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EG243 Control Systems 08 paper

# EG243 Control Systems 08 paper - PRIFYSGOL ABERTAWE SWANSEA...

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P AGE 1 OF 6 PRIFYSGOL ABERTAWE SWANSEA UNIVERSITY School of Engineering SEMESTER 1 EXAMINATIONS JANUARY 2008 EG-243 CONTROL SYSTEMS LEVEL 2 UNIVERSITY CALCULATORS ONLY Translation dictionaries are not permitted, but an English dictionary may be borrowed from the invigilator on request. Time allowed: 2 hours Answer Question 1 and TWO other questions Formulae and Transform Tables included T URN O VER

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P AGE 2 OF 6 1. Attempt all parts For Question 1 parts (a), (b), (c) and (d) assume a control system with forward path G(s) and negative feedback path, H(s), given by: and ( 5) ( ) ( ) ( 1)( 2) ( 10) K s G s H s s s s = = + + + (a) Derive the closed loop steady state error (ie output - input) for (i) a unit step input (ii) unit ramp input. Assume K = 1. [5 marks] (b) Derive the system closed loop frequency response as 0 ϖ . Assume K=1. [5 marks] (c) Give an expression for the closed loop system impulse response, when K is just above zero. Numerical values for the expression coefficients are not required. [5 marks] (d) Sketch the Nyquist diagram giving values at (i) 0 ϖ and (ii) . ϖ → ∞ [5 marks] (e) For the control system in Figure Q1e derive the close loop transfer function, C(s)/R(s). T URN O VER + - R(s) E (s) C(s) G(s) H(s) Figure Q1abcd + - + + R(s) E (s) C(s) G(s) H(s) Figure Q1e J(s) [5 marks]
P AGE 3 OF 6 2. (a) Define the characteristic equation of a feedback control system in its canonical form.

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EG243 Control Systems 08 paper - PRIFYSGOL ABERTAWE SWANSEA...

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