**6. System modeling**

The EPAS includes a torque sensor, which senses the action of the driver along with the action of the automobile; an ECU, which performs calculations on assisting force based on signals from the torque sensor; a motor, which creates turning power based on the output from ECU; and a reduction gear, which increases the turning force from the motor and transfers it to the steering system and pinion and rack (**Figure 8**).

The parameters associated with the rack model are *Mr* (steering tie rod mass), *Br* (steering tie rod damping coefficient), *Rs* (radius of pinion steering), and *Kr* (tire spring rate) (**Table 5**).

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**Figure 8.** EAPS dynamic model.

**Figure 7.** Typical EPAS fuel consumption saving.

94 New Trends in Electrical Vehicle Powertrains

control or sliding mode control based on modern control theory [10].

(steering tie rod mass), *Br*

(tire spring rate) (**Table 5**).

(steering tie

Literature [11] using the motor current tracking control based on conventional PID achieved good results. But the system was not designed for different car speeds. Literature [12] established an EPAS mathematical model, and the simulation results showed that the strategy could achieve the desired characteristics, but the vehicle speed was not taken into account; the results had certain limitations [13, 14], using a sliding mode control that improved the system stability and anti-disturb capability but that increased the complexity of the control system, which set higher requirement of the computing power to the control ship. That is not beneficial to the promotion of products. The aim of this study in EPAS is to control the electric motor to supply the appropriate assist torque to decrease the driver's steering effort in various speeds. The EPAS control must ensure the generation of the desired assist torque, a stable system with a large amount of assistance. The most important issue is electric motor tracking precisely the target current. To develop the electric motor current tracking performance, particle swarm optimization (PSO) algorithm is applied as tuning mechanism for fractional-order PID (FOPID) controller.

The EPAS includes a torque sensor, which senses the action of the driver along with the action of the automobile; an ECU, which performs calculations on assisting force based on signals from the torque sensor; a motor, which creates turning power based on the output from ECU; and a reduction gear, which increases the turning force from the motor and transfers it to the

(radius of pinion steering), and *Kr*

the state-space model *H*<sup>∞</sup>

**6. System modeling**

rod damping coefficient), *Rs*

steering system and pinion and rack (**Figure 8**).

The parameters associated with the rack model are *Mr*


**Table 5.** Parameters of EPAS system [14, 15].

#### **7. EPAS controller**

The function of ECU is to collect the torque sensor and the vehicle speed signal, select a suitable motor target current by an assist characteristic curve, execute a control by comparing with the feedback actual current, and then drive the DC motor.

#### **8. Fractional-order PID (FOPID) controllers**

Fractional-order PID (FOPID) controller denoted by *PID* was proposed by Igor Podlubny [16] in 1997. It is an extension of conventional PID controller where λ and μ have fractional values. **Figure 9** shows the block diagram of FOPID controller. The fractional-order PID (FOPID) controller is a generalization of the PID controller. The transfer function of the controller is written by the equation below:

$$\mathbf{C}(\mathbf{s}) = K\_p + \frac{K\_i}{S^1} + K\_d S^\mu \tag{3}$$

in designing PID controller and gives an opportunity to better adjust the dynamics of control system. This increases the robustness of the system and makes it more stable. However, with increase in parameters to be tuned, the optimization problem associated with the system becomes more difficult [17]. For achieving a certain performance, it is desired to develop a

Worked Example of X-by-Wire Technology in Electric Vehicle: Braking and Steering

http://dx.doi.org/10.5772/intechopen.76852

97

**Figure 12** shows an open-loop response of system, as depicted in the figure below, that motor current cannot follow the step unit. The close-loop unit step response of EPAS system using

systematic algorithm for the FOPID optimization as shown in **Figure 11**.

**Figure 11.** (a) Classical PID controller and (b) FOPID controller.

classical PID controller and PSO-FOPID are shown in **Figure 13**.

**Figure 12.** Unit step response of EPAS open-loop system.

**9. Simulation results**

where *Kp* ,*Ki* , and *Kd* are the proportional gain, integral gain, and derivative time constants, respectively, and *λ* and *μ* are fractional powers.

where μ and λ are an arbitrary real numbers. Taking μ = 1 and λ = 1, a classical PID controller is obtained. Thus, FOPID controller generalizes the classical PID controller and expands it from point to plane as shown in **Figure 10**. This expansion provides us much more flexibility

**Figure 9.** Fractional-order PID controller.

**Figure 10.** Control strategy.

Worked Example of X-by-Wire Technology in Electric Vehicle: Braking and Steering http://dx.doi.org/10.5772/intechopen.76852 97

**Figure 11.** (a) Classical PID controller and (b) FOPID controller.

in designing PID controller and gives an opportunity to better adjust the dynamics of control system. This increases the robustness of the system and makes it more stable. However, with increase in parameters to be tuned, the optimization problem associated with the system becomes more difficult [17]. For achieving a certain performance, it is desired to develop a systematic algorithm for the FOPID optimization as shown in **Figure 11**.

