# Constant phase traces on a Nyquist plot: how?

• posted

I know how to trace closed-loop transfer function constant magnitude curves on a Nyquist plot.

I have not yet been able to find a geometric construct to trace closed-loop transfer function constant phase curves. I know these curves are perpendicular to the constant magnitude curves (why?).

Given M a point on the open-loop transfer function, O the origin, and A the point (-1, j0), arg(OM) - arg(AM) = constant should do it. Alas, it leads me nowhere.

Could you give me some tips?

Thank you very much in advance.

• posted

I don't have this at home, but I do have the equations for M and N circles for inverse Nyquist diagrams M being circles of constant magnitude or gain, and N being circles of constant phase:

u/y = X + 1 + jY M = | u / y |

1/M = SQRT [ (X+1)^2 + Y^2 ] 1/M^2 = (X+1)^2 + Y^2 Circle with centre at X=-1, Y=0, and radius r = 1/M

Lines of constant phase for the INVERSE Nyquist diagram are given by: alpha = /_ u / y = -tan^-1 ( Y / (X+1))

Hope this helps. I'll see if I can find the normal (not inverse) stuff tomorrow.

I used to have a classical control theory by Atkinson with this in. Loaned it to a colleague.

• posted

Yes, how many excellent books have we lost by lending them to colleagues!?

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.