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Fax initial observer

this is the first video on the state space observers so the previous section looked at state feedback and in other words it said how can we determine a feedback control law u equals minus KX so that we get the closed-loop behavior that we want now state feedback assumes that the states are known and if you look here you'll see it uses state information it uses X and therefore it was assumed that the states were available or could be measured easily so our next job is to consider how these state values can actually be estimated or observed so where do we get these state values from what's an observer there Sonne observer is an operator or a system which interprets that's the key word interprets available measurements so what we want to do is go for measurements to an actual value so here's an example I've got an inspector here and they can see some measurements they can see some footprints so what's their job their job is to say given what I can see what am I able to deduce so they can't actually see the state X they can see an alternative measurement and from that measurement they want to deduce something about the state and here's the question what extra knowledge are they going to use in order to make their deduction so we'll illustrate this an example so first of all we have to clarify what we mean by available knowledge show what measurements have we got we need to know what is the quality of these measurements and how much confidence do I have them so if you have a low quality measurement you may not believe in it you may not want to use it and critically what other knowledge can I introduce which is relevant to the measurements if I got other knowledge use this with the measurements to create additional knowledge now this latter point is really really important most measurements have got a context but understanding the context we're able to interpret the measurement much more reliably so don't just take a measurement as its given actually say what's the context that that measurements come from and then you will get more information from it so here's an example I'm an easy one to understand based on muddy footprints so I can see the muddy footprints but what I want to do is ask myself what can I infer from those muddy footprints apart from the fact that they exist - what extra information can I get well I can infer that someone walked this way since it last rained because if it rained it and washed the footprints away I can infer the size of shoe they had on because of the size of the footprint if the footprints are still damp then I can infer it's likely they were made recently because otherwise they would have dried if a limited number of people are around or go on this particular route then I can actually shortlist the possible people who made these footprints and so on so what you notice the more context knowledge I have some context knowledge such as has it rained what is a shoe people wear shoes etc etc so the more context knowledge I have the more information that I can actually get out of this single measurement the measurement tells me much more than just there are some footprints however what if we have a weak context what if I don't know what the weather's been like then I can't do date stamping so I can infer less what if I don't know which people around or which people normally go this route then I can't easily come up with a short list who might have made the footprints what if the footprints are really rather messy then I can't easily determine the shoe size or even the tread pan so without strong context knowledge then my measurement becomes much less valuable I can no longer make reliable deductions so I need both good quality measurement and also good quality context knowledge if I want to make that measurement give me a valuable inference so what's an observer so reverb is an operator or system which interprets available measurements and the key question we want to ask now is what knowledge can we use alongside the measurement in order to make the inferences or this interpretation so state space systems then first what measurements can I make one context knowledge do I have can I combine these efficiently and systematically to make reliable deductions and you remember what I'm actually trying to do is to find out what's the state x of t and so what we're going to say here is you cannot measure X of T directly you can measure something else and we want to infer X of T from available measurements so I happen to know the input I'm going to assume that I know the system dynamics so X dot equals ax plus bu y equals CX and I'm going to assume that I can measure the output so what we can do here is we can group this in two ways we can say the input and the system dynamics are the context knowledge which I have and the measurement I have is the output so I can't measure this state directly but I can measure the system output and the context knowledge I have are the underlying system system dynamics and the input so what's the concept of a state of zero given knowledge of the input knowledge of the measurements of the output a knowledge of the state space model can I determine the state X of T for now we're going to assume that the parameters a B and C are known exactly and the measurements are good now this is an assumption and one of the things you might want to ask yourself is what would happen if you did not know a B and C reliably or if the measurements were poor would you still be able to determine the States X of T so final thing we want to look at is what can we draw out from this system model now typically a human will do a form of that calculation so they'll say in order to arrived at position P with a given speed and timing it's likely I went through position M with a related speed and timing and what we're doing here is a human is we're embedding awareness of system dynamics so we're saying that there's only certain transitions that are possible cars can only go so fast they can in turn so quickly they can only stop so quickly they have to stay on roads so in other words unlimited forms of transition are feasible now why is that important because what we do is a human is we postulate different initial conditions and then we say all right let's simulate forward in time with the model dynamics I've got from those initial conditions and find out can I get the output that I've observed and you'll find there's only a limited number of initial conditions which will match what I've observed and so we narrow down the possible initial conditions by making use of the system dynamics of the key word here is we use our awareness of the underlying system dynamics in order to shortlist so here's a summary we've introduced the concept in observer an observer combines different forms of knowledge facts and measurements to make inferences about a system state so typically in a state space model and we'll combine knowledge of past inputs available measurements of outputs and knowledge of model parameters which implicitly means system dynamics so what we're going to do in the next video is we're going to look at how we can use this information to come up with a mathematical definition of an observer which will give us the system estimates