A simple connection between closed-loop transient response and open-loop frequency response

The phase-margin concept of the behaviour of the Nyquist diagram in the vicinity of the critical point is extended to give a more generalized formula. This relates the damping of the principal oscillatory mode of a closed-loop feedback system to the shape of the Nyquist diagram. All the quantities involved can be obtained from this diagram without further mathematical analysis or graphical construction on the diagram. A theoretical foundation for the formula is given and experimental verification is included.