Didviding and multiplying transfer functions

Hi all,

I have a question on transfer function division and multiplication. If I calculate the closed loop function using:

G/(1+G*H)

I obtain different results than if I try calculating it by hand or using command.

feedback(G,H)

For example

                4.244e-12 s^3 + 8.004e-08 s^2 + 8e-07 s
    ------------------------------------------------------------------------
    1.801e-19 s^5 + 6.792e-15 s^4 + 6.407e-11 s^3 + 4.308e-08 s^2 + 0.0008 s

This is the closed loop using first command. This is with feedback command:

             0.0001 s + 0.001
  -------------------------------------------
  4.244e-12 s^3 + 8.004e-08 s^2 + 8e-07 s + 1

While calculating it by hand gives:

               0.0001 s + 0.001
  -------------------------------------------
  4.244e-12 s^3 + 1.224e-07 s^2 + 8e-07 s + 1

Do you know how is this possible?

Thanks!

[J. Carlos Aguado]

You just have to apply "minreal" to your result, and you will see that minreal(G/(1+G*H)) = feedback(G, H). MatLab should you that automatically.

[Syndi Katya]

Nice trick

Answer 1

[Debarati Banerjee]

Can you first apply the function ' minreal ' on your 'G' and 'H' functions before applying the closed loop formula? This 'minreal' function will reduce the systems into minimal order.

Also, can you please provide the G and H functions with which you arrived at these results?

Cheers!

Debarati

Answer 2

[yu-hsien chen]

https://au.mathworks.com/help/control/examples/using-feedback-to-close-feedback-loops.html

This is a really really late reply but the above link explained it.

[J. Carlos Aguado]

That link does not work any more

[Walter Roberson]

The link is valid.

https://www.mathworks.com/help/control/ug/using-feedback-to-close-feedback-loops.html