Define the first order differential equations

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Reference no: EM131082988

1. For the linear control system with input r(t) and output y(t) which is described by the simulation diagram shown below:

a. Define the first order differential equations using the state variables i.e.,

x^.(t) = A(t) x(t) + B(t) r(t)

b. Define a state variable model for the system in a matrix notation.

c. Use the state space mode to find the transfer function using the following formula:

Y(s)/R(s) = C(SI - A)^-1B + D

2. For the feedback control system shown in the block diagram below, find the transfer function

3. For the feedback control system shown below, sketch the Root-Locus for 0 < k < ∞ on the S-Plane.

where: G(s) = ((S + 2)(S + 4)(S + 6))/((S+ 1)(S + 3)(S+ 5)(S +7)(S +9)(S + 11))

Reference no: EM131082988

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