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HW6 Solution

# HW6 Solution - MFGE4376 Homework6 Due 2:00pm April 11...

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MFGE4376 Homework6 Due: 2:00pm, April 11 Question 1: (40pts) For a control system shown in the following figure, Determine the range of K for the following cases: (a) the system is stable; (b) the system is marginally stable; (c) the system is unstable. Solution: K s K s s s K s T K Ks s s s s K s s s s K s s s s K s KG s KG s T s s s s s s s s s s s s s s s s s s s s G 3 20 ) 10 ( 9 ) 3 ( ) ( 3 20 10 9 ) 3 ( 20 10 9 3 1 20 10 9 3 ) ( 1 ) ( ) ( 20 10 9 3 30 7 10 17 8 3 10 17 8 ) 10 )( 3 ( 1 10 17 8 3 ) ( 2 3 2 3 2 3 2 3 2 3 2 2 3 2 3 2 3 3 s 1 10+K 2 s 9 -20+3K 1 s (110+6K)/9 0 0 s -20+3K 10 s If the system is stable: 3 20 Hence . 3 20 and 6 110 0 3 20 , 0 9 6 110 K K K K K If the system is unstable: 3 20 Hence . 3

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HW6 Solution - MFGE4376 Homework6 Due 2:00pm April 11...

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