#### **9. Simulation results**

**7. EPAS controller**

96 New Trends in Electrical Vehicle Powertrains

where *Kp*

,*Ki* , and *Kd*

The function of ECU is to collect the torque sensor and the vehicle speed signal, select a suitable motor target current by an assist characteristic curve, execute a control by comparing

Fractional-order PID (FOPID) controller denoted by *PID* was proposed by Igor Podlubny [16] in 1997. It is an extension of conventional PID controller where λ and μ have fractional values. **Figure 9** shows the block diagram of FOPID controller. The fractional-order PID (FOPID) controller is a generalization of the PID controller. The transfer function of the con-

*K*\_\_*i*

where μ and λ are an arbitrary real numbers. Taking μ = 1 and λ = 1, a classical PID controller is obtained. Thus, FOPID controller generalizes the classical PID controller and expands it from point to plane as shown in **Figure 10**. This expansion provides us much more flexibility

are the proportional gain, integral gain, and derivative time constants, respec-

*<sup>S</sup><sup>λ</sup>* <sup>+</sup> *Kd Sμ* (3)

with the feedback actual current, and then drive the DC motor.

**8. Fractional-order PID (FOPID) controllers**

troller is written by the equation below:

tively, and *λ* and *μ* are fractional powers.

**Figure 9.** Fractional-order PID controller.

**Figure 10.** Control strategy.

*C*(*s*) = *Kp* +

**Figure 12** shows an open-loop response of system, as depicted in the figure below, that motor current cannot follow the step unit. The close-loop unit step response of EPAS system using classical PID controller and PSO-FOPID are shown in **Figure 13**.

**Figure 12.** Unit step response of EPAS open-loop system.

When the input torque of driving wheel *Td*

**11. Conclusion**

time.

good assistant in different speeds.

University, Birzeit, Palestine

Putra Malaysia, Selangor, Malaysia

\* and Mohd Khair Hassan2,3\*

\*Address all correspondence to: asider@birzeit.edu and khair@upm.edu.my

**Author details**

Selangor, Malaysia

Ameer Sider1

and *Tdmax* <sup>=</sup> <sup>7</sup>*<sup>N</sup>* . *<sup>m</sup>*, motor current has a rising with *Td*

is above *Tdmax*, the motor output is a constant torque.

does not provide power, so the assist current would be zero, when *Td*

In this study, a design of fuzzy-PID controller for BBW system is presented. In addition to that, a design structure for BBW is proposed which helps to elaborate a principle of work of the suggested BBW system. The braking mechanism and operation of BBW system are grasped and realized by obtaining mathematical derivation of the brake system based on quarter car model. Two controller algorithms based on PID and fuzzy-PID controllers are then implemented to check the validity of mathematical derivation on the one side and to operate braking mechanism of BBW on the other side. The simulation result which is conducted on different road types and conditions shows that fuzzy-PID controller is a superior and outstanding controller as compared to PID controller, where the fuzzy-PID controller assists to reduce stopping vehicle time 60% and the most important thing is the ability of fuzzy-PID controller to improve the system performance by eliminating steady-state error to zero. Besides, the result analysis and investigation demonstrate that larger adhesion characteristics lead to produce larger brake force which in turn assists to reduce vehicle stopping

For EPAS system, FOPID (fractional-order PID) controller has been presented, and it was tuned to control the motor current. All simulations for the whole EPAS system are implemented by MATLAB/Simulink software showing a comparison of classical PID and optimal PID tracking performance. PSO algorithm has been implemented to find optimal values of FOPID parameters. From the simulation results, it fulfills the control objectives and achieves

1 Department of Mechanical and Mechatronics Engineering, Faculty of Engineering, Birzeit

2 Department of Electrical and Electronic Engineering, Faculty of Engineering, Universiti

3 Institute of Advanced Technology, Faculty of Engineering, Universiti Putra Malaysia,

is less than the threshold value *Td*<sup>0</sup> <sup>=</sup> <sup>1</sup>*<sup>N</sup>* . *<sup>m</sup>*, motor

Worked Example of X-by-Wire Technology in Electric Vehicle: Braking and Steering

, and it depends on the car speed. When *Td*

http://dx.doi.org/10.5772/intechopen.76852

is between *Td*<sup>0</sup> <sup>=</sup> <sup>1</sup>*<sup>N</sup>* . *<sup>m</sup>*

99

**Figure 13.** Unit step response of EPAS system using classical PID and optimal FOPID.
