Question

The following control system is given U(s) E(s) 7s +12 (s+2)(+6) G() GS) At the time t=0 the input signal is utt a). Determine the output Ys) b). Determine the output Yſt)

Answer 1

75+12 $(5+2)(8+6) open lopp transfer function (AC)) = and His)=) closed loop transfer function - (for -ve feedback) AC) 1 + H() ACS C(s) = 75+12 S(5+1)(8+6) 76 112 1+ SIS+2.) (5+6) 75+12 Sist)s+) +75+12 70)+12 s+85+125-475-412 15-12 c(s - $+85€ + 195+12 also given input (6) Et sult) and LÀ SUCO) - unitstep signal OS) - output y) = (1 0(s) 1 75 +12 8?+85 +195+12 1/3

75 +12 YO! Ś (5+015+4)(8+3) het, - = $15+1)(519)5+3) 75+12 A + B +sti 5+4 st3 15+12 This > A[ sis+vis+3)(s+a)] +B[ sus+)(st335+43] ++ [575+3)(+4) ] +D[5*6+1)(5+3)] te [ ${s+v(5+43] put S=0 >>) 122 A (12) + Blo) + (lo) + DIO+EO) put s=-1 3) 160+12 = Aro) +B(0)+ (HDC+2)(+3)] + dlo) E(O) The 5= ([6] [7=5767 put s=-3 71-) +2 = A(0) + Blo) + ((o) +010)+ EC 133(-2)(0) put -q = E( 96-2)] -112 s=-4 1-4) +12= AW) + Blo) te (64)2-1(0] +0 (44)(-3) (-12] +ECO) 16 = º(+16]6) [p=13] 2/3

3 75+12 - WLES+25+3)(8+4)] + b[ses+01+3)(8+13) + [5'(5+3) (s+)) - { $'$t121543) +{{s'is+y)s+43] compaye the co-efficients of 4 0 0 + B + O=B+ 5 -213 0= B t e 3 yes)= - 3 - V3 5 + 3 1 4 - STA" 513 tsult) 7 / sutt) H5 easults i s ta - yes= [4 -1 13 ") sit where Sult) - unit step signal 3/3