Question

Suppose that feedback to the steering mechanism of the boat contains one term that is proportional to the error, e(t) = y(t) - g(t), and a second term that is proportional to e'(t). Then: (I)y''(t) = -ke(t) -ue'(t), where I is the moment of inertia of the steering shaft, and k and u are positive constants. (Here, y(t) is the actual direction of the boat, and g(t) is the intended direction). Suppose that the intended direction is a constant (that is, g(t) = a), and that y(0) = y'(0) = 0. Determine e(t) under the assumption that u<2((Ik)^.5)

Answer 1

I'm supposed to solve this using Laplace transforms and the initial conditions

Answer 2

the left side = I(s^2)Y

Answer 3

the right side = -kE + u(sE)

Answer 4

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