Fall 2001 16.3111-2 This is a bit strange, because previously our figure of merit when comparing one state-space model to another(page 8-8)was whether they reproduced the same same transfer function Now we have two very different models that result in the same transfer function Note that i showed the second model as having 1 extra state but i could easily have done it with 99 extra states!! So what is going on The clue is that the dynamics associated with the second state of the model 2 were eliminated when we formed the product G(s)=[30] because the a is decoupled and there is a zero in the C matrix Which is exactly the same as saying that there is a pole-zero cancellation in the transfer function G(s) 6 6(s+1) s+2(s+2)(s+1 会G( Note that model #2 is one possible state-space model of G(s has 2 poles For this system we say that the dynamics associated with the second state are unobservable using this sensor( defines the C matrix There could be a lot "motion associated with o. but we would be unware of it using this sensorFall 2001 16.31 11—2 • This is a bit strange, because previously our figure of merit when comparing one state-space model to another (page 8-8) was whether they reproduced the same same transfer function — Now we have two very different models that result in the same transfer function — Note that I showed the second model as having 1 extra state, but I could easily have done it with 99 extra states!! • So what is going on? — The clue is that the dynamics associated with the second state of the model x2 were eliminated when we formed the product G¯(s) = £ 3 0 ¤ " 2 s+2 1 s+1 # because the A is decoupled and there is a zero in the C matrix — Which is exactly the same as saying that there is a pole-zero cancellation in the transfer function G˜(s) 6 s + 2 = 6(s + 1) (s + 2)(s + 1) , G˜(s) — Note that model #2 is one possible state-space model of G˜(s) (has 2 poles) • For this system we say that the dynamics associated with the second state are unobservable using this sensor (defines the C matrix). — There could be a lot “motion” associated with x2, but we would be unware of it using this sensor