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The longitudinal control of an autonomous vehicle consists of speed control and position control, which are implemented as cascaded control loops. It is known that, the vehicle uses an induction motor with the following transfer function, V(8) T(S) 10.0 0.25s + 15,6 where is the torque request and v is the longitudinal velocity of the vehicle. The speed controller must obey the speed limit during its motion and the vehicle can surpass the limit by 10% which is the maximum value permitted by the traffic regulation. a) Design a PI controller for 10% overshoot using dominant pole placement. Choose the dominance factor at least equal to m = 10. Explain your decisions. Uret) Speed Controller Induction Motor Figure 1: The speed control loop for a) Pres) Note that the closed loop for the speed controller designed in a) has an input-output relation The position control of the vehicle is another loop on top of the speed control loop, which means that, the plant of the position control is the closed loop transfer function acquired in a) with an integrator connected to its output, since c = v. The vehicle is allowed to position itself with 5% deviation, but for the controller the deviation is considered as positive deviation, namely, for a reference change of 100 m, the vehicle is allowed to position itself at 105 m. The settling time for the position loop is chosen as 10 sec. b) Design a PI controller for 5% overshoot and 10 sec settling time using dominant pole placement. Aim to maximize the dominance factor of the closed loop. Provide the results and your comments on the results. c) Repeat b) with a PD controller. d) Repeat b) with a PID controller. e) Repeat b) with a PI-PD controller. f) Give the whole autonomous vehicle control system structure with the speed controller and the best performing position controller. Prest) Position Controller Position Plant Figure 2: The position control loop for b)-e)