Question

Nise Ch. 10, Problem 10.(**Ignore book question**) Here is is the questions for each system, (a) Use MATLAB to draw/plot the root locus (b) Obtain the limits for stable gain. (c) Get bode plot (d) Get gain margin and limits for stable K/gain. (It should be the same as the values obtained from the locus) -Suggestion ) Use the commands like 'rlocus, riocfind' and 'bode, in Matlab. C(s) R(s)+ | (s + 2) -ㄒㄧ System I R(s) + C(s) (s + 2)(s+4) System 2 R(s) + K(s -1) C(s) (s- 2) (s + 2) System 3 FIGURE P10.4

Answer 1

matlab for all parts:

clc;

clear all;

s=tf('s');

g1=1/((s+2)*(s+4)*(s+6));

g2=(s^2-4*s+13)/(s*(s+2)*(s+4));

g3=(s-1)*(s-2)/((s+1)*(s+2));

rlocus(g1);

title('root locus of g1')

figure

rlocus(g2);

title('root locus of g2')

figure

rlocus(g3);

title('root locus of g3')

figure

margin(g1);grid

figure

margin(g2);grid

figure

margin(g3);grid

File Edit View Insert Tools Desktop Window Help root locus of g1 14 -12 10 Real Axis (seconds )

File Edit View Insert Tools Desktop Window Help root locus of g2 .2 3 -10 Real Axis (seconds )

File Edit View Insert Tools Desktop Window Help root locus of g3 05 0.5 1.5 0.5 2.5 05 1.5 25 Real Axis (seconds )

File Edit View Insert Tools Desktop Window Help Bode Diagram Gm- 53.8 dB (at 6.63 rad/s), Pm Inf 80 -140 -180 .90 180 10 2 100 102 10 10 10 Frequency (rad's)

File Edit View Insert Tools Desktop Window Help Bode Diagram Gm- 2.85 dB (at 1.5 rad/s), Pm- 16.6 deg (at 1.26 rad/s) 10 20 30 10 2 102 10 10 Frequency (rad's)

File Edit View Insert Tools Desktop Window Help Bode Diagram Gm 0 dB (at 141 radis),Pm-0 deg (at 1.41 rad's) 0.4 0.4 0.6 0.8 102 10-1 10 Frequency (rad's)

For bode plot the margins are given in the figure.

the gain with rlocfind is :

clc;

clear all;

s=tf('s');

g1=1/((s+2)*(s+4)*(s+6));

g2=(s^2-4*s+13)/(s*(s+2)*(s+4));

g3=(s-1)*(s-2)/((s+1)*(s+2));

rlocus(g1);k1=rlocfind(g1);

figure

rlocus(g2);k2=rlocfind(g2);

figure

rlocus(g3);k3=rlocfind(g3);

the answer is

>> k1

k1 =

468.5750

>> k2

k2 =

1.4686

>> k3

k3 =

1.0240