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Control Systems Engineering | 7th Edition | ISBN: 9781118170519 | Authors: Norman J. Nise
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For the unity feedback system given in Figure P9.1 with Gs

Chapter 9, Problem 22

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QUESTION:

For the unity feedback system given in Figure P9.1 with

G(s) = \(\frac{K}{s(s+5)(s+11)}\)

do the following: [Section: 9.4]

a. Find the gain, K, for the uncompensated system to operate with 30% overshoot.

b. Find the peak time and \(K_v\) for the uncompensated system.

c. Design a lag-lead compensator to decrease the peak time by a factor of 2 , decrease the percent overshoot by a factor of 2, and improve the steady-state error by a factor of 30. Specify all poles, zeros, and gains.

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QUESTION:

For the unity feedback system given in Figure P9.1 with

G(s) = \(\frac{K}{s(s+5)(s+11)}\)

do the following: [Section: 9.4]

a. Find the gain, K, for the uncompensated system to operate with 30% overshoot.

b. Find the peak time and \(K_v\) for the uncompensated system.

c. Design a lag-lead compensator to decrease the peak time by a factor of 2 , decrease the percent overshoot by a factor of 2, and improve the steady-state error by a factor of 30. Specify all poles, zeros, and gains.

ANSWER:

Step 1 of 8

Part (a)

Find the gain, , for the uncompensated system to operate with 30% overshoot.

Solution:

The relation to find the gain , is given as follows:

For 30% overshoot it is given as,

Here,  is the overshoot percentage.

Inserting the value of overshoot in above equation, we get:

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