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P4: The car model of a cruise control system is given in the following transfer function block diagram ms + b Where v is the car speed u is the control force m is the mass of the vehicle, 1000 kg b is the damping coefficient, 50 N s/m More details are available here (1) Derive the differential equation relating y(t) to u(t) (2) Determine the time constant of the car dynamics (from u to v) If a proportional feedback control is used in cruise control as shown below: ms + b Where ^ is the reference speed, 10 m/s e is the tracking control error Kp is the proportional control gain (3) Derive the closed-loop transfer function from reference R to the actual car speed (4) Determine the expression for the time constant of the closed-loop transfer function obtained in (3) Discuss the relationship between the closed loop time constant and the time constant of the vehicle a. (5) IfKp-2455 N -s/m, Determine the time constant of the closed-loop system The steady state error. [Ans: 290] a. b.
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