Question: The differential equation model for a certain speed control system for a vehicle is where the actual speed is , the desired speed is

The differential equation model for a certain speed control system for a vehicle is

ü + (1 + Kpv + Kp = K,va + Kpd

where the actual speed is υ, the desired speed is υ_d(t), and K_p and K_I are constants called the control gains. Use the Laplace transform method to find the unit-step response [that is, υ_d (t) is a unit-step function]. Use zero initial conditions. Compare the response for three cases.

a. K_p = 9, K_I = 50

b. K_p = 9, K_I = 25

c. K_p = 54, K_I = 250

+ (1 + Kpv + Kp = K,va + Kpd

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