Fuzzy-PID Control for Electric Power Steering

Transcription

1 2017 2nd International Conference on Mechatronics, Control and Automation Engineering (MCAE 2017) ISBN: Fuzzy-PID Control for Electric Power Steering Van-Giao NGUYEN 1,2,3, Xue-xun GUO 1,2,3,*, Cheng-cai ZHANG 1,2 and Ci CHEN 1, 3 1 School of Automotive Engineering, Wuhan University of Technology, Wuhan , China 2 Hubei Key Laboratory of Advanced Technology for Automotive Components 3 Hubei Collaborative Innovation Center for Automotive Components Technology *Corresponding author Keywords: Electric Power Steering, Fuzzy-PID, Return-to-center, Co-simulation technique. Abstract. This paper investigates and designs the fuzzy-pid controller for the Electrical Power Steering (EPS) system. Different from existing controller, in this paper, we establish the on-line fuzzy control rules to adjust the PID parameters. The fuzzy control rules are designed based on the practical conditions and the expert experience. Therefore, this control strategy can overcome the traditional PID controllers. The main advantage of the proposed control algorithm has able the adaptive of control parameters, which will greatly improve the stability of EPS system. Therefore, our fuzzy-pid controller improves significantly the steering maneuverability and steering wheel return ability. In addition, our control strategy improves system performance and robustness. Finally, based on Matlab/Simulink, the simulation model with CarSim is established to demonstrate the effectiveness of proposed controller. Introduction EPS system is gradually replacing the conventional steering system in modern vehicles. They have many advantages compared to the traditional hydraulic power steering systems such as fuel economy, compact size, environment friendliness and increase the vehicle active safety [1,2]. In addition, desired steering feel can be change without major physical modification to valve shape, torsion bar stiffness and boost pressure. This motivated a greatly increase in the demand for EPS system recently. There are two important functions in EPS system, namely, the assist function and the return-tocenter function. The first function can reduce steering torque and present various steering feels. The second function, the EPS system can improve return-to-center performance of steering wheel when it is steered. Meanwhile, the steering wheel is turned and then released during cornering, it returns to the center position by the so called self aligning torque exerted on the tires by the road [3]. However, the motor and reduction mechanism cause the friction and damping effects of steering system increase, which reduce the vehicle return ability [3,4,5]. For this reason, the return control logic for the EPS system has received a lot of attention from the researchers in recent years. Motivated by these observations, several works have been investigated and obtained some valuable results. For example, in [6], the authors have proposed the steering angle feedback control algorithm bases on road reaction torque estimation; in [7], the authors have proposed sliding mode return control. Therein, the controller requires road reaction torque estimation and triggers rules for switching between the assist control and the return control. Also, the PID controller has been proposed by [3], that is, to improve the return-to-center position. In addition, in [8], the authors have designed the PID controllers, which have simple structures and low implementation cost. However, their performance is degraded in the presence of disturbance and uncertainty such as tire forces and friction in the EPS system. In fact, the traditional PID controller certainly cannot deal with the non-linear systems. Besides, EPS system often has the non-linear factors and the time varying parameters. Therefore, it brings the difficulties to establish the precise mathematical models. In [9,10], the authors have improved the system 105

