Question

Question 3 The temperature (in °C) in the water heating process is given by the transfer function T(s) 3 U(s) TS+2 (a) Sketch THREE forms of input force function with its time response graph. (3 marks) (b) (12 marks) Calculate the time response of the system when, i) unit impulse is imposed on the system. ii) unit step is imposed on the system. (c) Sketch the diagrams of two responses and label the relevant values, given t = 5. (5 marks)

Answer 1

) step input =) Ult) = 1 ulth L Ramp input: ult) ult) = t. in loop blalt i parabolic input & ult) = ť ult) a t - Given: given ut) - olt) 2015)-1. * TIS) 3 UIS) 2st2

(1) TIS us). 3 est2 TIS) = 1 3 Applying inverse liste els+2) laplace transform Lellett). TOLt) = 3 Tit) = t 3 e unit step -) ult): 1 2) uls) = 1/s TIS) U15) esta TIS) US) esta 3 S ({st2 3 - stale) e 372 ) 15yr.) al S Ts) Taking inverse laplace transform. TLEDE 3 1 1 - 2)

C) Given 1-5. For unit response impulse time othe. TH) = 3 it -oout 5 TL) 2 0-6 qorut

06 Hoob & out step unit 103 $112th Time response Tit) 1-5 2) Tlt) = Ballet TLE) 311.2048) 276 to