‫Welcome back.
‫So now that we have an expression for our thrust force, for one murder, we can compute the control
‫inputs you one, you two and three.
‫And remember, the thrust force for model one was the thrust factor.
‫See T times the angular velocity of the model squared.
‫So first, let's look at you one.
‫So this is our drone here and here you have all these four mortars and of course, this is your body
‫frame by frame X-axis and body frame y axis.
‫And let's put here a body frame, a Z axis.
‫The thrust force produced by more than one will be this one.
‫So time one equals C. Sometimes Omega squared, and now since we're dealing with multiple murders here,
‫then let's specify the angular velocity here.
‫So this angular velocity, it belongs to more one because each motor can rotate differently at a different
‫angular velocity.
‫Then this one could be the thrust force for murder two, which is seize up the times omega two squared.
‫So that's the angular velocity form or two.
‫And note that we assume that for all the murders, the trust factor will be the same because essentially
‫the blades are the same for each model is just each murder rotates at a different angular velocity than
‫this one will be thrust force four more three, which is again the same thrust factor times Omega three
‫squared and finally time four equals C 70 times Omega four and squared.
‫So to get you one, which is the total thrust force generated by all the models of the drone, you can
‫find it like this.
‫You want equals thrust from model one, from model to from three and from more four.
‫You can also rewrite it in this form here.
‫And now you can just factor out the trust factor.
‫And then in the parentheses.
‫You will simply have the squared values of all your angular velocities for all your Maurer's.
‫And you one, of course, has the units of Newton, because it's a control force, and even though omega
‫two and Omega four have negative rotation, but since you square them.
‫In this way, then they will still be positive omega two squared and positive Omega four squared.
‫So that's your total control thrust force generated by the four models that you have.
‫You simply sum up each individual thrust force from each model, and then you will have your total thrust
‫total, you won.
‫Now, if you remember then you was your control moment about the body frame X-axis.
‫So the drone would angular really accelerate about the body frame, X-axis like this, so the rotation
‫would happen about the body frame x axis and about the body frame x axis only, not about the X and
‫Y axis now, only about the X axis.
‫And to create this situation, what we had to do, we had to have equal thrust force by model three
‫and by more one.
‫Both of these thrust forces, they are equal and they have to be equal because if they were not equal,
‫then the drone would start rotating about the body frame y axis.
‫But we don't want that.
‫But we do want the drone to rotate about the body from x axis, and so in order to do that, we're going
‫to apply less thrust here and we're going to apply more thrust here.
‫So your T sub M2 is bigger than your T sub M4 and also from the center of each mortar to the origin
‫of the drone.
‫You have a distance and let's call this distance El.
‫So the moment from more to is about the positive x axis, if you follow your right hand rule, so it
‫would be t sup m two times L because the distance from this point, up until the origin of the drone,
‫that's also L so it will really equal C T times Omega two squared and that's the thrust part.
‫And then times the length of this rod from the center of the drone to the center of the model.
‫Now there is also a moment generated by motor for but this time, according to the right hand rule,
‫your thumb would point in the negative X direction and therefore the moment generated by M4 will be.
‫Minus T, up M, four times L equals minus C, D times Omega, four squared times L.
‫And so the first equation was the moment generated by M2 and this was the moment generated by M4, and
‫so youtoo equals M sub M to minus M sub M for.
‫And when you do that in your moment from M-2 is bigger than your moment from and for because you're
‫thrust force from M-2 is bigger than from and for, but your links are the same.
‫If that's the case, then there will be a positive net moment about the body from X-axis, and that's
‫when the universe will start rotating about this axis.
‫And so you can rewrite this equation in this form and then what you can do, you can factor out see
‫safty times now and then in the parentheses you will have omega two squared, minus Omega four squared,
‫and that will be your Yutu or your pitch control moment.
‫And similarly, if we want to produce the control roll moment or U3, then what we have to do, we have
‫to keep the thrust forces equal in M4 and M2.
‫And that means that the moments that these two task forces generate, they will cancel each other out
‫and then the drone will not rotate about the body frame x axis.
‫However, we do want to have rotation about the body frame Y-axis.
‫And to achieve that, we're going to have a small thrust force in M1 and we're going to have a big thrust
‫force for M three this time your T sub M3 is bigger than your T sub M one.
‫However, both lengths they will be the same.
‫So a positive moment about the body frame y axis will be generated by more three M's up M three.
‫And you know, that is positive because if you take this thrust force and you multiplied by this distance
‫here, then according to the right hand rule, you will start rotating about the body from y axis,
‫meaning that your thumb will point in that direction.
‫And then the moment from Model one will be in the opposite direction, it will rotate about the negative
‫body frame y axis and now you simply rewrite them like this.
‫This is moment three and minus, this is moment one.
‫And so if you factor them out, then this is what you will get, this will be your U3, your role control
‫moment, and that will make the drone rotate like this as shown here.
‫And note that U2 was a moment, so its units are Knewton meters and the same thing applies to U3.
‫It's also a moment.
‫But you one was a force and therefore its unit is Newton, so now we have related you won you two and
‫you three with the Omega's.
‫However, to find the control moment called your, which is EUFOR.
‫For that, we have to dig a bit deeper.
‫And we're going to do that in the next video.
‫Thank you very much.