Design of Integral Control
PROBLEM: Consider the plant of Eqs. (12.116):
\dot{x} =\left[\begin{matrix} 0 & 1 \\ -3 & -5 \end{matrix} \right] x +\left[\begin{matrix} 0 \\ 1 \end{matrix} \right] uy=\left[\begin{matrix} 1 & 0 \end{matrix} \right] x
a. Design a controller without integral control to yield a 10% overshoot and a settling time of 0.5 second. Evaluate the steady-state error for a unit step input.
b. Repeat the design of Part a using integral control. Evaluate the steady-state error for a unit step input.