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‫Welcome back.

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‫I think it's good now to look at the big picture.

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‫You have your plant and you have your controller.

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‫The controller takes in the reference values.

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‫X, Y, Z.

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‫Which are the position, reference values and Fifita and BPCI, which are the attitude, reference values.

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‫Right now, we don't care about the controller, we only care about the plant, the controller right

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‫now is a black box.

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‫We don't know what's inside there.

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‫We're almost done with the plant so soon, very soon, we're going to go and start unpacking the controller.

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‫The thing is that our controller will, in fact, need a lot of stuff.

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‫It will need the state values in the body frame, so you, the W, P, Q and R and you get it from the

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‫plant.

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‫So in this plant, you have a box, a mini box inside the big box where you have you that weeda w dot

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‫p q that an r that this mini box consists of all these six states based equations.

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‫Because this is where you get your due date with the W dot and then that Cuidad and R dot from these

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‫equations, so that many boxes for these equations here and then you put it through an integration box

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‫and that integration box, it will give you U, V, W, P, Q and R, and this integration box is for

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‫these equations here where you take your state now, the time derivative of your state, your sample

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‫time interval and then your end value and then you compute your new state.

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‫So that's the integration box over there.

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‫And so these new states then go into the controller, but not only.

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‫If you look at this set of state base equations, then you see that in order to compute the time derivatives

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‫of your states, you need the states themselves.

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‫You see, you have the here you have WQ are because remember, the states based equations mean that

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‫your state time derivatives, they are a function of your states and inputs.

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‫So you need the actual states in these equations as well.

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‫That means that these body frame states, they have to go back into this box as well.

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‫So the states that leave the plant, they leave the plant as states at K plus one, but then the same

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‫states the same numbers that leave the plant when they go back into this box here, then they go into

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‫this box as states at K, then you compute the new derivatives, you perform the integration again,

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‫and then you compute the new states that will be states at K plus one.

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‫And then these new states, they will go back into the plant and into this state's basic equation box.

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‫And when they do again, they will enter this box as states at K.

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‫And then again you perform the integration new states at Kapos one, and that's how the loop goes.

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‫And in the meantime, of course, these states enter the controller because as you will see in the future,

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‫the controller will need them to.

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‫One additional remark, this integration method here, this is called an oilor integration method.

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‫In this oilor integration method is the simplest one, however, it is also the most imprecise one,

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‫which is why often times you need some kind of end value here in order to integrate it with smaller

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‫intervals.

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‫In the previous course in this series, I used this method, however, in this course, I'm going to

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‫teach you a more advanced method to perform this kind of integration.

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‫So this is the Euler method.

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‫It is the simplest, but also.

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‫It is not that much used anymore, especially in advanced projects, because there are some issues associated

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‫with it.

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‫There are some problems with it and I'm going to talk about it very soon.

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‫So in this course, I'm going to teach you a method called Runga Kutta.

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‫More precisely, a fourth order wrong Akutan integrator.

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‫It's a very popular integration technique in order to compute new states.

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‫It is very widely used.

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‫For example, in Matlab, there is a very advanced, integrated function called Odie's forty five.

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‫And they created that function using the fourth order Runga Kouta method.

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‫And that's why you have four here.

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‫I'm not sure what the five stands for, but what I know is that four stands for the fourth order.

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‫Wrong Kutta integrated method.

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‫This is going to be a slightly more complicated than the Oilor method that we used in the previous course.

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‫However.

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‫Learning that would be very beneficial to you, because in the engineering community, it's very popular

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‫and very widely used, so we're going to talk about it very soon in this section, in fact.

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‫So in this integrated box, you can use either Oilor, which is this one here in yellow or.

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‫Runga Kouta.

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‫OK, so let's carry on now.

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‫Now, we also had another box here.

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‫We had an omega box.

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‫Which had to be as a function of the control inputs, the use, remember, the controller will give

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‫you four system inputs.

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‫It will give you you one, you two, you three and you four, and we needed that box because the state's

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‫basic equation box also needs the Omega's, right.

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‫So from this box, you will get your omega one Omega to Omega three and Omega four like this, because

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‫if you look at the states basic equations here, then you see you need an Omega.

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‫And this total Omega is composed of four Omega's from each model.

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‫So to be precise, this box will actually give the total sum of all the omega three.

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‫Because inside this box, once you have your four or Mangahas from your four mortars, you will add

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‫them all up and then you will send that total Omega into this state base equation box.

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‫But to be honest with you, that even our controller will need that Omega.

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‫So what will really happen is that.

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‫This Omega will not only go to that box, but it also needs to go into the controller, so this Omega

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‫will go into the controller, then the controller will compute.

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‫You want you to use 3U for it will go into this omega box and then a new Omega will come out.

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‫And of course, we're going to treat that box as well.

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‫And now if you look at your state base equations, then you see that you also have you want you to use

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‫three and you four here.

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‫So that means that they use that go into this omega box.

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‫The same use need to go into the state's basic equation box.

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‫So the same you want you to use three and you four will go into this box as well.

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‫Then if you look at your integrator, in this case, Oilor and later Runga Kutta, which by the way,

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‫will also be used in the code.

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‫So this time in the code, I will use Runga Kutta, but in either case, in order to compute a new state,

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‫you need a present state.

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‫You see you have your EUC, V.K., W.K., etc. It means that these body frame state values, they also

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‫have to find their way into this integrated box.

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‫So there you go.

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‫The same body frame states go also into this integrated box.

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‫And now due to the fact that the reference values these ones here they are all in the inertia frame.

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‫Your states that come out of the planned model must also be in the inertia frame.

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‫So not only in the body frame, but you also have to convert them into the inertia frame and then they

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‫also have to get out of the plant and into the controller.

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‫Otherwise, if you don't do the conversion, then you compare the inertia frame reference values to

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‫the body frame states and that would be like comparing apples with oranges.

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‫You shouldn't compare measurements that are made in different reference frames.

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‫It would simply not make sense.

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‫It's like comparing two distances and one is in kilometers and the other one is in miles.

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‫So in addition to the body frame states, the controller will also need the states in the initial frame.

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‫So it will need X, Y, Z and Fifita and BPCI.

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‫However, thanks to the massive previous chapter that you had, you now have tools in your tool bag

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‫to perform this conversion in an easy way.

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‫So let it be your exercise now you have your states which are translational and angular velocities in

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‫the body frame, you BWP, you are they are in the body frame and your job now is to convert them into

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‫the inertia frame.

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‫So knowing your body frame states, what do you need to do in order to.

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‫Get your states in the inertia frame.

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‫What do you need to do to get them in this state?

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‫So how do you get your X, Y, Z position values and then Fifita and BPCI attitude values?

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‫Again, no calculations are necessary.

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‫It's a concept testing one or two minute exercise.

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‫I want you to think in terms of general steps of what you would do in order to get that.

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‫What would be your blueprint for that?

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‫So I'll tell you that in the next video.

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‫But first, try yourself as well.

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‫All right.

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‫So see you in the next video.

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‫Thank you very much.