If have a system with 4 open loop poles, all at say s=-2, how would the locus approach each of the four asymptotes?
yes it does. but it's not really asymptotes. the loci of the roots really are the four corners of a square centered at s=-2. as K gets bigger, the square gets bigger (not proportionately). (i am presuming that K is the signed, linear gain in series with G(s) and that the feedback is negative feedback with unity gain.)anyway, do you mean that the open loop transfer function G(s)=1/(s+2)^4 would become something like Gc(s)=K/[(s+2)^4+K]?
I still can't really visualise what the locus would look like though. Does it just expand outwards from s=-2, following the four asymptotes?