Question

P7.3 Consider a unity feedback system with open-loop transfer function $\frac{K}{(s+a)(s+b)}$. When the closed-loop system is subjected to a step input, the output has an overshoot of $16.3 \%$ but ultimately attains the final value of 1 . The response to a ramp input has a steady-state error of 0.0625 . (a) Find the value of $K, a$ and $b$. (b) Mark the closed-loop poles. (c) If the gain is doubled, find the closed-loop poles and mark it on the s-plane. (d) Find percentage overshoot corresponding to the gain obtained in (c).

   P7.3 Consider a unity feedback system with open-loop transfer function $\frac{K}{(s+a)(s+b)}$.
When the closed-loop system is subjected to a step input, the output has an overshoot of $16.3 \%$ but ultimately attains the final value of 1 . The response to a ramp input has a steady-state error of 0.0625 .
(a) Find the value of $K, a$ and $b$.
(b) Mark the closed-loop poles.
(c) If the gain is doubled, find the closed-loop poles and mark it on the s-plane.
(d) Find percentage overshoot corresponding to the gain obtained in (c).

Modern Control Systems

Dorf 11th Edition

Chapter 7, Problem 3

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Step 1

The percentage overshoot (PO) is given by $ PO = 16.3\% $. The relationship between the percentage overshoot and the damping ratio $ \zeta $ of a second-order system is given by: \[ PO = 100 e^{-\frac{\pi \zeta}{\sqrt{1-\zeta^2}}} \] Solving for $ \zeta $ Show more…

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P7.3 Consider a unity feedback system with open-loop transfer function $\frac{K}{(s+a)(s+b)}$. When the closed-loop system is subjected to a step input, the output has an overshoot of $16.3 \%$ but ultimately attains the final value of 1 . The response to a ramp input has a steady-state error of 0.0625 . (a) Find the value of $K, a$ and $b$. (b) Mark the closed-loop poles. (c) If the gain is doubled, find the closed-loop poles and mark it on the s-plane. (d) Find percentage overshoot corresponding to the gain obtained in (c).

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