Question

30.00 M- I M1.I 20.00 M 12 0.00 Ma 1.6 3 radisec 0.00 8 radisec 10 M-0.70715 rad/sec M -10.00 20 rad/sec M-0.3 -20.00 -270.0-247.5-225.0-202.5-180.0-157.5-135.0-112.3-90.0 Phase (deg) Fig. Q.1. Using the nichols, ngrid Cnew') and logspace functions/commands, obtain the Nichol's diagram with a grid for the following transfer function, where 0.1 sws10: 1 5 marks ] 24 s'+9s+265+24 G(s) Determine the approximate phase and gain margins from the Nichols charts and label the charts accordingly? 1 3x5 marks |

Answer 1

>>w={0.1,10} % set the frequency limits w in (0.1,10) rad/s %

w =

[0.1000] [10]

>> G=tf([24],[1 9 26 24]) % Given transfer function of the system %

G =

24
-----------------------
s^3 + 9 s^2 + 26 s + 24

Continuous-time transfer function.

>> nichols(G,w) %plot nichols chart for transfer function G with frequency limits%

On obtaining the plot, using the properties of plot parameters are obtained and screenshots attached as below:

From the 3rd figure, Gain margin: 18.8 dB

From the 4th figure Phase margin: 180 deg (greater than 173.2 deg)