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EG243 Control Systems 09 paper

# EG243 Control Systems 09 paper - PRIFYSGOL ABERTAWE SWANSEA...

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JSM/EG-243_09 Page 1 of 7 PRIFYSGOL ABERTAWE SWANSEA UNIVERSITY School of Engineering SEMESTER 2 EXAMINATIONS MAY/JUNE 2009 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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JSM/EG-243_09 Page 2 of 7 1. Attempt all parts For all parts in Question 1 assume a control system with forward path G(s) and negative feedback path, H(s), shown in Figure Q1 and given by: ( 29 ) )( )( ( c s b s a s K s GH + + + = (a) Derive the closed loop transfer function. Assume H(s) =1. [2 marks] (b) Derive the closed loop frequency response as 0 ϖ . Assume H(s) =1. [2 marks] (c) Derive the closed loop steady state error for inputs (i) unit step (ii) unit ramp. Assume H(s) =1. [5 marks] (d) Sketch the Nyquist diagram giving values as 0 ϖ and ϖ [5 marks] (e) Sketch the Bode diagrams giving values for ( 0 | = ϖ ϖ j GH and ( = ϖ ϖ | j GH [6 marks] (f) Sketch the root locus diagram indicating the stabilily limit and show the vectors that would enable you to find the value of K at the stability limit (you are not required to calculate K). [5 marks] T URN O VER + - R(s) E (s) C(s) G(s) H(s) Figure Q1
JSM/EG-243_09 Page 3 of 7 2. (a) Define the characteristic equation in the context of a negative feedback control system and define the two conditions for the system to be at the stability limit.

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EG243 Control Systems 09 paper - PRIFYSGOL ABERTAWE SWANSEA...

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