Question

P6.16 A system has a closed-loop transfer function \begin{equation} T(s) = \frac{1}{s^3 + 5s^2 + 20s + 6} \end{equation} (a) Determine whether the system is stable. (b) Determine the roots of the characteristic equation. (c) Plot the response of the system to a unit step input.

          P6.16 A system has a closed-loop transfer function
\begin{equation} 
 T(s) = \frac{1}{s^3 + 5s^2 + 20s + 6}
\end{equation}
(a) Determine whether the system is stable. (b) Determine the roots of the characteristic equation. (c) Plot the response of the system to a unit step input.

P6.16 A system has a closed-loop transfer function

T(s) = (1)/(s^3 + 5s^2 + 20s + 6)

(a) Determine whether the system is stable. (b) Determine the roots of the characteristic equation. (c) Plot the response of the system to a unit step input.

Added by William M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

Step 1

If all the roots have negative real parts, then the system is stable. (b) The characteristic equation is obtained by setting the denominator of the transfer function equal to zero: s^3 + 5s^2 + 20s + 6 = 0 Show more…

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P6.16 A system has a closed-loop transfer function 1 T(s)= s3 + 5s2 + 20s + 6 (a) Determine whether the system is stable. (b) Deter- mine the roots of the characteristic equation. (c) Plot the response of the system to a unit step input.