查找增益交叉频率? [英] Find gain cross over frequency?

问题描述

对于G(s)= K/(s(s + 0.5)(s + 4.6))，使用K作为标量进行选择，

For G(s) = K/(s(s+0.5)(s+4.6)) with K a scalar to choose,

G(s) =   
            1
  ---------------------
  s^3 + 5.1 s^2 + 2.3 s

找到增益交叉频率，它将获得45度的相位裕度.

find the gain cross over frequency which would give a 45 degree phase margin.

我使用sisotool解决了这个问题，根据我的回答，我的答案是0.42，但我的教程表显示答案是0.23.请有人可以帮我这个忙吗?

I solved this using sisotool and according to me my answer is 0.42 but my tutorial sheet shows the answer to be 0.23. Please can someone help me with this?

推荐答案

以下功能正在寻找收益:

The following function is finding the gain:

function findGainM()

phasemargin = 45; 

s = tf([1 0],1);               % definition of Laplace-Operator
A = 1/(s*(s+0.5)*(s+4.6));     % Transferfunction with K=1

disp(A)
fun = @(x) findGain(x,phasemargin,A); 
fzero(fun,1);

% display result
K = evalin('base','K');
w = evalin('base','wco');
disp( ['absolute gain: ' num2str(K)] )
disp( ['logarithmic gain: ' num2str(20*log10(K)) ' dB'] )
disp( ['crossover frequency: ' num2str(w) ' rad/s'] )
disp( ['crossover frequency: ' num2str(w/(2*pi)) ' Hz'] )

figure(1)
bodeplot(K*A)
grid on;

end

function rootPhase = findGain(w,phasemargin,A)
[mag,phase] = bode(A,w);
disp([mag,phase])
rootPhase = 180 - phasemargin + phase;
gain = 1/mag;
assignin('base','K',gain)
assignin('base','wco',w)
end

返回:

absolute gain: 1.2536
logarithmic gain: 1.963 dB
crossover frequency: 0.4169 rad/s
crossover frequency: 0.066352 Hz

我还检查了sisotool得到的结果与我的函数相同.

I also checked the sisotool getting the same results like my function.

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