‫Welcome back.
‫So this is our general control structure here and now let's zoom in into this feedback lionization controller.
‫This is our magnifying glass here.
‫And now we're going to see what's inside this feedback penalization box.
‫So this is the feedback lionization controller block.
‫And here you have the reference values, X, R and X dot are.
‫Then here you have Y are.
‫And why dot r and then the Z R and then the Z dot are these are your reference values that come from
‫the planner.
‫So they are all positive here.
‫So I'm going to put Plus's here.
‫And then from the reference values you subtract the true X and the true X dot, then you also subtract
‫the true Y and the true Y dot and then you subtract the true Z and the true Z dot and as a result you
‫have your error X and then error dot X, then you have error Y and then error dot Y and then you have
‫error Z and error dot z.
‫And then you have this low key vector for the X values, for the Y values and for the Z values, and
‫so as a result, you will receive a control input, you X here, you Y and you Z.
‫And so, as you can already see in this controller, we are treating the X, Y and Z dimensions separately
‫from the planner.
‫You will get your X are an X dot are then why are and why that are.
‫And then also the Z, R and Z dot are these are your reference position states and their time derivatives.
‫And then you will get X and X dot and then also Y and Y dot and then the Z and Z dot, these are the
‫true values.
‫You get the X, Y, Z, and then you've W states from the planet.
‫And then additionally the U V, W states need to go through the rotation matrix.
‫So you have to multiply the rotation matrix by a vector that contains you, VW, a column vector, and
‫that's how you get X, Y and Z dot.
‫And so the error vectors look like this.
‫Then the error vector in the X dimension is ESOP X and E dot sup x or you can also write them down like
‫this X up R minus X and then here you will have X dot sub R minus X dot and the same thing applies to
‫the error vector in the Y dimension.
‫The first element in this vector is the actual error in the Y dimension.
‫And then the second element is the time derivative of that error, the time derivative of the error
‫in the Y dimension.
‫And you can also rewrite them like this, of course.
‫And then finally, this is for the error vector in the Z dimension.
‫And so then their control inputs are like this use up X equals the row vector of key values, times
‫the error vector in the X dimension.
‫And then of course you will get a scalar like this.
‫This will be your scalar k one times the error plus key two times the error dot.
‫Then you're you.
‫Why would be the same thing, it would look like this, and then this would be your scaler, of course,
‫and finally your use of Z would also be like that.
‫There you go.
‫It will be like that.
‫You will have a scalar value here.
‫Note that use up X of Y and then use Z.
‫They are not your phi are theta are and you one that the controller needs to produce for the NPC controller
‫and for the plant.
‫In fact they are intermediate control inputs.
‫These intermediate control inputs will be later converted into fly are theatergoer and you want control
‫input.
‫But first, let's understand this intermediate part better.
‫The question now becomes what the right key values are.
‫That's the question we need to answer.
‫And in order to answer that question, we need to talk a bit about differential equations.
‫So I'm going to leave the schematics B for now and then I'm going to come back to it later.
‫And so in the next video, we're going to talk about differential equations.
‫Thank you very much.