For a discrete time system
\( \frac{Y(z)}{R(z)}=\frac{z^-1+z^-2}{1+1.3z^-1+0.4z^-2}\)
Rewritting into a state space form
\(X_{n+1}=\Phi X_{n} + \Gamma U_{n}, y_{n}=CX_{n}\)
I have found the following to the question
\(\begin{array}{1}X_{1}\\ X_{2}\end{array} =\begin{array}{1}0&1\\ -0.4&-1.3\end{array}\begin{array}{1}X_{1(k)}\\ X_{2(k)}\end{array}+\begin{array}{1}0\\ 1\end{array}uk\)
\(y(k+1)=\begin{array}{1}1&1\end{array}\begin{array}{1}X_{1(k+1})\\ X_{2(k+2)}\end{array}\)
Using state variable technique design a controler with z=±0.5
This is where I am not sure if I times \(\begin{array}{1}0&1\\ -0.4&-1.3\end{array}\) by ±0.5 to get the answer....
\( \frac{Y(z)}{R(z)}=\frac{z^-1+z^-2}{1+1.3z^-1+0.4z^-2}\)
Rewritting into a state space form
\(X_{n+1}=\Phi X_{n} + \Gamma U_{n}, y_{n}=CX_{n}\)
I have found the following to the question
\(\begin{array}{1}X_{1}\\ X_{2}\end{array} =\begin{array}{1}0&1\\ -0.4&-1.3\end{array}\begin{array}{1}X_{1(k)}\\ X_{2(k)}\end{array}+\begin{array}{1}0\\ 1\end{array}uk\)
\(y(k+1)=\begin{array}{1}1&1\end{array}\begin{array}{1}X_{1(k+1})\\ X_{2(k+2)}\end{array}\)
Using state variable technique design a controler with z=±0.5
This is where I am not sure if I times \(\begin{array}{1}0&1\\ -0.4&-1.3\end{array}\) by ±0.5 to get the answer....