1
00:00:00,740 --> 00:00:01,610
‫Welcome back.

2
00:00:02,150 --> 00:00:07,070
‫I hope you gave a thought to our small concept exercise from the previous video.

3
00:00:07,700 --> 00:00:11,720
‫So how do you get from this to this?

4
00:00:12,320 --> 00:00:17,810
‫Well, first of all, remember that there is this relationship here.

5
00:00:18,440 --> 00:00:31,160
‫So you know that you one equals c t times all of that, then you two equals C T times L and then all

6
00:00:31,160 --> 00:00:32,930
‫that, then this is you.

7
00:00:32,930 --> 00:00:33,350
‫Three.

8
00:00:33,950 --> 00:00:34,730
‫And this is you.

9
00:00:34,730 --> 00:00:35,180
‫Four.

10
00:00:35,780 --> 00:00:43,970
‫Now, since you have your omega men and omega max using these equations here, you can calculate your

11
00:00:44,630 --> 00:00:47,810
‫minimum use and maximum use.

12
00:00:48,260 --> 00:00:52,130
‫So what would be your you one minimum?

13
00:00:52,760 --> 00:01:00,020
‫Well, if you look at this equation here, the first one and you replace all these omega s with Omega

14
00:01:00,020 --> 00:01:04,100
‫Men's, then you will get this most possible you one right?

15
00:01:04,610 --> 00:01:14,690
‫So you will have C times omega one mean squared plus omega two mean squared plus omega three mean squared

16
00:01:15,290 --> 00:01:18,260
‫and plus omega four min squared.

17
00:01:18,800 --> 00:01:27,680
‫However, since we have the same type for all the models, then we can say that omega one min equals

18
00:01:28,340 --> 00:01:29,420
‫omega two men.

19
00:01:30,050 --> 00:01:34,160
‫And it also equals omega three men and omega for men.

20
00:01:34,760 --> 00:01:39,200
‫And we can call all that omega men and the same thing.

21
00:01:39,200 --> 00:01:48,770
‫We can say that omega one max equals omega two max that equals omega three max, and that equals omega

22
00:01:48,770 --> 00:01:49,450
‫four max.

23
00:01:50,060 --> 00:01:53,600
‫And we can say that all that equals omega max.

24
00:01:54,290 --> 00:02:03,020
‫Therefore, instead of writing it like this, what I can do, I can simply write you one min equals

25
00:02:03,680 --> 00:02:08,600
‫c t times four times omega min squared.

26
00:02:09,230 --> 00:02:14,300
‫I can do that because all this omega men's here, they would be the same.

27
00:02:14,480 --> 00:02:17,480
‫So that's why I can just multiply them by four.

28
00:02:18,050 --> 00:02:29,480
‫And then in the same way I can write you one max equals c t times four times omega max squared again.

29
00:02:29,480 --> 00:02:37,190
‫If you look at this formula, then if you replace all the omega with omega max, then you will get the

30
00:02:37,190 --> 00:02:39,950
‫biggest possible use one that you can have.

31
00:02:40,430 --> 00:02:47,130
‫But now, if we look at you two, then you can see that here you have a difference.

32
00:02:47,780 --> 00:02:51,650
‫So what makes you two the smallest or the biggest?

33
00:02:52,220 --> 00:02:54,920
‫Well, it has to do with the difference here, right?

34
00:02:55,460 --> 00:03:05,240
‫So you two a minimum would be when you have the biggest possible negative difference and you two maximum,

35
00:03:05,240 --> 00:03:10,220
‫you would have it when you have the biggest possible positive difference.

36
00:03:10,910 --> 00:03:18,440
‫And so you get the biggest possible negative difference when you right here omega mean squared minus

37
00:03:18,440 --> 00:03:20,240
‫omega max squared.

38
00:03:20,780 --> 00:03:28,640
‫So let's see if omega mean squared is three and then omega max squared is 10, then you would have three

39
00:03:28,640 --> 00:03:31,670
‫minus 10 and there would be minus seven.