2 stability and anti -disturbance capability based on the robust control theory, but that increased the complex of the system control. This is difficult to be implemented in practical applications. To overcome these problems, this paper investigates the fuzzy-pid controller for the EPS system. It is well-known that the fuzzy controller have a good control effect for the non-linear systems and uncertain properties. Although, the fuzzy-pid control algorithm for EPS system has been investigated in [11,12], their control algorithms is not return-to-center for researching EPS system. In proposed fuzzy controller, the fuzzy control rules are designed based on the practical conditions and the expert experience. Therefore, this controller can overcome the traditional PID controllers, which will greatly improve the stability of EPS system. In addition, our control strategy improves system performance and robustness. Finally, based on Matlab/Simulink, the simulation model with CarSim is given to demonstrate the effectiveness of proposed controller. Principle of C-Type EPS System When a driver steers, the steering torque is detected by a torque sensor, which is placed between the steering wheel and the motor. The measured torque is used as an approximation of the torque that the driver has applied to the steering wheel to determine the amount of assist torque to be provided by the electric motor. The amount of assist torque is typically calculated from the tunable torque boost based on the vehicle s speed and the steering torque applied to the steering wheel. The output torque of the motor is multiplied by the gear arrangement. This assisted torque, combined with the driver s torque, overcomes the steering resistance together, to complete the turning action. The EPS system consists of a torque sensor, a vehicle speed sensor, ECU, motor, and assist mechanisms such as gear box and gear rack. A typical schematic diagram of C-type construction is illustrated in Figure 1. When the vehicle speed surpasses the certain limiting value or the control system certain parts appears the breakdown, Assist mode is shut off forcefully and then turn to completely manual steering mode. The control effect of the EPS is decided to suitable the size and the speed of the assist torque. Figure 1. Column electric power steering system model. Dynamic Model of EPS System The EPS dynamic model establishes a relationship between the steering mechanism, the motor s electrical dynamics, and the tire/road contact forces. EPS can be divided into three subsystems which are Steering column - steering shaft, assist motor and rack - pinion. Each subsystem is represented in the equations (1) to (7). According to Newton s laws of motion, the motion equations can be written as follows: Kinetic equation of steering wheel is expressed as: = + (1) Tc= ( ) (2) Kinetic equation of assist motor is expressed as: 106

3 = (3) kt (4) = (5) Ta= (6) Kinetic equation of rack and pinion is expressed as: = + (7),,, are motor electromagnetic torque, sensor measurement torque, driver torque, assist motor torque, respectively.,, are motor voltage, inductance motor, resistance motor, current motor, respectively., are the steering column inertia and inertia motor, respectively.,,,, are steering column damping coefficient, motor damping coefficient, steering tie rod damping coefficient, respectively.,, are column stiffness, motor stiffness and crack stiffness. G is the gear ratio, respectively. is the radius of pinion steering. C-EPS System Control Strategy Fuzzy-PID controller must provide appropriate assist torque under different operating condition and improve return-to-center performance. To control EPS system, firstly, we need to indicate the steering system current state. When steering wheel angle and angular velocity are in the same direction and the steering torque, Td>T0 (T0 is threshold level), the power assist control mode is selected. When steering wheel angle and angular velocity are in the opposite direction, return-tocenter control mode begins to work. Then add a return compensation current I return to the basic current to improve the vehicle return ability. The return compensation current I return is calculated by closed-loop fuzzy-pid control based on the steering wheel angle. Block diagram of EPS system structure control strategy is described as in Figure 2. Figure 2. Block diagram of EPS system structure control strategy. Design of Fuzzy-PID Controller Fuzzy controller modified PID control parameters based on the input variable s changes during the dynamic process, improving the speed of dynamic response and the ability of resisting disturbance of the EPS system. The inputs of fuzzy-pid controller are error (ER) and error s changes (EC). The fuzzy-pid controller is designed as in Figure 3, where R denotes the reference steering wheel angle. Difference between reference steering wheel angle and real steering wheel angle is ER. 107

4 Figure 3. Block diagram of fuzzy-pid controller. The definition of ER quantity are divided into seven fuzzy subsets {N3, N2, N1, ZO, P1, P2, P3},. The definition of EC quantity are divided into seven fuzzy subsets {N31, N21, N11, ZO, P11, P21, P31}, We select the triangle membership function for the input/output variables membership function. Mandani reasoning and centroid defuzzy algorithm are selected to build the fuzzy control table. After the fuzzification, fuzzy reasoning and defuzzy, fuzzy controller gets the proportion coefficient ΔKp, and the integral coefficient ΔKi. In this way, the controller can meet the needs of parameters of the PID self-tuning in different moments. Establishment of the Simulation Model This research utilizes the co-simulation technique to develop the suitable Fuzzy-PID for the EPS system. We uses the 27 D.O.F.(degrees of freedom) full vehicle model of CarSim. Integrating Matlab/Simulink with CarSim is helpful to design control logic accurately and make it easy to realize the influence of the EPS system on the vehicle motion. Figure. 4 shows the simulation block of the EPS system and the full car model of CarSim in Matlab/Simulink environment. Simulation Results Figure 4. Simulation model of the EPS with CarSim. Figure 5. shows that when the vehicle is driving low speed, the torque steering wheel is small, which makes the steering lightly and maneuverability. Besides, when the vehicle is driving high speed, the torque steering wheel is increasing, which makes the steering steady and stability. In addition, driver torque in situ without assist control is heavy. 108

