Project-02: Starting from the continuous-time component model of car dynamics developed and used in the previous project and using the same parameters given in the previous project, we wanted to regulate the speed of the car at a desired speed by adding cruise contraller to it. The cruise controller will be used to compute the needed force "P" to move the car at the desired speed, for example use R-15 m/sec. 1. Add a proportional P-controller with gain Kp 600 to the car model as cruise controller. Test the controller performance for different grades of the road, i.e., of 0 8 deg, und 0-12 deg. In cach case plot the velocity (speed) response of the car as function of time. Explain what you have observed of the car responses? Set the total simulation time t = 120 soc. 2. Now add to the cruise controller an integral part with KI-40 so the controller becomes Pl-controller. Repeat item-! using the Pl-controller as the car cruise controller. Explain any difference between the performance of the P-controller and the l'1-controller? 3. Change the linearized disturbance input signal to follow a sinusoidal signal 0 (t)- (1/3)*sin(1/24) measured in radians. This function models change in the road condition as the car driving on it. Repeat items 1 and 2 above using the "p" then PI-controller as the car cruise controller. Plot the velocity (speed) response of the car for at least two cycle of the road disturbance. Explain any difference between the performances of the P-controller and the PI-controller it'any? 4. If no significant difference was observed between the performances of the two controllers on the car speed, try to tune (increase) the integral gain KI so that the variation in the car speed due to changing road incline will be less than 1% of the desired speed (15 m/sec). Which cruise controller would you buy Por Pl-controller? Explain why?