‫Welcome back.
‫So now let's go back to our feedback legalization controller.
‫This was it schematics.
‫And you can see that you have three control laws here.
‫One was here for the X dimension then.
‫One was for the Y dimension and one was for the Z dimension.
‫And just to remind you that in the vector matrix form, it was like this, so you had K one here and
‫then K two here, regardless of the dimension, and then you would multiplied by an error and error
‫dot, and then you received this scalar quantity for each dimension.
‫And so what we had also earlier established was that our you x this one here, USIP X, it turned out
‫to be our error double dot for the X dimension.
‫Then this use of why was our error double that for the why dimension and the use of BCU was our error
‫double dot for the Z dimension, that means that you have three homogeneous LTI differential equations
‫that are second order because your use of X is the error double derivative with respect to time use
‫of Y the same thing and use of Z, the same thing.
‫For the X, Y and Z dimension, respectively, so this differential equation here is for the X dimension,
‫this differential equation is for the Y dimension.
‫And this differential equation is for the Z dimension and so for each dimension, for each differential
‫equation, the polls that I chose are minus one and minus two because they showed very good tracking.
‫Therefore, Lambda one for the X dimension equals minus one and lambda two for the X dimension equals
‫minus two.
‫The same thing for the Y dimension.
‫And the same thing for the Z dimension.
‫And so if you put these polls in the equations that we had derived before, then you will get your key
‫values.
‫Your key one for the X dimension will be minus two.
‫And then your key to for the X dimension will be minus three.
‫The same thing for the Y dimension and the same thing for the Z dimension.
‫So we chose our numbers to be minus one and minus two because they would give us negative exponents.
‫And so that means that they would drive our errors down to zero like this and we would avoid isolation
‫because we don't have any imaginary poles here.
‫And based on our choice for Poles, we computed our key values to be minus two and minus three for all
‫our three dimensions.
‫And now let me show you the results with the simulation.