An Observer Design Strategy in Electric Power Steering System

Transcription

1 An Observer Design Strategy in Electric Power Steering System Jingying Lu,a, Wei Jiang,b, Tomokazu Abe 2, Yu Fujimura 2, Seiji Hashimoto 2,c an Mitsunobu Kajitani 3, Yangzhou University, Huayang west roa 96, Yangzhou 225, CHINA 2 Gunma University, -5- Tenjin, Kiryu, Gunma , JAPAN 3 Aichi University of Technology, 5-2 Nishihasama, Gamagori, Aichi , JAPAN a <58659@qq.com>, b <jiangwei@yzu.eu.cn>, c <hashimotos@gunma-u.ac.jp> an <kajitani@aut.ac.jp> Keywors: Electric Power Steering (EPS), observer, isturbance, HIL Abstract. In orer to achieve precise state variables in electric power steering system, three types of observer consiering applie isturbance are introuce. Disturbance is inclue in the observer s state variables an efine as the step an lamp signals. Designe three observers are compare an evaluate through simulations an experiments. The simulation is carrie out by the MATLAB/SIMULINK, an the experiment is investigate using the harware in the loop (HIL) simulator technology. Experiments guarantee that 5th orer observer can estimate the state variables with minimum error an noise, even though isturbance exists.. Introuction Steering system has been experience four stages of evelopment: manual steering, hyraulic power steering, electro hyraulic power steering an electric power steering (EPS)[,2]. EPS is becoming the mainstream of the steering system because of its avantages such as simple construction, energy saving an environmental protection [3,4]. EPS system is compose of the steering wheel, the electronic control unit, steering assist motor, angular sensor an its torque sensor, etc[5,6]. The EPS system uses steering assist motor to assist power by measuring an analyzing the irection an angle of steering wheel, with the avantage of applicability to autonomous riving [7-]. So the control of the steering assist motor is core technology of the EPS system. This paper compares three observers for the EPS system an evaluates them through simulations an experiments. The experimental results that conform to the simulation guarantee that 5th orer observer can estimate the state variables with minimum error an noise, even though isturbance exists. 2. System Structure 2. Moeling of EPS The representative EPS structure is shown in Fig., which consists of the steering wheel, the electronic control unit, steering assist motor, tire, angular sensor an its torque sensor, etc. The experimental system relate parameters are shown in table J. Tech. Soc. Sci., Vol., No., 27

2 Fig.. Basic construction of EPS system Table Experimental parameters I h.7 kg m 2 Steering wheel inertia I m.94 kg m 2 Motor inertia I T - kg m 2 Tire inertia K h 2.72 N m/ra Torsion bar stiffness K T.46 N m/ra Tire stiffness C T.4 N m s/ra Tire amping N T Steering gear ratio N m - - Motor gear ratio In the EPS system, the equations of motion can be expresse as (), I h θ ḧ + K h (θ h N t θ T ) = T h I m θ m + K h(n t θ T θ h ) + N N m N t T T = T m () m { I T θ T + C T θ T + K T θ T = T T In (), since the reuction ratio are ifferent among the steering shaft, assist motor an tire, it is converte to the tire axis. Two equations in () can be replace by the following equations, I { H θ H + K H (θ H θ M ) = T H (2) I M θ M + C T θ M + K T θ M + K H (θ H θ M ) = T M 2.2 Observer Design The state variables of the EPS system is efine as x = [θ H θ M θ M ] T, so the state space moel of the EPS system can be expresse in (3). Equations (4) an (5) are moifie moels of 5th orer an 6th orer consiering isturbance as step an ramp signals. In these moels, it is assume that the isturbance is applie to the EPS motor torque. θ H θ M ( θ M ) K θ H K H H I = H I H θ H + K H K H + K T C θ T M (3) M T ( I M I M I M ) ( θ M ) ( I M ) J. Tech. Soc. Sci., Vol., No., 27

