‫Welcome back.
‫So let's see how we can solve this exercise.
‫You want to put these equations that you have here, the simplified ones where you assumed that you're
‫fired.
‫Three triangles in the transfer matrix are zeroes.
‫So you take these equations.
‫And you want to put them in this form and it doesn't mean that you have an LPI system here, your matrixes
‫might end up being like this.
‫Let's first think about the state vector X.
‫The state vector contains all the states that the system has.
‫So what are the states in this simplified states based equation's version?
‫Well, you have five double dot equals something.
‫You have theta double that equals something and then you have citable.
‫That equals something.
‫And so from here, you can see that your fishable dot depends on Seeta dot and side that and also the
‫Omega, then your Theta double that depends on you find out and that and Omega and then PSI double.
‫That depends on that.
‫And see to that.
‫And of course, phi double dot, theta double dot and BPCI double that.
‫They also depend on you to Q3 and Q4 respectively.
‫Now you could count your Omega as a state as well.
‫However, in our case it's not necessary and you're going to see why.
‫The thing with states based equations is that remember your state's basic equations, they had your
‫states and then their first order derivatives.
‫So your first order derivatives are five double date, three to double that and double date and then
‫means that your states are Phi Dot, Theta dot.
‫And beside that, at this point, you don't have Omega Dot in your model.
‫However, remember that our output vector y must contain the variables Phi Theta and PSI right.
‫In order to compare them with fly our feet are Anasuya and in the previous course we learned then output's
‫in most cases are simply a set of selected states.
‫That means that also Phi Beta and PSI are your state's.
‫So your state vector looks like this, you have then you have fired that, then you have theta and theta
‫that, and then you have BPCI and then you have outside that.
‫And of course, it's a common vector.
‫It's a six by one vector.
‫And out of these six states that you have here, you choose three of them, you choose Phi Theta and
‫BPCI, you choose them as your outputs.
‫So right away, you know how this equation here looks like this is your output vector.
‫This is this Y and then this is your state vector.
‫Then this, of course, would be your C matrix.
‫This would be your control input vector and then, of course, this one would be your The Matrix.
‫And so in order to get this output vector here, your C matrix must be like this.
‫These ones here that you have in the C Matrix, they will extract your Phi Theta and PSI and of course
‫you don't need anything from here.
‫So this entire term here will be zero.
‫So you can just cancel it out altogether.