IMC tunning theory

Hello guys,
in attached .pdf you can find little more about IMC controller design. I can put more, but first we could discuss theory behind it. I'm trying to understand how IMC formulas are obtained. Peter's IMC controller design in my previous thread made me thinking about this.
Looking forward to your comments...

The tc is the closed loop time constant. The desired transfer function is 1/(tc*s+1). tc is just 1/lambda.

Peter Nachtwey said:

The tc is the closed loop time constant. The desired transfer function is 1/(tc*s+1). tc is just 1/lambda.

Click to expand...

So I guess, that this story about low pass filter is not good approach in explaining IMC.
Real truth is that one wants to design controller in such way to get desired closed loop transfer function 1/(Tcs+1), right?

Pandiani said:

So I guess, that this story about low pass filter is not good approach in explaining IMC.
Real truth is that one wants to design controller in such way to get desired closed loop transfer function 1/(Tcs+1), right?

Click to expand...

(1/(Tcs+1))^2 works too. This adds a pole to the controller so it becomes a lead lag controller. This may be desireable in some applications because pure integrators amplify 'noise' ( quantizing non-linearities ).

Look at this
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t1p1%20IMC.pdf
This is the way I would approach the problem. Notice that I added a randomizing factor to the plant. I can execute this as many times as I want to show the variance in response. Note, the response does not vary much. You can see in this example the changes are significant but the response is still good.