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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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')
Another way would be to find the roots of the step response of
tf([2 0 0],[1,12,20.02]);