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PID Control of Electric Power Steering System

Ashish Gupta

Department of Mechanical Engineering, MANIT, Bhopal, India &

Shailendra Kumar1

Department of Mechanical Engineering, IIT Bombay, Powai, Mumbai, India &

Rajesh Purohit

Department of Mechanical Engineering, MANIT, Bhopal, India

Abstract In this paper we have studied the electric power steering system for a front wheel- steered, rear-wheel driven four wheels vehicle. A controller has been designed for our model with the help of assist characteristics curves and PID action. We have carried out simulation on different types of vehicle paths which include circular and moose test path. We chose two different cases of steering and for each case we have carried out simulation by considering the two path states. Keywords: electric power steering system, assist characteristics curves, PID controller, circular and moose test path. 1. Introduction The aim of the present work is to develop a control strategy for electric power steering system to find out steering effort applied by the driver. Model based optimization and controls are now accepted by the automotive industry as an effective approach to innovative design to enhance fuel efficiency and reduced exhaust pollution. There are so many challenges in front of designers while designing the electric power steering system. Some of them are:

• To improve motor efficiency using complex algorithms for model-based control. • Minimizing driver torque and acoustic noise to improve human and machine interface. • Need of fast control loops with minimum cycle time to accurate measurement of key

parameters such as torque, motor current and speed of vehicle [1]. • To develop a controller for worst condition.

Fig. 1: EPS steering model[1] 2. PID controller 2.1 EPS based on PID controller In the simulated control system, the convectional PID control system is consists of PID controller and control object. The controller consists of three different parameters that respectively reduce the rise

 

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time, eliminate the steady state error and reduce the settling time and overshoot of the system [3]. Fig. 2 shows the structure of the controller connected to the plant. An error signal {e (t)}, which is the difference between the desired input and actual output is sent to the controller.

Fig. 2: Basic controller schematic [3]

PID controller is a linear controller, which can constitute a control error according to a given value of r (r) and the actual output of y (t), 𝑒  (𝑡)  =    𝑟  (𝑟)  −  𝑦  (𝑡)   (1)

Fig. 3:PID controller [4] It constitutes the control quantity by the linear combination of the proportion (P), integral (I) and differential (D) of error in order to control the objective [3]. The control rule is shown as equation 3[4].

𝑢 𝑡 =  𝐾!𝑒 𝑡 + 𝐾! 𝑒 𝜏 𝑑𝜏!

!+ 𝐾!

𝑑𝑒(𝑡)𝑑𝑡

(2)

Where 𝐾!, 𝐾! ,𝐾!is the proportion gain, parameter of integral, parameter of differential

respectively and 𝑢 𝑡 isthe current input from the controller. Considering the system stability, response time, overshoot quantity and steady-state accuracy, the effect of different parts of PID controller as follows.

Actually, for different control objects, it is not necessary to use all three parts of correction i.e. proportional, integral and derivative in PID controller. If there is only proportion part in the system, which is known as P control, if the system includes proportion part and differential part at the same time, which control known as PD control. Equation (1) shows formula for PD control,

𝑢(𝑡)  =  𝐾!𝑒(𝑡)+ 𝐾!𝑑𝑒(𝑡)𝑑𝑡

(3)

EPS is a system with error, so the controller cannot include in order to maintain the static error of the system. In the EPS, the motor torque and assist torque are decided by the angle difference between two sides of the sensor, therefore the proportion part is selected. If the EPS use the proportion control separately, the steering system can gain enough power torque just in the condition of high proportion coefficient. However the relative damping coefficient will be reduced and a driver can feel the impact caused by the uneven surface clearly. In order to prevent the excessive impact on steering wheel form road surface, differential part is required. 2.2 Tuning of the PID controller

The process of selecting the controller parameters to meet a given performance specification is known as controller tuning [5]. Zeigler and Nichols suggested rules for tuning PID controllers (i.e. setting the values,𝐾!,  𝑇!,  𝑇!) based either on experimental step responses or based on the values of 𝐾! that result in marginal stability when only proportional control action is used. The Ziegler-Nichols rules, which are briefly presented in Section 2.3, suggest a set of values of  𝐾!,  𝑇! and 𝑇! that will enable stable operation of the system. However, the resulting system may exhibit a large maximum overshoot in the step response, which is usually unacceptable. In such a case iterative fine tuning is required until acceptable results are obtained.