3 ( Journal of Technology an Social Science (JTSS) K θ H H K H θ θ H I H I H H θ = M K H θ M I ( K H + K T C θ M + T M (4) T θ ) M I M I M I M M I M ( ) ( ) ( ) θ H θ M θ M ) = 2.3 Simulation results K H K H I H I H K H K H + K T C T I M I M I M I M ) ( ( θ H θ M θ M ) + I M ( ) T M (5) The simulation is carrie out by the MATLAB/ SIMULINK, an the EPS moel an observer are built base on the state space moels expresse by (3) to (5). The EPS structure with power assist control is shown in Fig.2. Torsional torque etecte by torque sensor is amplifie with K as as to provie the assist torque by the EPS motor. The banwith for three observers was selecte at 3Hz which was ecie by using MATLAB butterworth filter comman. Observer estimates when a step isturbance is applie at 6s are shown in Fig.3. The estimation error of θ H an θ M by 3 observers are sufficiently small. The estimation error of an θ M by 4th orer becomes constant. The large oscillation appears in the estimation error of an θ M by 6th orer. On the other han, the estimation error of an θ M by 5th orer is small. The estimate isturbance for each observer is shown in Fig.4. The estimate isturbance by 6th orer is settle after.s with % overshoot; the estimate isturbance by 5th orer is settle after.5s with % overshoot. As a result, 5th orer observer is the most suitable to the EPS system. Kas Steering Torque T M T H P(s) K H (θ H -θ H ) θ H State Observer Fig. 2. EPS system with state observer J. Tech. Soc. Sci., Vol., No., 27

4 x (a) Estimation error of θ H (b) Estimation error of (c) Estimation error of θ M () Estimation error of θ M Fig.3 Estimate state variables by three observers, (a) θ H, (b), (c) θ M, () θ M actual isturbance 5th output isturbance 6th output isturbance Disturbance[Nm].5.5 Fig.4 Estimation isturbance by 5th orer an 6th orer observers 3. Experimental Verification The experiments have been implemente by the evelope HIL simulator, which inclues the steering wheel, the electronic control unit, steering assist motor, loa motor, angular sensor an torque sensor, etc. as shown in Fig.5. At first, the steering torque applie by han was evaluate. Moreover, the isturbance torque with step, ramp an sine singles which can be consiere as the roa isturbance was applie by the EPS motor in a pseuo manner J. Tech. Soc. Sci., Vol., No., 27

5 Fig.5 The photo of the experimental setup As a representative result, the observer estimates when the isturbance was applie by han are shown in Fig.6. The estimation error of θ H by 3 observers is sufficiently small. The estimation error of θ M by 3 observers are 5%, however the 4th orer s is bigger than the others as shown in Fig.6(c); the estimation error of an θ M by 4th orer is constant; the big oscillation appears in the estimation error of an θ M by 6th orer, however, the estimation error of θ Ḣ an θ M by 5th orer is small. The experimental results conform to the simulation, so 5th orer is the most suitable structure for the EPS system s observer estimate 6 7 ata by 8 6th orer (a) Estimation error of θ H (b) Estimation error of estimate 7 ata 8by 5th 9orer (c) Estimation error of θ M () Estimation error of θ M Fig.6 Estimate state variables by three observers, (a) θ H (b), (c) θ M, () θ M Moreover, the observer estimates when the step isturbance was applie by EPS motor in a pseuo manner are shown in Fig.7. The estimation error of θ H by 3 observers is sufficiently small J. Tech. Soc. Sci., Vol., No., 27

