Question

Suppose we have a second order open system.

K=1 T1=1 T2=12 with a delay of 3 seconds with proporcional regulator which has a koeficent (kp=12).

A) Draw and comment the characteriscit log and amplitudes (KLA) and characteristic log and phase (KLF)

B) If posible to get me started how to plot on matlab it would be great.

thank you very much for your help

Answer 1

solution the system : -STd The open loop transfer function of 419) (1+ST) (1+ST) K e Kp. Here Kp = 12 K = 1 T = 1 T2 =12 Td = delay = 3 .: 4/5) = 12. e (1+s) (i+ 125 35 For amplitude 1 G(S) / [ le /=1] 12. Trits) (1+125)/ Fox phase 29/s) - - 3W- tan "(W) - tan" (12 W) log amplitude plot ^ Characteristic 1916) 20,4B/ decade slope- (in dB) 21*58 elipe = 40 20 / decade CS Scanned with CamScanner (rad /sec)

For The cystein Gls) has a poles - one at the other at I given by 12 die, 20 lang.. (12) w< amplitude in dB scale 21. 58 dB For TRX W<1, amplitude starts decreasing at a cate of 20 dB/ decade W>,l, slope becomes -40 dB/ decade because of additional pole. زاد اله إلى 19 (jw) ) 12 11+12jWl [ Pole at sal isn't considered till W= 12 A 12 I+(120)2 √1+12² (: W=1 = 0.996 - 0:03 dB (in 20 legio scal) Fee phase, At Wzo, LG(jw) = 0 At w = 1 . Lalju) = - 3 x 1 / 2 - tan " (12 x 1 1/2 - 3x1 x 180 T - 59°32° Hlw=1", 24q-) = -3210 - tor (l) - Hun"(a) (n = 180° .: 3w = 3 x 72 - 302'12 3 x L x 180 T 12 ICS Scanned with CamScanner

Characteristic phase plot 2547107 21 12 (zed/se (zad/sec -59032 -302-12

Command Window New to MATLAB? See resources for Getting Started, stf('s'); >> G = 12*exp(-3*)/((1+5)*(1+12*s)) 12 exp(-3*) * 12 s^2 + 13 S + 1 Continuous time transfer function. >> bode (6) >> |

Eile Edit View Insert Tools Desktop Window Help Bode Diagram Magnitude (dB) -50 -100 0 <a -5760 Phase (deg) -11520 -17280 103 10-2 10-2 101 102 100 Frequency (rad/s)