Gain margins and phase margins for control systems with adjustable parameters

This paper presents a method for finding the gain margins and phase margins of control systems with adjustable parameters. The considered systems are first modified by adding an analytical gain-phase margin tester. Then, the characteristic equations are formulated. Finally, the stability equations are used to find the boundaries of constant gain margins and phase margins. The main advantage of the proposed method is to obtain complete information about the effects of adjustable parameters on gain margins and phase margins. As an example, the method is applied to a pitch-rate control system for a re-entry vehicle, and comparisons with the results in current literature are made.