Finding the point of inflection on a curve

Question

Wern-Juin Choy 2012-1-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/25153-finding-the-point-of-inflection-on-a-curve

回答： Osita Onyejekwe 2016-10-31

Hi everyone, I have a question.

Is there any code that allows one to find the point of inflection on a step response curve of a transfer function? An example is given below.

Ts = 0.0005;
%Continuous system
Ps = tf(2,[1,12,20.02]);
Pz = c2d(Ps,Ts,'zoh');
%response
figure(1)
hold on
step(Pz)
hold off

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Answer 1

Teja Muppirala 2012-1-4

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https://ww2.mathworks.cn/matlabcentral/answers/25153-finding-the-point-of-inflection-on-a-curve#answer_33148

在 MATLAB Online 中打开

You need to find where the 2nd derivative is zero. There are many different ways to approach this. This is one possible way:

Ts = 0.0005;
%Continuous system
Ps = tf(2,[1,12,20.02]);
Pz = c2d(Ps,Ts,'zoh');
%response
[y,t] = step(Pz);
plot(t,y);
hold on;
% Estimate the 2nd deriv. by finite differences
ypp = diff(y,2);  
% Find the root using FZERO
t_infl = fzero(@(T) interp1(t(2:end-1),ypp,T,'linear','extrap'),0)
y_infl = interp1(t,y,t_infl,'linear')
plot(t_infl,y_infl,'ro');