**11. Conclusion**

**10. Controlled system in different speeds and different driver** 

driver input torque is represented as a sine wave of 9 N.m amplitude.

**Figure 14.** Driver torque and motor current in 20 km/h.

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

**Figure 14** shows three signals (i) motor current tracking of the look-up table, (ii) driving wheel input torque and (iii) the electric motor output current. The vehicle speed is 20km/h while the

**torques**

98 New Trends in Electrical Vehicle Powertrains

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 time.

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 good assistant in different speeds.
