Question

$\dot{x}=\begin{bmatrix} 0 &1 \\ -3 & -5 \end{bmatrix}x +\begin{bmatrix} 0\\ 1 \end{bmatrix}u$

$y=\begin{bmatrix} 1 & 0 \end{bmatrix}x$

a. Design a state feedback controller with integral control to yield a 10% overshoot and a settling time of 0.5 sec. (tip: place the third pole to have the same real part as the two dominant, complex poles.)

b. Assume that the system is initially relaxed at t=0. With the controller design in (c), what is the steady-state response y(t) excited by the unit step reference signal r(t)=1, for $t\geq 0$ .

Answer 1

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