The dynamics of a car is described by the following equation F - Fd - Fj = mv wh

Question

The dynamics of a car is described by the following equation F - Fd - Fj = mv where F is the driving force generated by the engine, Fd is the force due to wind drag, Ff is the friction force acting on the tires, and v is the velocity of the car. The drag force and the friction force can be modeled as Fd = Kdv2, Fj = Kfv where Kd 1.1 N s2/m2 and Kf 0.095 N s/m. If the mass of the car is 1050 kg, find the transfer function for F as input and v as output at the operating velocity of v = V0 = 40 m/s.

Explanation / Answer

F -Fd -Ff = mv'
F - KdV2 - Kfv = mv'

take laplace transform

F(s) - kdV2(s) -kfV(s) = msV(s)

F(s)/V(s)   = (ms +40Kd +kf)

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