K-infinity in 'ncfsyn' command for loop shaping design procedure

Hi... Currently I'm trying to simulate a system that using Loop shaping design procedure as robust controller. Since this is McFarlane n Glover's, I use the command 'ncfsyn' in order to get the K.

So, I've tried the example in HELP. There is one paragraph for the HELP that I don't understand: "The closed-loop H∞-norm objective has the standard signal gain interpretation. Finally it can be shown that the controller, K∞, does not substantially affect the loop shape in frequencies where the gain of W2GW1 is either high or low, and will guarantee satisfactory stability margins in the frequency region of gain cross-over. In the regulator set-up, the final controller to be implemented is K=W1K∞W2."

MY questions: 1) What does this mean that K-inf does not substantially affect the loop shape? 2) Can we calculate K-inf? How? Please show me how.

Thank you

Answer 1

[James Whidborne]

1) What does this mean that K-inf does not substantially affect the loop shape?

Not at high or low frequencies (if you have got the loop shape right, i.e. high gain at low frequencys, low gain at high frequencies). The shape will be changed near cross-over, usually by the addition of phase advance that will improve the stability margins.

2) Can we calculate K-inf? How? Please show me how.

It is returned in INFO.Ks - see the help file.

There is an interactive gui on the File Exchange that can help perform the loop-shaping (lsdptool): http://www.mathworks.co.uk/matlabcentral/fileexchange/1285-lsdptool