Respostas AVA

Considere o sistema dado por: $\displaystyle\frac{{{Y}{\left({s}\right)}}}{{{U}{\left({s}\right)}}}=\frac{{{s}+{3}}}{{{{s}}^{{2}}+{3}{s}+{2}}}$ Assinale a alternativa que representa no espaço de estados a forma canônica observável.

$\displaystyle{\left[\matrix{{\dot{{x}}}_{{{1}}}{\left({t}\right)}\\{\dot{{x}}}_{{{2}}}{\left({t}\right)}}\right]}={\left[\matrix{-{2}&{0}\\{1}&-{3}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}+{\left[\matrix{{3}\\{1}}\right]}{u}{\left({t}\right)}$    $\displaystyle{y}{\left({t}\right)}={\left[\matrix{{1}&{0}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}$
$\displaystyle{\left[\matrix{{\dot{{x}}}_{{{1}}}{\left({t}\right)}\\{\dot{{x}}}_{{{2}}}{\left({t}\right)}}\right]}={\left[\matrix{-{2}&{0}\\-{3}&{1}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}+{\left[\matrix{{3}\\{1}}\right]}{u}{\left({t}\right)}$    $\displaystyle{y}{\left({t}\right)}={\left[\matrix{{0}&{1}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}$
$\displaystyle{\left[\matrix{{\dot{{x}}}_{{{1}}}{\left({t}\right)}\\{\dot{{x}}}_{{{2}}}{\left({t}\right)}}\right]}={\left[\matrix{{0}&-{2}\\-{1}&{3}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}+{\left[\matrix{{1}\\{3}}\right]}{u}{\left({t}\right)}$    $\displaystyle{y}{\left({t}\right)}={\left[\matrix{{0}&{3}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}$
$\displaystyle{\left[\matrix{{\dot{{x}}}_{{{1}}}{\left({t}\right)}\\{\dot{{x}}}_{{{2}}}{\left({t}\right)}}\right]}={\left[\matrix{{0}&{1}\\-{2}&-{3}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}+{\left[\matrix{{0}\\{1}}\right]}{u}{\left({t}\right)}$ $\displaystyle{y}{\left({t}\right)}={\left[\matrix{{3}&{1}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}$
$\displaystyle{\left[\matrix{{\dot{{x}}}_{{{1}}}{\left({t}\right)}\\{\dot{{x}}}_{{{2}}}{\left({t}\right)}}\right]}={\left[\matrix{{0}&-{2}\\{1}&-{3}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}+{\left[\matrix{{3}\\{1}}\right]}{u}{\left({t}\right)}$    $\displaystyle{y}{\left({t}\right)}={\left[\matrix{{0}&{1}}\right]}{\left[\matrix{{x}_{{{1}}}{\left({t}\right)}\\{x}_{{{2}}}{\left({t}\right)}}\right]}$

SISTEMAS DE CONTROLE II

Considere o sistema dado por: Assinale a alternativa que representa no espaço de estados a forma canônica observável.

Considere o sistema dado por: $\displaystyle\frac{{{Y}{\left({s}\right)}}}{{{U}{\left({s}\right)}}}=\frac{{{s}+{3}}}{{{{s}}^{{2}}+{3}{s}+{2}}}$ Assinale a alternativa que representa no espaço de estados a forma canônica observável.