Question

A closed-loop control system is shown in Figure P2.50. (a) Determine the transfer function $$ T(s)=Y(s) / R(s) . $$ (b) Determine the poles and zeros of $T(s)$. (c) Use a unit step input, $R(s)=1 / s$, and obtain the partial fraction expansion for $Y(s)$ and the value of the residues. (d) Plot $y(t)$ and discuss the effect of the real and complex poles of $T(s)$. Do the complex poles or the real poles dominate the response?

   A closed-loop control system is shown in Figure P2.50.
(a) Determine the transfer function
$$
T(s)=Y(s) / R(s) .
$$
(b) Determine the poles and zeros of $T(s)$.
(c) Use a unit step input, $R(s)=1 / s$, and obtain the partial fraction expansion for $Y(s)$ and the value of the residues.
(d) Plot $y(t)$ and discuss the effect of the real and complex poles of $T(s)$. Do the complex poles or the real poles dominate the response?

Modern Control Systems

Dorf 11th Edition

Chapter 2, Problem 50

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Step 1

- Without the specific diagram or system equations, we assume a general feedback system where $ G(s) $ is the forward path transfer function and $ H(s) $ is the feedback path transfer function. - The transfer function for a closed-loop system is given Show more…

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A closed-loop control system is shown in Figure P2.50. (a) Determine the transfer function $$ T(s)=Y(s) / R(s) . $$ (b) Determine the poles and zeros of $T(s)$. (c) Use a unit step input, $R(s)=1 / s$, and obtain the partial fraction expansion for $Y(s)$ and the value of the residues. (d) Plot $y(t)$ and discuss the effect of the real and complex poles of $T(s)$. Do the complex poles or the real poles dominate the response?

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