Explanation Given: The below representation of a system: - F ( s ) D O C ( s ) = K c 1 + K c m s 2 + b s + k − K c K f ( 1 T s + 1 ) and k = 2.1 × 10 4 N/m , b=0 .78 Ns/m , m=1 .2 × 10 − 4 kg , K c = 1.5 × 10 4 N/mm , T = 0.004 s Concept Used: Since we know that closed loop transfer function is as below: T ( s ) = G ( s ) 1 + G ( s ) H ( s ) use this to obtain characteristic equation i.e. 1 + G ( s ) H ( s ) , which will be the denominator of closed loop transfer function. For this 1 + G ( s ) H ( s ) make the Routh table. Since we know that number of sign changes in the first column of the Routh table will be equal to the number of closed loop right half plane poles and the system will be unstable. So, we will find the range of k so that system will be stable. Calculation: The characteristic equation 1+G(s)H(s) for the given system can be calculated as: - 1+G(s)H(s)= 1 + K c m s 2 + b s + k − K c K f ( 1 T s + 1 ) = 0 Or on further solving we can have: - = > K f ( m s 2 + b s + k ) ( T s + 1 ) + K f K c ( T s + 1 ) - K c ( m s 2 + b s + k ) = 0 = > K f ( m T s 3 + ( b T + m ) s 2 + ( k T + b ) s + k ) + K f K c ( T s + 1 ) - K c ( m s 3 + b s + k ) = 0 = > ( K f m T s 3 + ( b T + m ) K f s 2 + ( k T + b ) K f s + k K f ) + K f K c ( T s + 1 ) - K c ( m s 3 + b s + k ) = 0 = > K f m T s 3 + [ K f ( b T + m ) - K c m ] s 2 + [ K f

7th Edition

ISBN: 2819770197050

Author: NISE

Publisher: WILEY

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Question

Chapter 6, Problem 59P

To determine

Range of gainKf for the given system to be stable.

F(s)DOC(s)=Kc1+Kcms2+bs+k−KcKf(1Ts+1)

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Chapter 6, Problem 58P

Chapter 6, Problem 60P

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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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Range of gain K f for the given system to be stable. F ( s ) D O C ( s ) = K c 1 + K c m s 2 + b s + k − K c K f ( 1 T s + 1 )

Range of gainKf for the given system to be stable. F(s)DOC(s)=Kc1+Kcms2+bs+k−KcKf(1Ts+1)

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Chapter 6 Solutions

Range of gainKf for the given system to be stable.

F(s)DOC(s)=Kc1+Kcms2+bs+k−KcKf(1Ts+1)