, EPS system s actual mechanism of truck can e simplified to dynamic model which concludes steering wheel, power-assisted motor and steering shaft. The relational equation among c and m as follows: m Gm (9) c Where, c -- Motor angle; m -- Steering shaft angle; G -- Drive ratio from motor to steering shaft (That is m reduction ratio of Turine worm). The moment inertia and damp of each component have een decided y its material, size and movement relationship which can e gotten through MOTION software. In the control model, we usually ignore the influences on dynamics which frictions from moment inertia and each component. After simplifying, we can get the formula of steering dynamic model. Td Ta Tr (10) Where, Tr -- Steering resistance torque from steering shaft. After the astract and simplification of physical model, in the MATLAB/Simulink, control strategy model and powerassisted motor model are connected y intermediate. Each module is connected in accordance with the required data and we judge the direction of motor power- Fig. 6 The Simulation Model of EPS Control System Fig. 5 Power-assisted motor model assisted torque y adding switch module to avoid that rotating speed of output shaft affects the model when the motor doesn t provide power. The simulation model of EPS control system is as in Fig.6. DOI /IJSSST.a ISSN: x online, print

4 V. THE REALIZATION OF CO-SIMULATION ANALYSIS composed of two data acquisition cards, industrial personal computer 3 and the display etc. In order to achieve the co-simulation of steering and control system, we can use the standard interface etween MOTION modules and MATLAB/Simulink to connect control system and steering dynamic model. There are three steps to achieve this connection. First, the state are designed y the definition in LMS; Second, the corresponding input and output are defined in interface settings; Third, input and output of control system will e connected. The interface definition of co-simulation model is as in Tale 2 Co-simulation model developed y MATLAB/Simulink is as in Fig.7. Data name Tin Tm Tout Omegas Omega MD TABLE II. THE INTERFACE DEFINITION OF CO-SIMULATION MODEL Data representative Input torque from Steering wheel power-assisted torque Steering resistance torque Steering input shaft angle Worm angular velocity Fig. 7 Co-simulation Model MOTIO N output Input Simulink Input output VI. THE CONTRAST OF RESULTS OF SIMULATION AND EXPERIMENT STAND According to the target motorcycle type, design parameters and referring to relevant parameters of similar models, the required simulation parameters of co-simulation have een determined. It is shown in Tale.3. And the relevant experiment has een done y using the EPS performance experiment stand.the experimental and simulation results were analyzed comparatively, in order to verify the correctness of the model and the integrated design method. The EPS performance experiment stand is shown in Fig.8, including the experiment stand portion and the data acquisition system. The experiment stand portion includes EPS systems, sensors, signal generator 2, loading device for drag torque 1 and power supply. Data acquisition system is Fig. 8 Experiment Stand Portion And Data Acquisition TABLE III. PARAMETRIC OF CO-SIMULATION Parametric Motor torque constant Data K 0.07Nm/A a Armature resistance R 0.1Ω EMF coefficient K 0.012V s/rad A. The Contrast of Results of Power-assisted Current Characteristic When pivoting turn and the vehicle speed is 0km/h, the motor will output maximum power-assisted torque. This moment is the most representative, and has a highest request on the staility and real-time of the control system. For this situation, we make the co-simulation and experiments. The trapezoidal wave, which the amplitude is 5Nm, is used as an analog signal of input torque. And the other trapezoidal wave, which the amplitude is 100Nm, is used as an analog signal of resistance torque. According to calculate the worm shaft speed which is 103rad/s, the input shaft speed is 1r/s. This data is set as the amplitude of analog signal of the angular velocity of the worm shaft. During the experiment, the steering wheel has a full cycle from the intermediate position to the right limit, then to the left limit, and then to the intermediate position. The rotation is uniform, and the input torque value and steering wheel speed as much as possile stale in 5Nm and 1r/s, in order to ensure that the approximation of the experimental conditions and simulation. Data curves otained from simulation and experiments and their comparison curves are shown in Fig.9 to Fig.14. In Fig.9, it shows that according to the designed powerassist characteristic curve (corresponding curve of 0km/h),EPS can control the motor to output correct powerassisted torque which changes linearly and has no ovious fluctuation, ased on the input torque and the vehicle speed signal. The power-assisted effect is stale. The Simulation curve of Power-assisted characteristics is highly symmetry, DOI /IJSSST.a ISSN: x online, print

5 which shows that the power-assisted characteristic of the control system are asically consistent when the steering wheel clockwise and counter clockwise rotation. Aove phenomenon is realistic. Fig. 13 The Simulation Curve vs Experimental Curve of Motor Current Fig. 9 The Simulation Curve of Power-assisted Current Characteristic VS Design Curve Fig. 14 The Simulation Curve vs Experimental Curve of Power-assisted Current Characteristic Fig. 10 The Simulation Curve of Input Torque and Motor Current Fig. 11 The Experimental Curve of Input Torque and Motor Current In Fig.10 and Fig.11, respectively, the simulation and experimental results show that the relationship etween the input torque and motor current, and the relationship is asically consistent in each map. From Fig.11 to Fig.14 show that although people turn the steering wheel and the input torque has some fluctuations, the input torque, the motor current, the Power-assisted current characteristics and other experimental curves are asically consistent with the simulation curves. Thus the correctness of the simulation model is verified, and the characteristic of EPS can e reflected truly. B. The contrast of results of No-load rotation torque When the simulation is carried out, the amplitude of the analog signal of resisting moment is set to 0Nm, and the amplitude of the analog signal of input torque is set to 2Nm.The input shaft with the rotating speed of 1r/s from the intermediate position of the steering wheel egins to rotate clockwise and counter clockwise to 90% of the maximum angle (Rotating clockwise is regarded as positive direction and the input corresponding torque is regarded as negative numer when we are standing in front of the steering wheel.) When the experiment is carried out, the torque of the 2Nm is Fig. 12 The Simulation Curve vs Experimental Curve of Input Torque Fig. 15 The Simulation Curve vs Experimental Curve of No-load Rotation Torque DOI /IJSSST.a ISSN: x online, print

