1 00:00:00,460 --> 00:00:01,270 ‫Welcome back. 2 00:00:01,870 --> 00:00:12,700 ‫So in the previous course, you learned about the linear parameter, varying technique, or LP the and 3 00:00:12,700 --> 00:00:17,560 ‫the OPV technique is a highly researched topic and part of. 4 00:00:18,580 --> 00:00:20,050 ‫Robust control. 5 00:00:20,770 --> 00:00:31,000 ‫Now, the thing about HPV is that the variables in the Matrix five, that theater that and Omega, they 6 00:00:31,000 --> 00:00:33,260 ‫have to be within some kind of range. 7 00:00:33,970 --> 00:00:38,170 ‫You cannot have some crazy values for the otherwise. 8 00:00:38,170 --> 00:00:43,170 ‫Your NPC might not simply be able to control the wave. 9 00:00:44,020 --> 00:00:52,930 ‫However, for smooth trajectories like the ones proposed in this course, the OPV technique works very 10 00:00:52,930 --> 00:00:53,280 ‫well. 11 00:00:54,040 --> 00:01:05,140 ‫And so, as you can see, even though your system is not an LTI system, so your matrix is A, B, C 12 00:01:05,140 --> 00:01:09,630 ‫and D are not constant throughout the entire maneuver. 13 00:01:09,640 --> 00:01:12,170 ‫So it's not an LTI system. 14 00:01:13,000 --> 00:01:15,640 ‫In fact, you have a nonlinear system. 15 00:01:16,520 --> 00:01:26,390 ‫However, by using the LP we approach, you can still use the NPC methodology that you learned in the 16 00:01:26,390 --> 00:01:36,530 ‫previous course that was developed for the LTI systems, and that is great because that means that you 17 00:01:36,530 --> 00:01:41,380 ‫have so many more places in which you can use this knowledge. 18 00:01:42,110 --> 00:01:51,770 ‫Thanks to the LP approach, you can expand linear control techniques to non-linear systems, not all 19 00:01:51,770 --> 00:01:53,500 ‫of them, but to many. 20 00:01:54,230 --> 00:01:58,280 ‫And now I want to point out something earlier. 21 00:01:58,670 --> 00:02:08,540 ‫Due to a small angle approximation, our transfer matrix, it became an identity matrix that allowed 22 00:02:08,540 --> 00:02:15,650 ‫us to say that fi dot equals P Theta. 23 00:02:15,650 --> 00:02:18,650 ‫That equals Q and BPCI. 24 00:02:18,650 --> 00:02:21,290 ‫That equals R. 25 00:02:22,380 --> 00:02:32,040 ‫That allowed us to take the original state based equations with P, Q, R variables and rewrite them 26 00:02:32,040 --> 00:02:36,890 ‫in terms of five that setar that and decide that. 27 00:02:37,680 --> 00:02:46,290 ‫However, we only made the small angle approximation to get those modified equations because that made 28 00:02:46,290 --> 00:02:52,280 ‫it very easy for us to put it in the LP form. 29 00:02:53,190 --> 00:03:02,340 ‫However, when you get your P, Q, R states from the plant or from a sensor on a V, you will still 30 00:03:02,340 --> 00:03:11,430 ‫first adjust them with the transfer matrix like this in order to get your FIDA Theta that inside that. 31 00:03:12,330 --> 00:03:22,520 ‫And only then you send your file dot and theta that to this LP V form into this a matrix. 32 00:03:23,550 --> 00:03:26,640 ‫And why do I say only that and theta that. 33 00:03:27,390 --> 00:03:32,700 ‫Well, because there is no upside that here in this a matrix that doesn't appear here. 34 00:03:33,570 --> 00:03:44,040 ‫So you don't equate phi that theta that and upside that with p, q r when you update your A matrix every 35 00:03:44,040 --> 00:03:53,730 ‫zero point one second you use the transfer matrix and that makes the actual real time data that enters 36 00:03:53,730 --> 00:03:56,710 ‫into the Matrix more accurate. 37 00:03:57,480 --> 00:04:04,690 ‫So you used the statements like five equals P and C two. 38 00:04:04,710 --> 00:04:12,810 ‫That equals Q and that equals R in order to have your A matrix in this form. 39 00:04:13,500 --> 00:04:23,520 ‫However, when you start actually using this form, then you do not equate your P, Q and R with five 40 00:04:23,520 --> 00:04:31,950 ‫dot feet that imply that the new states that you get from a plant or from census, you still modify 41 00:04:31,950 --> 00:04:33,630 ‫them using the transfer matrix.