Fall 2001 6.3111-4 Of course it can get even worse because we could have C+ 0-1 ●5 o now we have 20 30 0-1 s+2s+1 +2 e Get same result for the transfer function, but now the dynamics associated with a are both unobservable and uncontrollable unnary Dynamics in the state-space model that are uncontrollable, un observable, or both do not show up in the transfer function Would like to develop models that only have dynamics that are both controllable and observable called a minimal realization It is has the lowest possible order for the given transfer function But first need to develop tests to determine if the models are ob- servable and or controllableFall 2001 16.31 11—4 • Of course it can get even worse because we could have x¯˙ =   −2 0 0 −1   x¯ + ∙ 2 0 ¸ u y = £ 3 0 ¤ x¯ • So now we have G ](s) = £ 3 0 ¤  sI −   −2 0 0 −1     −1 ∙ 2 0 ¸ = £ 3 s+2 0 s+1 ¤ ∙ 2 0 ¸ = 6 s + 2 !! • Get same result for the transfer function, but now the dynamics associated with x2 are both unobservable and uncontrollable. • Summary: Dynamics in the state-space model that are uncontrollable, un￾observable, or both do not show up in the transfer function. • Would like to develop models that only have dynamics that are both controllable and observable V called a minimal realization — It is has the lowest possible order for the given transfer function. • But first need to develop tests to determine if the models are ob￾servable and/or controllable