I need to graphically obtain two equation intersection on a array vector and store it for plotting. I have achieved the plot but the intersection is not at the required place and doesn't match the analysis on my paper. There is something which i am missing out. the last code in the script indicates on the plot where the equations must meet as per the anaylsis i did on paper and the image attached.
the equation is for Ki, Lambda with a delay plant
clear all; close all; clf; clc tc2=0.4; %Time constant value
delay2=0.01; %Delay
wc=10; phasemargin=50; h=1; for lambda=0:0.001:2; %Equation 1
t=tan(atan(wc*tc2)+phasemargin+delay2*wc); M=(((wc^(-lambda))*(sin((lambda*pi)/2)))+((wc^(-lambda))*(cos((lambda*pi)/2)*t))); ki(h)=-t/M; %Equation 1
%Quadratic Equation 2
A=(tc2/(1+((wc*tc2)^2)))+delay2; B=2*A*(wc^(-lambda))*cos((lambda*pi)/2)-(lambda*(wc^(-lambda-1))*sin((lambda*pi)/2)); a=A; b=B; c=wc^(-2*lambda); ki1(h)= (-b+sqrt(b^2-4*(a^2)*c))/(2*a*c); %Equation 2
lms(h)=lambda; h=h+1; end figure(1); plot(lms,ki,'r', 'Linewidth',1);hold on plot(lms,ki1,'k-','Linewidth',1);hold on; %this codes will tell where the equation must intersect.
plot(0.8731,11.059,'ro', 'MarkerSize', 10) axis([0 2.5 -5 15])
If I remove the lambda array from lambda 0:0.001:2 and place lambda=0.8731 then ki=11.059 is the output similar to the graph i want to obtain.
Please help me identify and obtain the graph at the intersection on the red circle for lambda and Ki values.
Thank you!
Best Answer