Explanation Given: G F C ( s ) = ( 0.5 + 2 s ) G V ( s ) = ( 1 1 + 3 s ) G L C ( s ) = ( 0.5 + K s ) G f w ( s ) = 2 s ( 25 s + 1 ) ( 2 s 2 + 2 s + 1 ) Concept Used: From the given block diagram representation obtain the characteristic equation. And by using the characteristic equation make the Routh table. And as we know that for system stability the values in first column of the Routh table must be positive. Thus, find out the range of gain for all positive values in first column of the Routh table. Calculation: On solving the given block diagram: G F C ( s ) × G V ( s ) = ( 0.5 + 2 s ) ( 1 1 + 3 s ) = 0.5 + 2 s 1 + 3 s On solving the inner feedback loop T ' ( s ) = G ( s ) 1 + G ( s ) H ( s ) = 0.5 + 2 s 1 + 3 s 1 + 0.5 + 2 s 1 + 3 s = 0.5 + 2 s 1 + 3 s 1 + 3 s + 0.5 + 2 s 1 + 3 s = 0.5 + 2 s 5 s + 1.5 G L C ( s ) × T ' ( s ) + G f w ( s ) = ( 0.5 + K s ) 0.5 + 2 s 5 s + 1.5 2 s ( 25 s + 1 ) ( 2 s 2 + 2 s + 1 ) On solving for the characteristic equation: - 1 + G ' ( s ) H ( s ) = 1 + ( 0.5 + K s ) 0.5 + 2 s 5 s + 1.5 2 s ( 25 s + 1 ) ( 2 s 2 + 2 s + 1 ) × 1 = 0 ( 5 s + 1.5 ) ( s ( 25 s + 1 ) ( 2 s 2 + 2 s + 1 ) ) + ( 0.5 + K s ) ( 0.5 + 2 s ) ( 2 ) = 0 ( 5 s + 1.5 ) ( 25 s 2 + s ) ( 2 s 2 + 2 s + 1 ) + ( 1 + 2 K s ) ( 0.5 + 2 s ) = 0 ( 5 s + 1.5 ) ( 50 s 4 + 50 s 3 + 25 s 2 + 2 s 3 + 2 s 2 + s ) + ( 1 + 2 K s ) ( 0.5 + 2 s ) = 0 ( 5 s + 1.5 ) ( 50 s 4 + 52 s 3 + 27 s 2 + s ) + 0.5 + 2 s + K s + 4 K s 2 = 0 250 s 5 + 260 s 4 + 135 s 3 + 5 s 2 + 75 s 4 + 78 s 3 + 40.5 s 2 + 1.5 s + 0.5 + 2 s + K s + 4 K s 2 = 0 250 s 5 + 335 s 4 + 213 s 3 + 45.5 s 2 + 3.5 s + K s + 4 K s 2 + 0.5 = 0 250 s 5 + 335 s 4 + 213 s 3 + ( 45

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ISBN: 9781119185666

Author: NISE

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Chapter 6, Problem 61P

To determine

The range of level controller’s derivative gain K for the system stability.

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Chapter 6, Problem 60P

Chapter 6, Problem 62P

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Chapter 6 Solutions

CONTROL SYSTEMS ENGINEERING

Ch. 6 - Prob. 1RQ Ch. 6 - Prob. 2RQ Ch. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQ Ch. 6 - Prob. 6RQ Ch. 6 - Prob. 7RQ Ch. 6 - Prob. 8RQ Ch. 6 - Prob. 9RQ Ch. 6 - Why do we sometimes multiply a row of a Routh...

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