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Draft esign observer

hello we're now we're going to talk about observers and the motivation here comes from state feedback so last time we saw that through this state feedback control law we were able to manipulate properties of the open loop system in particular we were able to place all of the closed loop poles wherever we wanted so no matter what the open loop system was through designing our state feedback we could place the poles of the closed loop into arbitrary locations now this came with a catch um in that state feedback assumes that uh we can measure the system state which you can't in practice and this is what the role of an observer is in all of this so we cannot measure the system state so what we're going to do is design an observer to estimate the system state and then rather than applying our state feedback to the true state which we can't measure we're instead going to apply it based on our estimate of the state instead and we'll talk about that a little bit uh in the next lecture um now we're just going to talk about observer design um so state feedback assumes we can measure the state we can't um so let's try to estimate it with an observer so what's going on well we have some state space model x dot is equal to ax plus b u y is equal to c x and we can measure this so we can measure why and we want to estimate this so we want this because then we can apply state feedback and we can place our closed loop holes so that they're nice and stable or something like that and um we'll talk more about where you should place the the poles in this sort of bonus video that i was talking about last time so here we have our state space model this is what we can measure this is what we want to do and our state observer is also a feedback system that tries to update its estimate of the state based on the measurements that it takes and the way it does this is as follows so we introduce a new variable this variable is internal to the observer so this is part of our control system and we're going to call it x hat and this is our state estimate um let's just write in a little bit more so and what the first thing we're going to do is we're going to build a copy of our system so this isn't the true system this is well a copy and it also corresponds to what we think our system is so we've talked before about how models are only approximations of reality so a b and c these are really our model um this is what we think our system is they're not the actual system um so the observer is based on our...