Question

For the second question please.For the second question please.

1. Given G(a) = +2 sketch the Nyquist plot and determine the range of K for closed-loop stability. 2. Repeat for G(s) = (+1) 3. Repeat for G(s) =

Answer 1

Polca / Nyquist plot: It is a plot of magnitude in polae coddinater while 'w' and es phase varied of GCS) H(S) from o to co. The sinusoidal function and transfer function is given by Gljw) is a complen Glów) = 1G(joll LG (jo) G(jw) = M L

From the above ear, it is seen that G (jw) may be represented as a phasor of magnitude M and phase angle & As the ill frequency w is varied from o too, the magnitude in and phase angle o change and hence the tip of the phasol G (jw) traces a locus in the complen plane. The locus they obtained is known as pole plot

Now Given problem is Q- TK 1 968) ?

2) Gls) = G(S) H() = k S(5+1)2 S(5+12 we to need magnitude and phase. to M find La at w=0 - 90 - tain' (W) - tann (w . اہم کر دیا ها K L-98 E & L-90 at was = a K L-90 - tani (0) - tanto) o L-90 – 90-90 o L-270

Now at w=wp MLP At w= wpc Law) H(o) = -185 - - 180 = -98 - tant(6) - tanille) ao =. 2 tan' I w tan' (w) = 45 w = wpc = 1

Altanate method: (Crest check ) R-H citeria Chae an is 33 +25² + stk L -2 For be a any system sign to be changes stable in there first should not column. the : k-2 >0 k >2 e range of a for stability is k>2