‫Welcome back.
‫I hope you gave a thought to our small concept exercise from the previous video.
‫So how do you get from this to this?
‫Well, first of all, remember that there is this relationship here.
‫So you know that you one equals c t times all of that, then you two equals C T times L and then all
‫that, then this is you.
‫Three.
‫And this is you.
‫Four.
‫Now, since you have your omega men and omega max using these equations here, you can calculate your
‫minimum use and maximum use.
‫So what would be your you one minimum?
‫Well, if you look at this equation here, the first one and you replace all these omega s with Omega
‫Men's, then you will get this most possible you one right?
‫So you will have C times omega one mean squared plus omega two mean squared plus omega three mean squared
‫and plus omega four min squared.
‫However, since we have the same type for all the models, then we can say that omega one min equals
‫omega two men.
‫And it also equals omega three men and omega for men.
‫And we can call all that omega men and the same thing.
‫We can say that omega one max equals omega two max that equals omega three max, and that equals omega
‫four max.
‫And we can say that all that equals omega max.
‫Therefore, instead of writing it like this, what I can do, I can simply write you one min equals
‫c t times four times omega min squared.
‫I can do that because all this omega men's here, they would be the same.
‫So that's why I can just multiply them by four.
‫And then in the same way I can write you one max equals c t times four times omega max squared again.
‫If you look at this formula, then if you replace all the omega with omega max, then you will get the
‫biggest possible use one that you can have.
‫But now, if we look at you two, then you can see that here you have a difference.
‫So what makes you two the smallest or the biggest?
‫Well, it has to do with the difference here, right?
‫So you two a minimum would be when you have the biggest possible negative difference and you two maximum,
‫you would have it when you have the biggest possible positive difference.
‫And so you get the biggest possible negative difference when you right here omega mean squared minus
‫omega max squared.
‫So let's see if omega mean squared is three and then omega max squared is 10, then you would have three
‫minus 10 and there would be minus seven.
‫Your smallest possible negative difference.
‫And then you two max.
‫Well, it would be in reverse omega max squared minus omega men squared.
‫Then your you three men and you three max.
‫They follow the same logic.
‫You need the biggest possible negative difference and the biggest possible positive difference.
‫And now finally, in order to get your you minimum and you for maximum, well, if you look at this
‫formula here, you have two negative terms here and two positive terms here.
‫And so in order to get the smallest possible you for value, you would write you for minimum equals,
‫then CQ Times minus two times omega max squared plus two times omega mean squared.
‫Since you put your omega max here, where your negative terms are and you put your omega men, where
‫your positive terms are, then will give you the smallest possible you for.
‫And you can think about it in this way as well.
‫If instead of omega mean squared, I had put here omega max squared, then everything that you have
‫here in the parentheses, it would be zero, right?
‫Both terms would cancel each other out, and that would make your UE4 zero.
‫But if I put Omega Max here and omega men here, that will stretch this UE4 in the negative direction
‫in the biggest possible way.
‫And then finally, you are you for Max.
‫It would be in reverse.
‫You would have minus two times omega mean squared, plus two times omega max squared.
‫Again, it makes sense because if you take your smallest omega and you put it where your negative terms
‫are and then you put your biggest omega square positive terms are, then that will stretch you for in
‫the positive direction as much as possible.
‫So you can see that using omega men and omega max values, we were able to get our minimum and maximum
‫use if we had used omega was somewhere in between omega min and omega max.
‫Then your use would be greater than these minimum use and they would be smaller than your maximum use.
‫If you remember, then you one came out of your feedback unionization block and then it went straight
‫into your plan box and only you to Q3 and Q4 came out of your NPC block.
‫Here you say that if your you one is less than you one minimum, then you will simply assign this you
‫one minimal value to your you one variable and you are simply going to send your you one minimum to
‫your plan box.
‫And similarly, if your you one is greater than you one max, then you will simply send you one max
‫to your plan box.
‫So that's how we constrain our you one values.