How to programatically get the point of intersection between the unit circle and root locus

I know I can use rlocfind and roughly estimate the value of gain by picking the intersection on the plot but I was wondering if I could get the precise value for gain at the point where unit circle intersects with root locus.

Answer 1

[Matt J]

Since you have a good initial estimate (from the plot, as you mentioned), it would make sense to refine that estimate using fminsearch or fzero. I.e., write a function d(K) of the gain K that measures the difference between the modulus of the root and 1. Then find the root of d(K) with fzero or minimize abs(d(K)) with fminsearch.

[Matt J]

Hasan Ghorbani commented:

Thanks Matt.

After posting the question, I realised that I can 'zoom in' my plot as much as I need before running rlocfind . That way I can get a quite good level of precision with my response. The only problem with this approach is that the cursor jumps between Real axis values due to high level of zoom. Is there any way I can chop the Real axis units to be finer values?