Question

c) A system can be modeled by using differential equation, di +5 di = 2v, where y and i are input and output for the system, i determine the transfer function for the system. [2 marks] ii. if the system input used is as shown in the Figure 2 (e), determine the time response for the system. [3 marks 0.5 Figure 2(c) d) The open loop pole-zero plot of a unity feedback control system is shown in Figure 2(d). Draw the root locus as the gain is varied. Show necessary calculations. [10 marks o -X Imaginary Axis, jo X X 4 -35 -25 0 05 -15 Real Ads,

Answer 1

Sol 40 d1042 -+ Solution- Given differential en is, y d²i de = 2V. visovieb Assume inivia) conditions are zero. to sur If X(t) and YLE) the ilp and ble or O SA shem, then me corresponding Laplace transforms are xcs) and yes). Transfer function yes) courrit s Xcs) 4052 YCS) XCS) 19 noitepoodt 2 YNOLOG Now, apply Laplace transform on both sides, are Xos) (input) s? 1 (5) +(5.5) i(s) = 2 NCs) (8+55) ils) = 2V05) Nes) 5²455 ics) S2+5.5 GNIS) Seletorn ics) 2 20 21 ror (ro) - Moore