A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.From the free body diagram, the ordinary differential equation of the vehicle is:m * dv(t)/ dt + bv(t) = u (t) Where:v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass,u [N] is the engine force.Question:Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):A. Use Laplace transform of the differential equation to determine the transfer function of the system. A velocity of a vehicle is required to be controlled and maintained constant even if there aredisturbances because of wind, or road surface variations. The forces that are applied on thevehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, andinertial force (m*a). A simplified model is shown in the free body diagram below.buWhere:mFrom the free body diagram, the ordinary differential equation of the vehicle is:dv(t)dt-+bv(t) = u(t)mv = ia = v= ïv [m/s] is the velocity of the vehicle,b [Ns/m] is the damping coefficient,m [kg] is the vehicle mass,u [N] is the engine force.Question:Assume that the vehicle initially starts from zero velocity and zero acceleration. Then,(Note that the velocity (v) is the output and the force (u) is the input to the system):a. Use Laplace transform of the differential equation to determine the transfer functionof the system.

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.

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