Gain and phase margins of SISO systems from modified root locus plots

Graphically based methods for determining the gain margin and phase margin of linear time-invariant single-input, single-output (SISO) control systems are treated. The gain margin can be found from a graph showing the angle of each closed-loop system eigenvalue in the complex plane as a function of real gain. At any constant real gain, the phase margin can be identified from a graph of the angle of each closed-loop system eigenvalue in the complex plane as a function of gain angle. The proposed methods do not require frequency calculations and highlight the importance of root sensitivity, with the practical design guideline of not selecting control gains that place eigenvalues near break points.<>