 

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Table 1: PID controller characteristics in a closed loop system [5]

Controller Response Rise Time Overshoot Settling Time Steady State Error 𝐊𝐩 Decrease Increase Small Change Decrease 𝐊𝐢 Decrease Increase Increase Eliminate 𝐊𝐝 Small Change Decrease Decrease Small Change

3. Simulation results

Simulations were performed in Matlab /Simulink in order to evaluate assist characteristic of EPS and torque sensor responses. The simulations were carried out for the vehicle following a particular path. Two type of path were considered i.e. (1) circular path and (2) moose test path. Also simulations were carried to observe, how assist vary with load of thevehicle. PID controller is used with different values of𝐾!,𝐾! ,𝐾!. The controller takes signals from torque and speed sensor. According to the signal input, controller decides how much torque is required, according to that it sends the current signal to the assist motor as shown in Fig. 6.

Fig. 4: Simulink control block for EPS

3.1: With EPS and without EPS at load 15 N

In case of EPS driver torque is less than 15 N-m while in case of without EPS it is more than 15 N-m. This shows that driver needs to apply more torque in case of without EPS.

Fig. 5: Driver torque at circular path at 15 N Fig. 6: Driver torque at moose test path at 15 N

 

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3.2 Driver torque at different road stiffness

Fig. 7: Driver torque at circular path for

different road stiffness Fig. 8: Driver torque at moose test path for

different road stiffness 3.3 Time responses of three types of steering

Fig. 9: Time responses

4. Conclusions The simulation result shows that the introducing of a feedback to EPS is an effective way to

improve the vehicle performance. EPS with torque control play a significant role in portability when the vehicle is turning at low speed and cornering. We can say that our controller can provide good steering efforts. The EPS control logic for reduction in steering torque, realization of various steering feels have been proposed in this research. In addition, the torque sensor capable of measuring the steering torque and steering wheel angle is devised, and it provides sufficient accuracy of steering torque for the EPS system. With the EPS logic for a reduction in steering torque, the driver can turn the steering wheel with a significantly reduced steering torque. It is also shown that the steering torque can follow the reference steering torque determined from a torque map reasonably well, independent of load torques which tend to vary depending on the driving conditions. References [1] Jeongjun Lee, Hyeongcheol Lee, Jihwan Kim, JiyoelJeong “Model-Based Fault Detection and

Isolation for Electric Power Steering System”, International Conference on Control, Automation and Systems, Oct. 17-20, 2007, COEX, Seoul, Korea

[2] H. Harun, “Simulation an Active Suspension System for PEUGEOT 206,” Universiti Teknikal Malaysi, 27 June 2013.

[3] X. Chen, T. Yang, X. Chen, K. Zhou. ( 2008) “A Generic Model Based Advanced Control of Electric Power Assisted Steering Systems”, IEEE Transaction on Control Systems Technology, vol. 16, pp. 1289-1300.

[4] Fan Chang-sheng, GUO Yan-ling. (2012) “Design of the Auto Electric Power Steering System Controller”, Procedia Engineering, Vol. 29, 2012, pp. 3200 – 3206.

[5] Tsung-Hsien Hu, Chih-Jung Yeh, Shih-Rung Ho., “Design of Control Logic and Compensation Strategy for Electric Power Steering Systems”, IEEE vehicle power and propulsion conference (VPPC), September 3-5, 2008 Harbin, China.