1
00:00:00,690 --> 00:00:03,270
‫OK, so that was for the vehicle.

2
00:00:03,720 --> 00:00:05,060
‫How about the wave?

3
00:00:06,030 --> 00:00:17,340
‫Remember that the reason why we wanted the LTI system was because we wanted to use the easiest NPC version

4
00:00:17,340 --> 00:00:21,840
‫that was developed to handle linear time invariant systems.

5
00:00:22,900 --> 00:00:25,570
‫They are easier to deal with than.

6
00:00:26,750 --> 00:00:37,340
‫It is with robust and non-linear NPC control strategies, and so the question is, can we use this NPC

7
00:00:37,340 --> 00:00:40,130
‫technique that we used in the previous course?

8
00:00:40,700 --> 00:00:43,070
‫Can we use it for the UAE as well?

9
00:00:43,730 --> 00:00:52,130
‫Well, you might think that we can if we can put the UVs states based equations in the LTI form and

10
00:00:52,130 --> 00:00:53,600
‫so can we.

11
00:00:54,540 --> 00:01:00,990
‫Let's see, these are the US states based equations in the body frame.

12
00:01:01,960 --> 00:01:06,070
‫This is a screenshot from the previous section, seen this course.

13
00:01:07,210 --> 00:01:15,640
‫Remember that the NPC only takes care of the Oves attitude, not its position, and therefore we only

14
00:01:15,640 --> 00:01:18,580
‫need these three equations from here.

15
00:01:19,060 --> 00:01:24,300
‫P dot equals something, Cuidad equals something, and ah, that equals something.

16
00:01:25,150 --> 00:01:32,250
‫But of course, we also have to be able to move between the inertial frame and the body frame.

17
00:01:32,860 --> 00:01:35,920
‫And for that we use the transfer matrix.

18
00:01:36,990 --> 00:01:40,350
‫And that's how the transfer matrix looked like.

19
00:01:41,300 --> 00:01:50,780
‫This transfer matrix was unique for our convention, which was our step Z, Y, X, that we first rotate

20
00:01:50,780 --> 00:01:58,430
‫about the moving frame Z axis, then we rotate about the moving frame Y axis and then about the moving

21
00:01:58,430 --> 00:02:00,010
‫frame x axis.

22
00:02:00,020 --> 00:02:03,080
‫And that's why you have Z, Y, X.

23
00:02:04,270 --> 00:02:12,070
‫And they are lower case letters because they indicate the body frame axes, not the initial frame axes.