How to find the max Phase lead provided by a Compensator?

If I have a compensator such as s+1/s+3, is there a command to find the max phase lead angle provided by it?

Answer 1

[David Goodmanson]

Hi Gidel,

It's not a single command and it's numeric, but is

w = 0:.001:10; maxangle = (180/pi)*max(angle((i*w+1)./(i*w+3)))     % degrees
maxangle =  30.0000

sufficient?

Answer 2

[Sam Chak]

Hi @Gidel

You can also check using the bodeplot() for visual and the bode() for finding the max angle.

sys = tf([1 1], [1 3])

sys =
 
  s + 1
  -----
  s + 3
 
Continuous-time transfer function.

h = bodeplot(sys);
setoptions(h, 'FreqUnits', 'Hz', 'MagVisible', 'off');
grid on

[mag, phase, wout] = bode(sys);
maxAngle = max(phase)

maxAngle = 30.0000

[Gidel]

Thank you, also is it possible to find the maximum gain from this?

[Sam Chak]

Hi @Gidel

Since your original question has been answered, perhaps you would also like to determine the compensator's magnitude at the frequency where the maximum phase angle occurs.

% Transfer function of the Lead Compensator
sys = tf([1 1], [1 3])

sys =
 
  s + 1
  -----
  s + 3
 
Continuous-time transfer function.

h   = bodeplot(sys); grid on

% Extract data points from Bode plot
[mag, phase, wout] = bode(sys);

% Max phase angle
maxAngle = max(phase)

maxAngle = 30.0000

% Frequency at which the max phase angle occurs, ω_max
idx      = find(phase == maxAngle);
wmax     = wout(idx)

wmax = 1.7321

% Compensator's magnitude at ω_max
magwmax  = mag(idx)

magwmax = 0.5774

% Check mag dB
magdB    = 20*log10(magwmax)

magdB = -4.7712