(Solved): linear control systems Question 1 2. Consider the state-space model x=[51410]x+[11 ...

linear control systems

Question 1 2. Consider the state-space model $\begin{array}{l}\stackrel{?}{\mathbf{x}}=\left[\begin{array}{cc}?5& 1\\ 14& 0\end{array}\right]\mathbf{x}+\left[\begin{array}{l}1\\ 1\end{array}\right]u,\\ y=\left[\begin{array}{ll}1& 0\end{array}\right]\mathbf{x}.\end{array}$ Suppose we want to apply full-state feedback to the system, of the form $u=?K\mathbf{x}$. (a) Without computing the transfer function, identify the open-loop system poles and zeros. (b) Select $K$ such that the closed-loop system poles are placed at the roots of $s^2+2?{?}_{n}s+{?}_n^2=0$ (c) Use your analytic expression for $K$ to support the following claim: "To move the poles a long way takes large gains." (d) Select $K$ such that the closed-loop system poles are placed at $s=?9$ and $s=?4$.