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EG243 Control Systems 08 Ans

# EG243 Control Systems 08 Ans - Page:1 of 6 SCHOOL OF...

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Page : 1 of 6 SCHOOL OF ENGINEERING EXAMINATION MODEL ANSWER SHEET Paper Title: Control Systems Paper No : EG-243 MAY/JUNE 2008 Examiner(s) : JSM Question No Marks JSM/EG-243_08 1. ( 29 ( 5) ( 1)( 2)( 10) K s GH s s s s = + + + (a) [5 marks] (b) (c) 2 10 ( ) t t t c t Ae Be Ce - - - = + + (d) Nyquist diagram: (e) K/4 -1 Re(GH(jw) ) Im(GH(jw) + ( 29 ( 29 0 1( 5) ( 1)( 2)( 10) 1( 5) 5 1/ 5 20 5 C j j R j j j j C j R ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ = + + + + + = = + ( 29 2 1 ( 1)( 2)( 10) ( ) ( ) 1 ( 1)( 2)( 10) ( 5) FVT : ( ) ( ) 20 ( ) step: ( ) 1/ then ( ) 4 / 5 20 5 ( ) ramp: ( ) 1/ then ( ) t s t t s s s E s R s R s GH s s s s f t sF s i R s s e t ii R s s e t →∞ →∞ →∞ →∞ + + + = = + + + + + + = = = = + = =∞ 0 ( ) arg(0) 4 K GH j ϖ ϖ ( ) 0, arg( 180) GH j ϖ ϖ → ∞ - [5 marks] [5 marks] and ( 5) ( ) ( ) ( 1)( 2) ( 10) K s G s H s s s s = = + + + [5 marks] + + R G/(1+GH) J/G R + E G J _ H whence . 1 1 + + = G J GH G R C [5 marks] C

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Page : 2 of 6 SCHOOL OF ENGINEERING EXAMINATION MODEL ANSWER SHEET Paper Title: Control Systems Paper No : EG-243 MAY/JUNE 2008 Examiner(s) : JSM Question No Marks JSM/EG-243_08 2. (a) CE is: 1+GH = 0 [2 marks] (i) Importance: indicates nature of closed loop system output [3 marks] (ii) RL: locus exists at any point in s plane when angles subtended by poles – angles subtended by zeros approximates 180 o thereby meeting phase condition of CE. [4 marks] (b) ( 29 2 3 2 ( 4)( 1) . ( 10) K s s GH s s s + + = + The system output for: 0<K<K 1 2 (complex) oscillatory terms, one unstable.
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EG243 Control Systems 08 Ans - Page:1 of 6 SCHOOL OF...

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