**4. Simulation result and analysis**

in error on the other hand; therefore, the quantification of the certainty that each rule base applies to the current condition can be obtained upon providing specific values for the

**Figure 5.** Membership functions and their corresponding values. (a) Membership functions and their values for error input *e*(*t*). (b) Membership functions and their values for change of error ∆*e*(*t*). (c) Membership functions and their values for proportional gain. (d) Membership functions and their values for integral gain. (e) Membership functions and their

**2.** Determining the conclusion (what the control action to take) that should be applied by using selected rules to relate to the current situation. This conclusion is classified with a fuzzy set that signifies the certainty that the input to the plant should undertake various

error and change in error.

90 New Trends in Electrical Vehicle Powertrains

values for derivative gain.

values.

The vehicle model and controller algorithms are examined in MATLAB software. For the results of investigation and analysis, the initial vehicle-wheel speeds are set to 100 Km/h, whereas the desired vehicle speed is set to 5 Km/h. The reason of choosing 5 Km/h as the desired vehicle speed instead of zero Km/h is because slip ratio magnitude goes to infinity as vehicle speed approaches zero which in turn leads to inappropriate output behavior. On the other hand, selecting the desired low speed helps to examine maximum slip ratio that controls algorithm derives; hence, the ability to evaluate control performance and output response of the system will be more effective and visible.

The output responses of fuzzy-PID controller for dry asphalt road type are presented in **Figure 6**, whereas **Figure 6(a)** demonstrates the output responses of vehicle-wheel, and **Figure 6(b)** shows the output responses of slip ratio. Yet, the output responses of traditional PID controller are imposed in the same figure (**Figure 6**) to illustrate the comparison between traditional PID controller and fuzzy-PID controller.

As shown in **Figure 6(a)**, both controllers could derive stable output response smoothly. However, the output performance of the fuzzy-PID controller is much better than conventional PID controller since PID controller derives large steady-state error on the one hand and takes long time (approximately 15 seconds) to approach the desired vehicle speed (5 Km/h) on the other hand. In contrast, fuzzy-PID controller overcomes these problems being provided better output performance with zero steady-state error. As a result, fuzzy-PID controller could obtain the required vehicle speed within approximately 9 seconds which in turn assists to reduce stopping vehicle time 60% as compared to PID controller and more importantly the ability of fuzzy-PID controller to eliminate steady-state error to zero. Therefore, fuzzy-PID controller shows superior and outstanding controller.

On the other side, the output response of slip ratio associated with vehicle-wheel speed as shown in **Figure 6(b)** reveals smooth output response particularly before attaining the desired output speed. As depicted from the figure, the maximum slip ratio is the same for both controllers which approximately equals to 0.027. Though the maximum slip ratio magnitude seems a small value, the main cause for vehicle-wheel deceleration is considered since friction force between road surface and wheel surface principally depends on the slip ratio magnitude even though if the slip ratio possesses very small magnitude that may reach to mili-slip ratio.

The other significant notice that can be observed from **Table 4** is the maximum slip ratio of fuzzy-PID controller which is slightly larger than the one derived by PID controller, meanwhile fuzzy-PID performance is considered superior and much better than PID performance as demonstrated above. Accordingly, the slip ratio magnitude is considered extremely important in braking operation even though if it possesses very small value since braking process depends on the road-wheel surfaces. Nonetheless, a certain magnitude range of slip ratio is permissible where if its magnitude exceeds that range, the operating system may undergo unwanted behavior (wheel locks up or losses the control) particularly if it goes to a large value (more than 0.5).

**Road-type controller-type Max. adhesion char. PID Fuzzy-PID** Asphalt (dry) 1.18 0.027 0.028 Asphalt (wet) 0.8 0.035 0.035 Concrete 1.1 0.028 0.029 Cobblestone (dry) 1 0.085 0.087 Cobblestone (wet) 0.34 0.26 0.33

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

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

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It is also concluded that the mathematical derivation and its investigation of the brake system model are accurate and valid particularly because the examination and exploration of the output results are entirely identical to the analysis and investigation of each system's variable as demonstrated in Section 3. Besides, the suggested feedback control signal which is based on wheel speed was able to deliver detailed and thorough information about the status of

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

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

braking system which assists to update system's variable effectively.

**Table 4.** Maximum derived slip ratios for PID and fuzzy-PID controllers.

**5. EPAS system**

and up to 3.5% in city driving [6].

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

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 controller and 0.33 for fuzzy-PID controller).


**Table 4.** Maximum derived slip ratios for PID and fuzzy-PID controllers.

The other significant notice that can be observed from **Table 4** is the maximum slip ratio of fuzzy-PID controller which is slightly larger than the one derived by PID controller, meanwhile fuzzy-PID performance is considered superior and much better than PID performance as demonstrated above. Accordingly, the slip ratio magnitude is considered extremely important in braking operation even though if it possesses very small value since braking process depends on the road-wheel surfaces. Nonetheless, a certain magnitude range of slip ratio is permissible where if its magnitude exceeds that range, the operating system may undergo unwanted behavior (wheel locks up or losses the control) particularly if it goes to a large value (more than 0.5).

It is also concluded that the mathematical derivation and its investigation of the brake system model are accurate and valid particularly because the examination and exploration of the output results are entirely identical to the analysis and investigation of each system's variable as demonstrated in Section 3. Besides, the suggested feedback control signal which is based on wheel speed was able to deliver detailed and thorough information about the status of braking system which assists to update system's variable effectively.
