Instructions Simulate in MATLAB Credit for innovation and originality of code an
ID: 2080548 • Letter: I
Question
Instructions Simulate in MATLAB Credit for innovation and originality of code and solution No collusion allowed. No credit if violation found Submit MATLAB file compatible with MATLAB R 2014 b with documentation. Submit a report briefly explaining your code and approach to the solution. State all assumptions and display outputs clearly (marking labels, legends, no snapshots). Report must include code as well. Credit for clarity of report and quality of output. Problem Statement for 3 different and unique combination of initial values and input u plot the phase plane plot (x_1 vs x_2) and output plots of the non-linear system using MATLAB. For same 3 combination of initial values and input u used in (a) plot the phase plane plot (x_1 vs x_2) and output plots of the linearized system using MATLAB.Explanation / Answer
use the following program for taylor series linearization
L=100;
m=1000;
g=9.8;
syms x1 x2 u
f1=[x1+x2,-L*x1.^2-g*L*x2+u*2/m];
h1=x1.*(x2).^4;
f2=[-x1+x1.*x2,x2-x1.*x2+u];
h2=x1-x2.^5;
A=taylor(f1,[x1,x2,u],1, 'Order', 3);
B=taylor(h1,[x1,x2],1, 'Order', 3);
C=taylor(f2,[x1,x2,u],1, 'Order', 3);
D=taylor(h2,[x1,x2],1, 'Order', 3);
fplot([A B C D])
xlim([-4 4])
grid on
legend('approximation of f1(x)','approximation of h1(x)','approximation of f2(x)','approximation of h2(x)','f(x) and h(x)','Location','Best')
title('Taylor Series Expansion')