Inverted Pendulum:

P$3.(30$ points$)$ Use the Simulink to simulate the differential equations for inverted pendulum

system given below:

$x_1^{}=x_2$

$x_2^{}=\frac{mglsin(x_1)-x_2+u(t)}{m{l}^2}$

The values of parameters are: $m=0\mathrm{.}2kg,l=1m,g=9\mathrm{.}8m{s}^{-2},=0\mathrm{.}05N.m.s,u=2N.$

Which value of input $(u)$ is giving the constant value of $x_1$ and at which value the $x_1$ blows up$.$

Record your results for both values.

Note:

Submit your pdf$,$ Simulink, and matlab files for all the above problems in a zipped folder.