Q9Control System
Question
Q.9. What are constant M and N circle?
Answer
Constant M and N circles are loci on the G(jω) plane representing constant closed-loop magnitude (M circles) and constant closed-loop phase (N circles) for a unity feedback system, used in the Nichols/Nyquist-based design of closed-loop frequency response.
For a unity-feedback system, constant-M circles are loci of points in the G(jω)-plane (real vs imaginary axes) along which the magnitude of the closed-loop transfer function |C/R| = |G/(1+G)| remains constant at a specified value M; each value of M traces a distinct circle (centered on the real axis, except M=1 which is a straight vertical line). Similarly, constant-N circles are loci along which the closed-loop phase angle ∠(C/R) remains constant at a specified value N; these circles pass through the origin and the point (-1, j0). Overlaying the open-loop polar plot G(jω) on this M-N circle grid (the basis of the Nichols chart) allows direct graphical readout of closed-loop magnitude and phase response, and hence resonance peak Mr, resonant frequency ωr, and bandwidth, without algebraically deriving the closed-loop transfer function.