TECHNICAL NOTE 1265

Model-based development for anelectric power steering systemW Ren1,2∗, H Chen1,2, and J Song2

1CAD Center, Huazhong University of Science and Technology, Wuhan, Hubei, People’s Republic of China2State Key Laboratory of Automotive Safety and Energy Conservation, Tsinghua University, Beijing,People’s Republic of China

The manuscript was received on 27 October 2007 and was accepted after revision for publication on 25 February 2008.

DOI: 10.1243/09544062JMES925

Abstract: A model-based development method for electric power steering (EPS) system hasbeen explored. A practicable model for the EPS system has been established in a full vehiclemechanical system environment. The performance of the electric control system of the EPSsystem has been evaluated in this static analysis environment. The model has then been usedin a dynamic test environment based on dSPACE hardware and software, including Software-in-the-Loop and Hardware-in-the-Loop. The test result validates the simulation model, and showsthat this development method can be used to evaluate the conceptual design of the EPS systemas well as the control software design and testing.

Keywords: electric power steering, model-based development, dSPACE

1 INTRODUCTION

Electric power steering (EPS) system is a very impor-tant component for improving automotive handlingand stability [1]. One of the most important parts ofthe EPS system is the electric control system. It canreceive the signals collected by the sensors for vehi-cle speed, steering angle, steering torque, etc. andcontrol the assistant motor for giving the requiredassistant torque. It has been used in more and morevehicles, and can improve vehicle performance aswell as its efficiency and energy conservation. Thereare some researches for the EPS control strategies toimprove its performance, which is crucial for the EPSdevelopment [2–5].

An EPS system includes the mechanical subsys-tem and the electronic and control subsystem, andit has to work in the full vehicle mechanical system[6–8]. In the development process of the EPS sys-tem, the different subsystems have to be developedin parallel so as to reduce the time and cost of sys-tem development. Cooperation between engineers for

∗Corresponding author: CAD center, Huazhong University of

Science and Technology, 1037 Luoyu Road, Wuhan, Hubei 430074,

People’s Republic of China. email: renweiqun@tsinghua.org.cn

developing different subsystems is also needed. There-fore, a model-based development is a rational way forthis parallel developing and cooperation.

In this paper, a model-based development methodfor EPS system has been explored. A practicable modelfor the EPS system has been established in a full vehiclemechanical system environment. The electric con-trol system performance of the EPS system has beenevaluated in this environment. This model has beencorrelated with test data using Hardware-in-the-Loop(HiL) method and dSPACE hardware and software.

2 MODEL-BASED DEVELOPMENT PROCESS

The model-based development method has beenwidely used for the vehicle component development,especially for the electric control systems. The pro-cesses include the development requirement from thefull vehicle level to the component level. A simulationmodel is established, and the static analysis as wellas the Model-in-the-Loop (MiL) simulation has beenfinished for the review. Thus, the software and hard-ware have been developed using the Rapid ControlPrototype tools. And the Software-in-the-Loop (SiL)simulation and HiL simulation have been finished inthe dynamic test. All these processes, which are shown

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Fig. 1 Model-based development method [9]

in Fig. 1, are based on the reuse of the simulationmodel [9].

The method above is used for EPS development,simulation, and evaluation. The first phase of this pro-cess is the building of a reusable system-level model.The EPS model should be involved in a full vehi-cle model. The second phase is using this simulationmodel for MiL evaluation. The model is reviewed andoptimized in this static analysis phase. The third phaseis to transfer the optimal model to the SiL and HiLenvironment, and the performances for the controlsystem software and hardware can be checked andmade sure in this dynamic test phase. After severalphases’ evaluation and optimization, the control sys-tem software and hardware can fulfill the requirementof the EPS system completely. The mechanical systemand control system can be jointed, and this model-based development process can be used for the EPSsystem development.

3 MODELLING AND STATIC ANALYSIS

An EPS system includes subsystems of different types.Hence, the EPS system model should include these dif-ferent types of subsystems, and it should be a hybridmodel. The model should be in system level, so thatit can be used for evaluating the effect of differentcomponents for the full system.

