‫And how about the other part, how about this X that equals and then this entire business here?
‫Well, your state director is a six by one vector and your control input vector is a three by one vector.
‫And that means that you're a matrix is a six by six matrix and your B matrix is a six by three matrix.
‫So if we look at this format here, then this would be your state vector.
‫This would be your control input vector.
‫This here would be the time derivative of your states.
‫So if you have FYE here, you need to have five dots here, then find that here means that you have
‫five double dot here and then also theta dot and theta double dot and then Seidel's and Passi double
‫dot.
‫And so this here is your six by six a matrix and this is your six by three B matrix.
‫And so the game is to find the elements of the A and B matrices.
‫And so in order to do that, then in addition to having these equations here that you need to compact
‫into this form, in addition to that, you need to have three equations more.
‫So these equations that you have here, they take care of the second, the fourth and then the sixth
‫element.
‫Right.
‫But you need to have an equation for this one and for this one and also for this one here.
‫And these are actually very easy equations.
‫You can just write them like this five that that you have here equals five.
‫That theta dot that you have here equals on that.
‫And then BPCI, that equals upside.
‫That's why did I write them like this?
‫Well, then I can connect this thing here with this thing here.
‫That means all I need to do is to put one here and then the rest will be zeroes.
‫Right.
‫So it's that easy.
‫And the same thing here, theta that equals theta that.
‫So you connect this with this.
‫So it would be one here, the fourth element, and then the rest would be zeroes and that's it.
‫And then finally you have your side that equals upside, that you connect this thing with this thing.
‫It means that you will have one here and then the rest of the elements will simply be the zeros.
‫And then you use these equations to fill in the blanks, so to fill in the remaining rows that you have
‫here, here and also here, and of course, you shouldn't forget about the B matrix here, you'll find
‫that it doesn't depend on you to neither on you three, neither on you four.
‫So that means that you have zeros here and the same thing goes for the dot.
‫So you have zeros here.
‫And also flip side that you have zeros here.
‫And it makes sense, right?
‫Because it's not like your five dot equals something plus you two.
‫Right.
‫It's not like that.
‫And therefore you have zeros here.
‫However, if you look at these arrows here, then not all of these elements will be Xeros, these equations
‫here will give you a hint what you should put in the B matrix as well.
‫So if you haven't done it already, if you haven't completed this A and B Matrix, then try it out now.
‫Try it out as an exercise.
‫And then in the next video, I will show you how the A and B matrices look like.