Why are the initial conditions of the integrator and engine in hw1cruise.mdl set to 55*50?

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At time=0, the car is not accelerating but is at a constant velocity, v=55 mph (so vdot=0). From the car dynamics 1000*vdot = -50*v + u, initially u = 50*v = 50*55.

Thus, the engine delay needs to have an initial output of u=50*55 to match the dynamics initial u. The integrator output must also be initialized to 50*55 because it is the only part of the controller that has any output at t=0 and this goes into the engine delay block. Note, the negative feedback cancels the ref=55 with the initial state of y=v=55, so there is no initial contribution from the proportional gain.

John