The system-level model includes a mechanical sub-system model for a full vehicle, and for the steeringsystem in detail. This mechanical model for the fullvehicle and the steering system is established in thesoftware MSC.ADAMS. It includes the suspensions forthe four corners. The steering system’s mechanicalmodel includes the steering wheel, steering column,steering rack/pinion, and some connection poles. Thechassis model is coupled with the road surface by tiremodel, which is built based on the MSC.ADAMS/TIRE

Fig. 2 Full vehicle’s mechanical system model

module. This method is used in vehicle dynamicsmodelling, and the full vehicle model is shown in Fig. 2.

This mechanical subsystem model for the full vehi-cle and the steering system can be used for gatheringthe necessary signals from the sensors, which is theinput for the control system. There are some variablessetting in the steering column, shown in Fig. 2, whichperform the functions of sensors. They can collect theuseful data from sensor signal, which can be used inthe control strategy, such as the steering angle, steer-ing torque, and vehicle speed. The mechanical modelis also the final implementation for the control sys-tem, which receives the control system output signaland performs correspondingly.

The control subsystem model includes signals fromthe sensors, signals to the actuators, and the controlstrategies for the signals. The controller receives inputsignals from the sensors, and sends output signalsto the actuators after calculating the control strat-egy. As the sensor signals are from the mechanicalsubsystem and the actuator signals are sent to themechanical subsystem, the mechanical model is cou-pled with the controller model. The control subsystemis modelled in MATLAB/Simulink, and the couplingof these two sets of software is implemented bythe MSC.ADAMS/Control module. The control systemmodel is shown in Fig. 3.

In the control scheme, the shadowed square is theblock exported from MSC.ADAMS/Control. From thismechanical subsystem model block, the control sys-tem input, including steering angle, steering torque,vehicle speed, etc, can be collected from the sensorsignals. These signals are sent to a typical proportionalintegral derivative (PID) controller, which is widelyused in EPS controllers. The PID controller processesthe signals from the sensors and gets a target currentfor the assistant motor. The target current is then com-pared with the current sensor signals of the motor,and the difference is used by the control strategy toproduce the controller output, which is serially sentto the pulse width modulation (PWM) and the motor.

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Fig. 3 Control system model for EPS, including full vehicle model exported from ADAMS

PWM is used to control the motor armature voltage,which can be expressed as a lag block following the PIDcontroller block in MATLAB/Simulink. The motor canproduce the assistant torque, which can be expressedas another lag block following the PWM block in MAT-LAB/Simulink. The assistant torque produced by themotor performs on the steering column directly, as themotor is installed on the steering column. In the simu-lation model above, the controller output torque signalis sent to the mechanical system, and it performs atorque on the steering column model.

As shown in Fig. 3, the use of MSC.ADAMSand Matlab together results in co-simulation. How-ever, the co-simulation is off-line simulation, asMSC.ADAMS simulation is not a real time one. TheMSC.ADAMS/Control exported block can be inte-grated into the MATLAB/Simulink model, and theMATLAB/Simulink solver can handle the communica-tion timestep issue. The mechanical system produceddifferential-algebra equations together with the con-trol system produced equations can be solved byMATLAB/Simulink arithmetic. As the STIFF problemcan be found in some issues, an appropriate arithmeticshould be chosen for solving this problem.

This off-line co-simulation model can be used toevaluate vehicle performance under the EPS controlsystem and control strategy effect. Several test condi-tions are the same as those in the physical prototypeexperiments chosen for the open-loop virtual tests,such as the step angular input test, impulse angu-lar input test, sinusoidal angular input test, and the

close-loop virtual tests, such as double lane changetest, slalom test, etc. The result includes the steeringtorques performed by the EPS system and the handtorques implemented by the driver. The virtual testresult with EPS system is compared with the test with-out EPS system. From the result, it is obvious that thesteering torque from the driver’s hands can be reducedwith the EPS system assistance.

