‫Welcome back.
‫So in the previous course, you learned about the linear parameter, varying technique, or LP the and
‫the OPV technique is a highly researched topic and part of.
‫Robust control.
‫Now, the thing about HPV is that the variables in the Matrix five, that theater that and Omega, they
‫have to be within some kind of range.
‫You cannot have some crazy values for the otherwise.
‫Your NPC might not simply be able to control the wave.
‫However, for smooth trajectories like the ones proposed in this course, the OPV technique works very
‫well.
‫And so, as you can see, even though your system is not an LTI system, so your matrix is A, B, C
‫and D are not constant throughout the entire maneuver.
‫So it's not an LTI system.
‫In fact, you have a nonlinear system.
‫However, by using the LP we approach, you can still use the NPC methodology that you learned in the
‫previous course that was developed for the LTI systems, and that is great because that means that you
‫have so many more places in which you can use this knowledge.
‫Thanks to the LP approach, you can expand linear control techniques to non-linear systems, not all
‫of them, but to many.
‫And now I want to point out something earlier.
‫Due to a small angle approximation, our transfer matrix, it became an identity matrix that allowed
‫us to say that fi dot equals P Theta.
‫That equals Q and BPCI.
‫That equals R.
‫That allowed us to take the original state based equations with P, Q, R variables and rewrite them
‫in terms of five that setar that and decide that.
‫However, we only made the small angle approximation to get those modified equations because that made
‫it very easy for us to put it in the LP form.
‫However, when you get your P, Q, R states from the plant or from a sensor on a V, you will still
‫first adjust them with the transfer matrix like this in order to get your FIDA Theta that inside that.
‫And only then you send your file dot and theta that to this LP V form into this a matrix.
‫And why do I say only that and theta that.
‫Well, because there is no upside that here in this a matrix that doesn't appear here.
‫So you don't equate phi that theta that and upside that with p, q r when you update your A matrix every
‫zero point one second you use the transfer matrix and that makes the actual real time data that enters
‫into the Matrix more accurate.
‫So you used the statements like five equals P and C two.
‫That equals Q and that equals R in order to have your A matrix in this form.
‫However, when you start actually using this form, then you do not equate your P, Q and R with five
‫dot feet that imply that the new states that you get from a plant or from census, you still modify
‫them using the transfer matrix.