5 Figure 5. Simulation of maneuverability with the different speed. In order to simulate the operation condition of return-to-center, a certain torque is input to the steering wheel. Then the steering torque should be wiped off immediately. For verifying the control effect of fuzzy PID control, some typical results are shown in Figure 6.(b) and Figure 7.(b) (a) (b) Figure 6. (a) Steering wheel torque input, (b) Angle output of steering wheel. Figure 6.(b) shows the simulation results in low speed (v=15 km/h) return-to-center test. The residual steering wheel angle is about 20.1 degree in the without control case, and is 2 degree in the with control case. Figure 7.(a) shows the input signal of steering wheel torque. (a) (b) Figure 7. (a) Steering wheel torque input, (b) Angle output of steering wheel. Figure 7.(b) shows the simulation results in high speed (v=65 km/h) return-to-center test. The residual steering wheel angle is about 9 degree in the without control case, and is 1 degree in the control case without overshoot. In addition when with control return-to-center respone time is reduced from 5s to 4.2s. Conclusion In this paper, the fuzzy-pid control algorithm for EPS system has been designed to improve the return-to-center performance, reduce driver torque, and realize various steering feels. The fuzzy-pid controller parameters could be adjusted on-line according to working conditions and the dynamic responses of the system. Moreover, we have established successfully co-simulation platform based 109

6 on Matlab/Simulink with CarSim, and the EPS fine model has been appropriately built the real vehicle condition, Finally, simulation results has demonstrated the effectiveness of proposed controller. Acknowledgement This research is supported by the National Natural Science Foundation of China (Grant No ) and the Fundamental Research Funds for the Central Universities (Grant No VII-005) 2014-VII-005). References [1] A. Badawy, J. Zuraski, F. Bolourchi, A. Chandy, Modeling and Analy Electric Power Steering System, SAE Technical Paper, , [2] Dan Holt, Power Steering Gets Electric Boost, Service Tech Magazine, pi 0-11, January [3] Kim Ji-Hoon, Song Jae-Bok, Control Logic for an Electric Power Steering System Using Assist Motor, Mechatronics, (2002) [4] Kurishige, M., Wada, S., Kifuku, T., Inoue, N. et al., A New EPS Control Strategy to Improve Steering Wheel Returnability, SAE Technical Paper , [5] Xu Jianping, He Ren, A Study on Returnability Control Algorithm for Electric Power Steering System. Automotive Engineering, (2004) [6] M. Kurishige, N. M. H. Tanaka, K, Tsutsumi, and T. Kifuku, An EPS control strategy to improve steering maneuverability on slippery roads, Soc. Autom. Eng., Int., Warrendale, PA, SAE Tech. Paper , [7] B. Chen, W. Hsu, and S. Huang, Sliding-mode return control of electric power steering, Soc. Autom. Eng., Int., Warrendale, PA, SAE Tech. Paper , [8] Guo Biao Shi, Rong Wei Shen, Yi Lin, Modeling and Simulation of Electric Power Steering System. Journal of Jilin University, 37(1):31-36, [9] Zhiguo Zhao, Zhuoping Yu, A research on H Robust Control Strategy for Electric Power Steering System, Automotive-Engineering, (2005) [10] N. Sugitani, Y. Fujuwara, K. Uchida and M. Fujita, Electric power steering with H-infinity control designed to obtain road information, In Proc, American Control Conf., (1997) [11] Zhanfeng Gao Wenjiang Wu, J.et al, Electric Power Steering System Based on Fuzzy PID Control, The Ninth International Conference on Electronic Measurement & Instruments, (2009) [12] Huaiquan, Z. and Shuanyong, Electric Power Simulation Analyze Based on Fuzzy PID Current Tracking Control, Journal of computational Information System (2011)