1
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‫And how about the other part, how about this X that equals and then this entire business here?

2
00:00:08,510 --> 00:00:18,140
‫Well, your state director is a six by one vector and your control input vector is a three by one vector.

3
00:00:18,380 --> 00:00:28,290
‫And that means that you're a matrix is a six by six matrix and your B matrix is a six by three matrix.

4
00:00:29,240 --> 00:00:35,070
‫So if we look at this format here, then this would be your state vector.

5
00:00:36,020 --> 00:00:38,470
‫This would be your control input vector.

6
00:00:39,320 --> 00:00:42,810
‫This here would be the time derivative of your states.

7
00:00:42,830 --> 00:00:50,090
‫So if you have FYE here, you need to have five dots here, then find that here means that you have

8
00:00:50,390 --> 00:01:00,830
‫five double dot here and then also theta dot and theta double dot and then Seidel's and Passi double

9
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‫dot.

10
00:01:02,360 --> 00:01:13,300
‫And so this here is your six by six a matrix and this is your six by three B matrix.

11
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‫And so the game is to find the elements of the A and B matrices.

12
00:01:20,270 --> 00:01:28,220
‫And so in order to do that, then in addition to having these equations here that you need to compact

13
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‫into this form, in addition to that, you need to have three equations more.

14
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‫So these equations that you have here, they take care of the second, the fourth and then the sixth

15
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‫element.

16
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‫Right.

17
00:01:45,530 --> 00:01:55,150
‫But you need to have an equation for this one and for this one and also for this one here.

18
00:01:55,760 --> 00:01:59,500
‫And these are actually very easy equations.

19
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‫You can just write them like this five that that you have here equals five.

20
00:02:06,740 --> 00:02:12,710
‫That theta dot that you have here equals on that.

21
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‫And then BPCI, that equals upside.

22
00:02:16,760 --> 00:02:19,700
‫That's why did I write them like this?

23
00:02:20,450 --> 00:02:25,480
‫Well, then I can connect this thing here with this thing here.

24
00:02:25,790 --> 00:02:32,920
‫That means all I need to do is to put one here and then the rest will be zeroes.

25
00:02:32,930 --> 00:02:33,330
‫Right.

26
00:02:33,860 --> 00:02:35,060
‫So it's that easy.

27
00:02:35,570 --> 00:02:38,540
‫And the same thing here, theta that equals theta that.

28
00:02:39,110 --> 00:02:42,140
‫So you connect this with this.

29
00:02:42,840 --> 00:02:52,640
‫So it would be one here, the fourth element, and then the rest would be zeroes and that's it.

30
00:02:53,180 --> 00:02:59,770
‫And then finally you have your side that equals upside, that you connect this thing with this thing.

31
00:03:00,230 --> 00:03:09,440
‫It means that you will have one here and then the rest of the elements will simply be the zeros.

32
00:03:10,590 --> 00:03:20,010
‫And then you use these equations to fill in the blanks, so to fill in the remaining rows that you have

33
00:03:20,010 --> 00:03:29,940
‫here, here and also here, and of course, you shouldn't forget about the B matrix here, you'll find

34
00:03:29,940 --> 00:03:35,580
‫that it doesn't depend on you to neither on you three, neither on you four.

35
00:03:36,150 --> 00:03:42,800
‫So that means that you have zeros here and the same thing goes for the dot.

36
00:03:42,960 --> 00:03:45,630
‫So you have zeros here.

37
00:03:46,320 --> 00:03:50,430
‫And also flip side that you have zeros here.

38
00:03:50,970 --> 00:03:52,290
‫And it makes sense, right?

39
00:03:52,470 --> 00:03:59,630
‫Because it's not like your five dot equals something plus you two.

40
00:03:59,700 --> 00:04:00,040
‫Right.

41
00:04:00,270 --> 00:04:01,350
‫It's not like that.

42
00:04:02,070 --> 00:04:03,990
‫And therefore you have zeros here.

43
00:04:04,940 --> 00:04:13,820
‫However, if you look at these arrows here, then not all of these elements will be Xeros, these equations

44
00:04:13,820 --> 00:04:18,240
‫here will give you a hint what you should put in the B matrix as well.

45
00:04:19,130 --> 00:04:27,730
‫So if you haven't done it already, if you haven't completed this A and B Matrix, then try it out now.

46
00:04:27,920 --> 00:04:29,620
‫Try it out as an exercise.

47
00:04:29,630 --> 00:04:34,850
‫And then in the next video, I will show you how the A and B matrices look like.