HW7 Solution

# HW7 Solution - stable. is system the , 5 . 1 , If 5 . 1 4 2...

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MFGE4376 Homework7 Due: 2:00pm, April 18 Question 1: For a control system shown in the following figure, (a) Determine the roots on the imaginary axis. What is the K value? (b) Roughly draw the root locus of the system. Solution: The open loop poles: -2 and -4. The open loop zeros: 2+j4 and 2-j4. The transfer function is: 8 20 ) 4 6 ( ) 1 ( ) 20 4 ( ) ( 2 2 K s K s K s s K s T 2 s 1+K 20K+8 1 s 6-4K 0 0 s 20K+8 For root on the imaginary axis according to the Routh-Hurwitz criteria: 5 . 1 0 4 6 K K The roots can be calculated using: 9 . 3 0 8 20 ) 1 ( 2 j s K s K ) 4 )( 2 ( ) 20 4 ( 2 s s s s K

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Question 2: For a control system shown in the following figure, (a) Draw the root locus of the system. (b) Determine the range of K such that the system is stable. The transfer function is: K s K s s K s T 2 3 ) 4 ( ) 2 ( ) ( 2 2 s 1 3-2K 1 s 4+K 0 0 s 3-2K According to the Routh-Hurwitz criteria:
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Unformatted text preview: stable. is system the , 5 . 1 , If 5 . 1 4 2 3 and 4 K K K K K ) 3 )( 1 ( ) 2 ( s s s K Question 3: For each of the root loci shown in the following figure, tell whether or not the sketch can be a root locus. If the sketch cannot be a root locus, explain wh. Give all reasons. Answer: (a) No: Not symmetric; On real axis to left of an even number of poles and zeros (b) No: On real axis to left of an even number of poles and zeros (c) No: On real axis to left of an even number of poles and zeros (d) Yes (e) No: Not symmetric; Not on real axis to left of odd number of poles and/or zeros (f) Yes (g) No: Not symmetric; real axis segment is not to the left of an odd number of poles (h) Yes...
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## This note was uploaded on 09/21/2011 for the course MFGE 4376 taught by Professor Chen during the Spring '11 term at Texas State.

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HW7 Solution - stable. is system the , 5 . 1 , If 5 . 1 4 2...

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