finding PM and GM for a system

I need help finding PM and GM for this system.

Here is what I have so far, but I'm not sure if its right for the PM and GM. I tried a couple things, and this is the first that didn't give me an error, but the numbers just seem wrong.

Any help is appreciated!

% Part 1 - plot nyquist plot for K=900 G = tf([900],conv([1 10],[1 4 4])); figure(1) nyquist(G); xlim([-5 1])

% Part 2 - plot bode plot for transfer function figure(2) bode(G) [Gm,Pm,Wcg,Wcp] = margin(G) display(Gm); display(Pm);

Answer 1

[William Rose]

@Cait,

Your results look reasonable to me.

% Part 1 - plot nyquist plot for K=15
G = tf([900],conv([1 10],[1 4 4]));
figure(1)
nyquist(G);
ylim([-4 4]); axis equal

% Part 2 - plot bode plot for transfer function
figure(2)
bode(G); grid on

[Gm,Pm,Wcg,Wcp] = margin(G)

Warning: The closed-loop system is unstable.

Gm = 0.6400

Pm = -11.3799

Wcg = 6.6333

Wcp = 8.1166

display(Gm);

Gm = 0.6400

display(Pm);

Pm = -11.3799

The plots show an unstable system: when the phase is -180, which appears to be at f=650 Hz, the gain exceeds unity. That indicates the system is unstable. If you change 900 to 300, the system is stable, and the plots show that. For example, the phase plot below crosses -180 at f=650 Hz. The gain plot below shows that the gain is <0 dB at f=650, i.e. system is stable.

% Part 1 - plot nyquist plot for K=15
G = tf([300],conv([1 10],[1 4 4]));
figure(1)
nyquist(G);
ylim([-4 4]); axis equal

% Part 2 - plot bode plot for transfer function
figure(2)
bode(G); grid on

[Gm,Pm,Wcg,Wcp] = margin(G)

Gm = 1.9201

Pm = 19.5922

Wcg = 6.6333

Wcp = 4.8005

display(Gm);

Gm = 1.9201

display(Pm);

Pm = 19.5922

[Cait]

Thank you!

[William Rose]

@Cait, you're welcome. Good luck with your studies.