This off-line simulation above can be described asan MiL environment. The MiL phase can be used forthe controller research and development. For instance,the parameters of the PID controller (Kp, Ki, Kd) can

Fig. 4 The structure of the EPS test system based ondSPACE

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1268 W Ren, H Chen, and J Song

be changed and the controller effect can be accessedin the full vehicle level environment. The most fitfulparameter can thus be chosen out, and the optimaldesign for the control strategy can ultimately be found.

4 DYNAMIC TEST

The MiL analysis and reviews can get the resultantoptimal design for the control strategy. But the resultabove is a theoretical one and needs to be checkedin the dynamic test for the performance, such as the

Fig. 5 Test system for EPS

real-time performance, robustness, etc. The dynamictest begins with the download of control software code,which can be using the Rapid Control Prototypingtools, dSPACE. The software code downloaded by thedSPACE system can be checked in the SiL environ-ment, as well as the controller hardware being checkedin the HiL environment.

In the laboratory, a dynamic test environment isestablished. The dSPACE system has been used forbuilding the SiL and HiL environment. The structureof the test system based on dSPACE is shown as Fig. 4.And the test system built up according to this structureis shown in Fig. 5.

In this dynamic test environment, an original steer-ing wheel system is connected with steering columnand steering rack-pinion, which is connected withtwo springs giving the resistant force similar to theroad load condition. This mechanical subsystem isconnected with the control subsystem, which is estab-lished surrounding the dSPACE kernel. A duplicatedsteering wheel is installed above the original steer-ing wheel. Inside the duplicated steering wheel, thereare sensors, which can collect the control input sig-nals such as steering angle and torque. As the testrig is fixed on the ground, the vehicle speed imita-tional signal has to be used from a signal producer. Allthe input signals are sent to the dSPACE I/O channel,

Fig. 6 The test result for the assistant torque in different speeds (a) v = 0 km/h, (b) v = 10 km/h,(c) v = 40 km/h, and (d) v = 80 km/h

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and the dSPACE is connected with a host computer.The MATLAB/Simulink control strategy can be down-loaded into the dSPACE ECU, and the output actuatorsignal is sent to the motor. The motor is installed inthe steering column, and it is connected to the PWMin its frontage. The motor produced assistant torque isused for reducing the hand produced steering torque,which is the basic function for EPS system.

This dynamic test environment can be used for eval-uating the control strategy and the performance of theEPS system. For example, the steering efforts test hasbeen implemented in this test system. The test con-dition is under four different vehicle speeds, as 0, 10,40, and 80 km/h. The steering wheel is given a sinu-soidal angular input, and the sinusoidal input beginsin the 5 s point and ends in the 25 s point, which showsa 20 s time period. The sinusoidal input amplitude is±360◦. The test result is shown in Fig. 6. In this result,Figs 6(a) to (d) show different vehicle speeds: 0, 10,40, and 80 km/h. In the figures, A is the current for themotor (Ampere), which can show the steering assistanttorque. B is the actual steering torque (Nm).

From Figs 6(a) to (d), it can be seen that the motorcurrent for the steering assistant torque at 0 and10 km/h is ≈15 A, and the assistant current is reducedto 7 A at higher speed. It shows that the control strat-egy shown in Fig. 3 can be implemented in the testsystem shown in Fig. 5. The assistant torque can ful-fill the requirement in different vehicle speeds. Theseresults also show that the model-based developmentmethod is valid in the EPS system development.

5 CONCLUSION

1. The model-based development method for the EPSsystem has been explored and can be validated.

2. A practicable model for the EPS system has beenestablished, including the full vehicle mechanicalsystem, the EPS mechanical system, and the EPSelectric control system.

3. The simulation model has been correlated with testdata using the HiL method and dSPACE hardwareand software.

ACKNOWLEDGEMENTS

This paper is sponsored by the Chinese NationalScience Funding (60674067), and the opening founda-tion of State Key Laboratory of Automotive Safety andEnergy Conservation (KF2006-02) in Tsinghua Univer-sity, Beijing, China, which is greatly appreciated. Thesupport from Henglong group, one of the most famousChinese automotive component manufacturers, isalso greatly appreciated.

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