40
00:03:32,300 --> 00:03:34,880
‫Your smallest possible negative difference.

41
00:03:35,480 --> 00:03:36,890
‫And then you two max.

42
00:03:37,520 --> 00:03:43,460
‫Well, it would be in reverse omega max squared minus omega men squared.

43
00:03:44,060 --> 00:03:47,300
‫Then your you three men and you three max.

44
00:03:47,960 --> 00:03:49,490
‫They follow the same logic.

45
00:03:50,000 --> 00:03:55,580
‫You need the biggest possible negative difference and the biggest possible positive difference.

46
00:03:56,240 --> 00:04:03,950
‫And now finally, in order to get your you minimum and you for maximum, well, if you look at this

47
00:04:03,950 --> 00:04:11,360
‫formula here, you have two negative terms here and two positive terms here.

48
00:04:11,960 --> 00:04:19,550
‫And so in order to get the smallest possible you for value, you would write you for minimum equals,

49
00:04:20,120 --> 00:04:30,260
‫then CQ Times minus two times omega max squared plus two times omega mean squared.

50
00:04:30,770 --> 00:04:38,420
‫Since you put your omega max here, where your negative terms are and you put your omega men, where

51
00:04:38,420 --> 00:04:43,940
‫your positive terms are, then will give you the smallest possible you for.

52
00:04:44,360 --> 00:04:46,520
‫And you can think about it in this way as well.

53
00:04:47,060 --> 00:04:55,460
‫If instead of omega mean squared, I had put here omega max squared, then everything that you have

54
00:04:55,460 --> 00:04:59,600
‫here in the parentheses, it would be zero, right?

55
00:05:00,290 --> 00:05:05,990
‫Both terms would cancel each other out, and that would make your UE4 zero.

56
00:05:06,590 --> 00:05:16,250
‫But if I put Omega Max here and omega men here, that will stretch this UE4 in the negative direction

57
00:05:16,880 --> 00:05:18,560
‫in the biggest possible way.

58
00:05:19,100 --> 00:05:22,280
‫And then finally, you are you for Max.

59
00:05:22,940 --> 00:05:24,230
‫It would be in reverse.

60
00:05:24,860 --> 00:05:32,180
‫You would have minus two times omega mean squared, plus two times omega max squared.

61
00:05:32,750 --> 00:05:40,700
‫Again, it makes sense because if you take your smallest omega and you put it where your negative terms

62
00:05:40,700 --> 00:05:49,100
‫are and then you put your biggest omega square positive terms are, then that will stretch you for in

63
00:05:49,100 --> 00:05:52,400
‫the positive direction as much as possible.

64
00:05:53,030 --> 00:06:01,010
‫So you can see that using omega men and omega max values, we were able to get our minimum and maximum

65
00:06:01,010 --> 00:06:07,550
‫use if we had used omega was somewhere in between omega min and omega max.

66
00:06:08,210 --> 00:06:17,720
‫Then your use would be greater than these minimum use and they would be smaller than your maximum use.

67
00:06:18,530 --> 00:06:25,040
‫If you remember, then you one came out of your feedback unionization block and then it went straight

68
00:06:25,040 --> 00:06:31,520
‫into your plan box and only you to Q3 and Q4 came out of your NPC block.

69
00:06:31,910 --> 00:06:41,720
‫Here you say that if your you one is less than you one minimum, then you will simply assign this you

70
00:06:41,720 --> 00:06:49,580
‫one minimal value to your you one variable and you are simply going to send your you one minimum to

71
00:06:49,580 --> 00:06:50,540
‫your plan box.

72
00:06:51,110 --> 00:06:58,760
‫And similarly, if your you one is greater than you one max, then you will simply send you one max

73
00:06:58,760 --> 00:06:59,810
‫to your plan box.

74
00:07:00,470 --> 00:07:04,040
‫So that's how we constrain our you one values.