Consider the following open-loop transfer functions, where G(s) = Y(s)/U(s). Y(s) is the Laplace transform of the output, and U(s) is the Laplace transform of the input control signal:

i.

ii.

iii.

iv.

v.

For each of these transfer functions, do the following:

a. Draw the signal-flow graph in phase-variable form.

b. Add state-variable feedback to the signal-flow graph.

c. For each closed-loop signal-flow graph, write the state equations.

d. Write, by inspection, the closed-loop transfer function, T(s), for your closed-loop signal-flow graphs.

e. Verify your answers for T(s) by finding the closed loop transfer functions from the state equations and Eq. (3.73).

(s+3) G(s) = (s +4)?