MATLAB: How to plot a symbolic time-domain function with long expressions

computer performancefplotMATLABspeed of matlab codesymbolicvpa

Greetings,
I'm writing a code to achieve gust response of a 2D airfoil section. I used "Symbolic" in order to solve the time-domain set of equations by applying Laplace transformation, Cramer (with Wronskian) and Inverse Laplace transformation. I successfully plot the 1-DOF gust response with using fplot. When I tried for 2-DOF, the graph goes blank. In addition, for both of the plotting process, my computer lagged. I want to see if the 2-DOF time-domain function is obtained or not, and I see that it is obtained but it is a long function:
I thought, maybe the graph is not plotted because of my computer performance (either I didn't update my computer for a while or I didn't update MATLAB for a while). I tried to simpify 2-DOF function, so that I can plot the graph. With help of "vpa", I find a simplified function. When I plotted both of the simplied function and 1-DOF function, I achieve this graph:
I thought that, I achieve this result because 1-DOF is already a simplified version of 2-DOF, and I probably obtained the 2DOF time-domain function correctly. The reference graph is:
Can you help me to plot the 2-DOF time-domain function and speed up my MATLAB code (both for this case and in general)? My MATLAB code is shown below: 
clc;clear;
syms s
Mu= 43.98;
Cl= 2*pi;
A= 0.0375 ;
V= 1;
r= 0.5;
r2= r*r;
x= 0;
a= 0;
Sigma= V*sqrt(A);
w0=1;
Kussner=1/s-0.5/(s+0.13)-0.5/(s+1);
Wagner=1/s-0.165/(s+0.0455)-0.335/(s+0.3);
Wgust=w0/s; % for sharp edge gust
% E=Cl*Wgust*s*Kussner/(Mu*V);
% F=(1+Cl*Wagner/Mu+Cl/(2*Mu))*s*s+A;
%  

% X=E/F;
%  
% Xi_1DOF=ilaplace(X);
K1=s*s+A+Cl*s*s/(2*Mu)+Cl*s*s*Wagner/Mu;
K2=x*s*s/r2-Cl*a*s*s/(2*r2*Mu)-Cl*Wagner*s*s*(1/2+a)/(r2*Mu);
K3=x*s*s+Cl*(s-a*s*s)/(2*Mu)+Cl*(s+(1/2-a)*s*s)*Wagner/Mu;
K4=s*s+1/(V*V)-Cl*(-(1/8+a*a)*s*s-(1/2-a)*s)/(2*r2*Mu)-Cl*(1/2+a)*((1/2-a)*s*s+s)*Wagner/(r2*Mu);
K5=Cl*Wgust*s*Kussner/(Mu*V);
K6=Cl*(1/2+a)*Wgust*s*Kussner/(r2*Mu*V);
X2=(K5*K4-K6*K2)/(K1*K4-K3*K2);
Xi_2DOF=ilaplace(X2);
% Xi_simplified = vpa(Xi_2DOF);
% 



% Xi_Diff = Xi_simplified - Xi_1DOF;
fplot(Xi_2DOF,[0,200])
% subplot(1,1,1)
% fplot(Xi_1DOF,[0,200])
% % fplot(Xi_1DOF,[0,200],'Linewidth',2)
% 
% hold on
% 
% fplot(Xi_simplified,[0,200],'--or')
% fplot(Xi_Diff,[0,200],'-.*c')
% legend('\xi_{1-DOF}','\xi_{Simplified}=vpa(\xi_{2-DOF})','\xi_{Diff }= \xi_{Simplified} - \xi_{1-DOF}')
% 
% hold off

Best Answer

fplot can do a lot of work to try to find singularities. This can make it very slow on complicated functions.
For plotting purposes it is often better to use matlabFunction to create a function handle and evaluate the handle on a vector of x values and use plot(). You will not get singularities marked on it but you probably do not care about that at the moment.
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