A simplified model for the control of a flexible robotic arm is shown below$\mathrm{.}4-)$

A simplified model for the control of a flexible robotic arm is shown below.

Here, $k$ is a spring constant which models the flexibility of the arm, $M$ represents the mass of the arm, $y,$ the output, is the

mass position and $u,$ the input, is the position of the end of the spring. Here, $\frac{k}{M}=900ra\frac{d}{s^2}.$

The equations of motion for this system are thus given by $M{y}^{}+k(y-u)=0.$ Define state variables $x_1=y$ and $x_2=y^{}.$

a$)$ Design a full state observer for the given system with observer eigenvalues at $s_{1,2}=-100+-$

$100j.($via hand calculation$)$

b$)$ Implement the observer that you obtain into the given system via MATLAB$/$Simulink$.$

c$)$ Obtain the necessary plots via MATLAB$/$Simulink and analyze them to prove that the observer

that you design works properly.

y

M

Here, k is a spring constant which models the flexibility of the arm, M represents the mass of the arm, y$,$ the output, is the mass position and u$,$ the input, is the position of the end of the spring. Here, k$/$M$900$rad$/$s$^2.$

The equations of motion for this system are thus given by Mij$+$k$($yu$)0.$ Define state variables $21$ y and x$2=.$

a$)$ Design a full state observer for the given system with observer eigenvalues at $$1,2-100\backslash$pm $100$j$.($via hand calculation$)$

b$)$ Implement the observer that you obtain into the given system via MATLAB$/$Simulink$.$

c$)$ Obtain the necessary plots via MATLAB$/$Simulink and analyze them to prove that the observer that you design works properly.