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 controlável.

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

SISTEMAS DE CONTROLE II

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

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 controlável.