6 All state variables by 4th orer are constant; the large oscillation appears in the estimation error of an θ M by 6th orer, however, the estimation error of an θ M by 5th orer is small enough. As a result, 5th is the best orer for the EPS observer (a) Estimation error of θ H (b) Estimation error of (c) Estimation error of θ M () Estimation error of θ M Fig.7 Estimate state variables by three observers, (a) θ H, (b), (c) θ M, () θ M Quantitative results to step isturbance were summarize in Table2. As can be seen from Table2, the result of 4th orer has largest error with small noise; the result of 6th orer has smaller error with noise; the result of 5th orer has the smallest error with small noise. The experimental results to the other isturbance when the ramp an sinusoial signal ha analogous characteristics. Therefore it can be conclue that the 5th orer becomes the best structure for the EPS system. Applie by EPS motor Applie by loa motor Table 2 Estimate state variables by three observers Max. error ratio Min. error ratio noise 4th 5th 6th 4th 5th 6th 4th 5th 6th θ H.54%.48%.5%.28%.23%.25% small small small 32.43% 23.64% 26.78% 4.3% 3.32% 3.83% small small meian θ M 2.35% 9.82%.62%.%.87%.93% small small small θ M 3.43% 8.45% % 2.2%.2%.85% small small large θ H.65%.6%.63%.3%.25%.26% small small small 38.34% 26.63% 28.4% 4.69% 3.89% 5.2% small small meian θ M 7.55% 3.44% 3.65%.5%.95%.96% small small small θ M 37.68% 5.43% 2.3% 2.52%.4%.97% small small large J. Tech. Soc. Sci., Vol., No., 27

7 4. Conclusion Journal of Technology an Social Science (JTSS) This paper compare three observers for the electric power steering (EPS) system. The simulation was carrie out by MATLAB/SIMULINK, an then the experiments were investigate using the evelope EPS harware in the loop (HIL) simulator. Experiments show that 5th orer observer can estimate the state variables with minimum error an noise, even though the roa isturbance exists. References [] E. Saito an S. Katsura, Position Control of Resonant System with Loa Force Suppression Using Wave Observer, IEEJ Journal of Inustry Applications, Vol.3, No., pp.8-25, 23. [2] C. Dannöhl, S. Müller an H. Ulbrich, H -control of a rack-assiste electric power steering system, Vehicle System Dynamics, Taylor & Francis, Vol. 5:4, pp , 22. [3] C. Chan, A. Bouscayrol an K. Chen, Electric, hybri, an fuel-cell vehicles: architectures an moeling, IEEE Trans. Veh. Technol, Vol.59, No.2, pp , 2. [4] R. Wang, H. Zhang an J. Wang, Linear parameter-varying controller esign for four wheel inepenently-actuate electric groun vehicles with active steering systems, IEEE Trans. on Control Systems Technology, Vol. 22, Issue 4, pp ,24. [5] V. Yanchevskiy an E. Yanchevskaya, Mathematical Moel of Tire Life Calculation in Real Conitions, Applie Mechanics an Materials, Vol.838, pp , 26. [6] S. Fankem, T. Weiskircher an S. Mller, Moel-base Rack Force Estimation for Electric Power Steering, Proc. of 9th IFAC Worl Congress, Vol.47, Issue 3, pp , 24. [7] J. Lu, P. Wang an Z. Zhan, Active vibration control of thin-plate structures with partial SCLD treatment, Journal of Mechanical Systems an Signal Processing, Vol.84, Part A, pp.53-55, 26. [8] V. Piccirillo, J. M. Balthazar, A. M. Tusset, D. Bernarini an G. Rega, Application of a Shape Memory Absorber in Vibration Suppression, Applie Mechanics an Materials, Vol. 849, pp , 26. [9] Y. Saitho, H. Itoh, F. Ozaki, T. Nakamura an S. Kawaji, Design Metho for EPS Control System Base on KANSEI Structure, IEEJ Transactions on Inustry Applications, Vol.3, No2, 2. [] Mathias Wurges, New Electrical Power Steering Systems, Encyclopeia of Automotive Engineering, Publishe Online: Dec. 23, John Wiley & Sons, Lt., J. Tech. Soc. Sci., Vol., No., 27