Solving math by equal
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Solve math problems in 2 ways
1.Use MATLAB
2 Relieve your hands manually
someone please help me
5 个评论
cong
2025-4-28
Matt J
2025-4-28
We might be able to tell you what you're doing wrong if you show us what you've done.
Torsten
2025-4-28
Do you know about the MATLAB functions "tf" and "margin" ? If not, take a look at them: they should solve your problem.
Walter Roberson
2025-4-28
https://www.mathworks.com/matlabcentral/answers/1724785-calculation-of-phase-margin involves exactly the same system.
采纳的回答
Hi @cong
In my previous answer, the margin() function cannot accurately determine the phase margin because there are three gain crossovers between 1 rad/s and 2 rad/s, and the function only returns the margin at the frequency with the smallest stability margin. You need to zoom into the gain curve to see this clearly. In this situation, you should use the allmargin() function instead. To find the phase margin by hand, use this formula:
format long g
s = tf('s');
%% Case 1: manually find it!
K = 3.45850428040268842444505;
%% Case 2: matlabcentral/answers/1724785-calculation-of-phase-margin
% w = 1.49109560603497592889965; % crossover frequency
% K = sqrt(w^4 + (w^2)*(4 - w^2)^2) % gain formula derived from crossover frequency
%% Plant
G = K/(s*(s^2 + 1*s + 4));
%% Find the Phase margin using margin
figure
margin(G), grid on, grid minor
%% Zoom in to look at the gain curve around the phase crossover frequency
figure
bode(G, linspace(1.26, 1.76, 1000)), grid on, grid minor
% Estimate the Phase margin between 1.4 and 1.6 rad/s
allmargin(G, Focus=[1.4, 1.6])
%% Find the Phase margin using allmargin
allmargin(G)
更多回答（1 个）
Hi @cong
You can assign a value to K, compute the transfer function G(s), and then use the margin(G) command to find the phase margin (Pm). Here is the code snippet for the three steps:
However, I prefer not to provide advanced code at this stage, as I believe you may not yet be prepared for it. Anyhow, the real problem is, Can you really find the static gain K such that the Phase margin is exactly 50°?
s = tf('s');
%% When K = 3.44
K = 3.44;
G = K/(s*(s^2 + 1*s + 4));
figure
margin(G); grid on, grid minor
%% When K = 3.45
K = 3.45;
G = K/(s*(s^2 + 1*s + 4));
figure
margin(G); grid on, grid minor
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