Renter - page 13

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long, you say?... hmm... I could post the final formula here, say use it -- end of story... and whether or not you understand where it came from is none of my business...

but no, I show you step by step what, how, why...

You don't want to figure it out, just walk away.

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Actually, it's easier when you know what you're talking about. It's like having a multiplication table in your head, if you know the multiplication table. But you had to learn it sometime in order to use it now...

 

It looks depressing))

I'll pass with the derivative, I've forgotten a bit, I could be wrong. For a more or less sane student of any technical specialty, who has managed to survive to the second year (and has not yet survived the third), it is a 15-minute task.

The algorithm for solving the problem is:

1. The formula for the profit to be withdrawn for each month, you might say, is easily written down from the ceiling, without any mathematical manipulation.

2. the integral of this formula by month.

3. Finding the extremum is the derivative of that integral by the withdrawal coefficient.

ps. Matlab is evil. A normal maths reference book is much more useful.

 

Let's continue...

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Convert the structure diagram to the following form

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Let me remind you: at this stage of the problem we need to define the output processes in the time domain --- B (t) and C(t).

 
 

Next, let's see how the movement changes depending on the valve state, against the initial setpoints.

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withdraw 20% of the accrued

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. remove 40% of accrued .

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withdraw 60% of assessment

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withdraw 80% of assessment

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Here we notice that for q=30%, the maximum for C(t) is around 40% -- 60% withdrawal

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Then we can proceed to the third step of the problem.

 
Integer: For a more or less sane student of any technical speciality who has managed to survive to the second year (and not yet survived the third), this is a 15-minute task.
No, not 15. The main problem is solving the equation "the derivative equals zero". In the general case it doesn't seem to be solvable in finite form. So we have to find an approximate analytical solution and evaluate its accuracy. But first we need to understand what method to use to solve the equation. There are several parameters in the equation and this complicates the problem.
 
avtomat:

A couple more clarifying questions: are you familiar with the transfer function technique? and the Laplace transform technique for solving diff equations?

You know, avtomat, I have heard these terms in my time, but I have no practical experience with this apparatus of matanalysis.

We are waiting for the sequel. Very interesting.

Except that I don't understand how one can get "...smooth derivative of this process..." different from the one obtained above in the form:

df/dk=

Notice, it is also smooth (I mean infinitely differentiable).

 

Read us an ATS course, we know this stuff. It is not quite clear what this is all about, when you can just get the formula you need...

The Laplace transform won't help us solve a stupid algebraic equation anyway.

 
Maybe the trick here is to represent the original equation in another domain, where it has a digestible form and is easily solved... Well, roughly as we do with the integral in the infinite bounds of the normal distribution - it is not taken, but go to polar coordinates and a miracle happens - it is taken elementary.
 
Mathemat:

They read us the ATS course, we know that. It is not quite clear, why all this here, when you can just get the formula you need...

The Laplace transform will not help us solve the stupid algebraic equation anyway.

read... and know... --- not the same thing.

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"you can just get the right formula..." --- where is it? already got it?

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The Laplace transform is a very powerful tool. But I've always wondered how you can say "it won't work anyway" -- without knowing the subject... Did you learn that in your ATS course?

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And what is the solution to this "stupid algebraic equation" ?

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