Question

a) Develop the system response for a unit step function having the following transfer function. (5 <1) gs + f ss+260 $+02 b) Develop an equation that could be used to determine the rise time using the (0-100) criteria

Answer 1

wd GCS) - g Wd (st od ) 2 + wa Takeda Inverse Laplase transform both side - Odt cit) = esin wat g Wd & ont g sin Candi 62 t Cilt e on Ji-22 f f fjs Now Staron 822 Wast we ($ 3 S (32422 Wastwo?) Ca(s) St 2e wn (S+ 6d) ²+ wf St 20d (st od) ²+ w ${s fś - 64 Stod = 62 (5) (St Gdj²+ wa (st 8d) 24 wit 6268) fit stod Od Wd Wd ist od] 2 + wa The S (st Sd]? 4 wir (st od ) f 2 ปต์ Wel ht (st 6d)? 4 we? Indica (stody z wa

CH g Edt e sin (welt) + f -belt е sin lidtto) ولا S1-22 (6) Rise time If step input is applied then 6dt ey = f(! f e sin (wat to 51-22 at t=0, 10 = 1-1)= at tanity) = 2009. - - odtr fli- e -sinwatot 0 sin BIT So, sin | Welto to -) Wd to to = 0 IT = Wd to nito 2 to n To Well So, Rize time is for n=1. costa TT- "TI - tr d OnJ1-22