6 entered y means of manual rotation with a uniform speed of 1r/s. The contrast curve of simulation and experiment are shown in Fig. 15. The curve in the figure shows that the experimental curve has a certain fluctuation, which is a normal experimental condition. But the change trend of the curve and the simulation results is approximate, which verifies the correctness of the simulation model again. The simulation and experiment are carried out from two aspects of power-assisted current characteristic and no-load rotation torque. The results through contrasting fully show that the proposed method and model are correct and effective in this research. VII. CONCLUSIONS You This paper estalishes the three-dimensional dynamic model of steering y using CATIA and LMS, and the control system model y using MATLAB/Simulink. Based on the two models, mechatronic co-simulation and experimental analysis are carried out. The conclusions are as follows: 1)The simulation and experimental results are asically consistent, which proves the validity and the correctness of the model and method. 2)During the experiment, the input torque rought out y manual ways, which has certain influence on the experiment, such as the fluctuation prolem of the experimental curve, however, reflects the authenticity of the experiment. 3 ) The model uilt can carry out the co-simulation analysis of different control strategies and steering parameters, which can realize the optimization matching of the mechanical and electrical system performance. 4)Based on LMS and Simulink, the model and method put forward y the integrated design of the recirculating-all EPS, solves the prolem of separate design etween control system and steering in the design of recirculating-all EPS. 5)The integrated design of the recirculating-all EPS ased on LMS and Simulink, overcomes the imprecise prolems of EPS model, when referred to the simulation y jointing control system model and vehicle model or y jointing EPS and vehicle model. It lays the foundation for the integrated study of the vehicle with EPS, has more accurate research on the steering performance and the overall performance of the steering and the control system,and has reference significance to the design and research for the mechatronic system. ACKNOWLEDGMENT This work was financially supported y The National Natural Science Foundation of China ( ) and the construction project of Beijing Municipal Education Commission research ase(pxm2014_014224_000065). REFERENCES [1] Dominke Peter, Ruck Gerhard, Electric power steering-the first step on the way to steer y wire, SAE Paper No , Mar [2] Chen J S, Control of electric power steering systems, SAE Paper, No , Fe [3] Chaaan R C,Wang Leyi, H control of electrical power assist systems, JSAE Review,vol.22,no.4,pp ,may [4] Bingying Jin, Yi Lin, Guoiao Shi, Modeling and control strategy of assist characteristic of recirculating-all EPS system for Bus, Transactions of the Chinese Society for Agricultural Machinery,vol.39,no.7,pp.36-41,Jul [5] Wanzhong Zhao, Guoiao Shi, Yi Lin, Bingying Jin, A study on the control strategy of power characteristics of recirculating Ball-Type electrical power steering system, Journal of Beijing Institute of Technology,vol.28,no.8,pp ,Aug [6] Guoiao Shi, Rongwei Shen, Yi Lin, Modeling and simulation of electric power steering system, Journal of Jilin University (Engineering Science),vol.37,no.1,pp ,Jan [7] Wuwei Chen, Peichen Shi, Lixin Gao, Qidon Wang, Liqin Chen, Co simulation study on EPS and full vehicle system ased on ADAMS and Matla, Transactions of the Chinese Society for Agricultural Machinery,vol.38,no.2,pp.22-25,Fe [8] Masahiko Kurishige, Osamu Nishihara, Hiromitsu Kumamoto, A new control strategy to reduce steering torque without perceptile viration for vehicles equipped with electric power steering, Journal of Viration and Acoustics-transactions of the asme, vol.132, pp ,Oct [9] Burton A W, Innovation drivers for electric power-assisted steering, IEEE Control System magazine,vol.23,no.6,pp.30-39,jun [10] Zhongming Xu, Kango Hu, Zhifei Zhang, Yansong He, Modeling and control strategy simulation for automoile EPS system ased on Adams and Matla, Journal of Chongqing University Of Technology (Natural Science),vol.24,no.10,pp.7-11,Oct [11] Dehao Sheng, Anyu Chen, Yongsheng Cao, Jiaxi Zhang, Application and experiment on EPS co-smiulation ased on ADAMS and MATLIB, Mechanical Research & Application,vol.22,no.01,pp.96-99,Jan [12] Jumin Jia,Hongji Wu,Jian Liu,Tianyuan Tang,Jiaqi Qin, Engagement principle recirculating all steering with gear ratio, Journal of Dalian University of Technology(Social Sciences),vol.34,no.03,pp ,Mar [13] Yi Lin, Rongwei Shen, Guoiao Shi, Development of electric control unit in electric power steering system of pure electric power us, Journal of Jiangshu University(Natural Science), vol.27,no.4,pp ,apr DOI /IJSSST.a ISSN: x online, print