**5. EPAS system**

**Figure 6.** Output responses of fuzzy-PID controller for dry asphalt road type. (a) vehicle-wheel speed. (b) Slip ratio.

controller and 0.33 for fuzzy-PID controller).

92 New Trends in Electrical Vehicle Powertrains

This fact is clearly observed from **Figure 6(b)**, especially within the time interval [2, 4] seconds, where the slip ratio of fuzzy-PID controller output response (blue line) has larger magnitude than PID output response (red line) by mili-values. This slight divergence that fuzzy-PID created, by trivial increases in slip ratio magnitude, leads to dramatically improve and enhance output response by decreasing vehicle stopping time 60% as compared to conventional PID controller. As shown in the table, the slip ratio increases as the adhesion characteristic decreases. For instance, the maximum adhesion characteristic of dry asphalt is about 1.18 which is considered a large value; hence, its magnitude-derived slip ratio is small (0.027 for PID controller and 0.028 for fuzzy-PID controller). In contrast, the wet cobblestone adhesion characteristic has a small value (0.34), and therefore its derived slip ratio has a large value (0.26 for PID EPAS presents the continuing future of power-assisted steering technology for passenger vehicles and has already been started to appear in high-volume, lead-vehicle applications; more flexible than traditional hydraulic power-assisted steering (HPAS) system, the fact of EPAS is to supply steering assistance to the driver utilizing an electrically controlled electric motor. EPAS is a classic exemplary case of a smart actuator operating under feedback control. It can provide necessary assist torque in different car speeds and different driver torques [6]. It has been reported in [6] that among electric power-assisted steering (EPAS) system available for passenger cars, EPAS systems provide the best fuel consumption [7–9]. The plot shown in **Figure 7** indicates that EPAS systems have the lowest fuel consumption in comparison to hydraulic power-assisted steering (HPAS) system with savings in excess of 3.0% in average and up to 3.5% in city driving [6].

According to the steering torque, automobile speed as well as road conditions, the system can provide the real-time assistant torque through assist motor to help driver steering and make steering easier and gentle, which guarantees that the driver has the best steering feel in the variety of operating conditions. At present, the design for the assist motor control have mainly two methods: the first one is motor current loop control based on classical control theory and the other one is

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

the state-space model *H*<sup>∞</sup> control or sliding mode control based on modern control theory [10]. 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.

**Figure 8.** EAPS dynamic model.

Driving wheel moment of Inertia *J*

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

**Parameters Symbols Value Units**

Pinion radius *Rs* 0.0078 m Rack and wheel assembly mass *Mr* 32 Kg Viscous rack damping *Br* 650.5 N/(

Motor gear ratio *G* 16.5

Driving wheel damping *Bs* 0.362 N.m.s.rad<sup>−</sup><sup>1</sup>

Motor stiffness *Km* 125 N.m.rad<sup>−</sup><sup>1</sup> Motor inductance *L* 0.0015 Henry Motor resistance *R* 0.15 Ohm

Motor torque constant *Ka* 0.02 N.m.s.rad<sup>−</sup><sup>1</sup> Motor EMF constant *Kb* 0.02 v.s.rad<sup>−</sup><sup>1</sup> Motor moment of Inertia Jm 0.000452 kg

Motor damping Bm 0.003339 N.m.s.rad<sup>−</sup><sup>1</sup> Steering column stiffness Ks 115 N.m.s.rad<sup>−</sup><sup>1</sup>

Tire spring rate Kr 91,061 N.m

*<sup>s</sup>* 0.04 kg

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

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

95

.m<sup>2</sup>

\_\_ m s )

.m<sup>2</sup>

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.
