Minor-Loop Gain as a Source of Information on Robust Stability and Transient Performance in an Interconnected System

Dynamic analysis of the interconnected regulated systems is commonly based on the minor-loop gain which composes of the ratio between the output and input impedances defined at an arbitrary interface within the system. The stability of the system is guaranteed, when the minor-loop gain satisfies Nyquist stability criterion. Usually, the stability conditions are expressed as a certain forbidden region in a complex plane out of which the minor-loop gain should stay for stability to exist. The robustness of the stability is guaranteed requiring certain phase and gain margins to exist. It is also natural to assume that the existence of robust stability means also the existence of acceptable transient behavior. The paper investigates the validity of those expectations. According to the investigations, the system-level minor-loop gain measured at an arbitrary interface does not necessarily contain any other information than the existence of stability. The theoretical analyses are based on a set of transfer functions describing the dynamics of a switched-mode converter. Practical evidence is provided based on a small-scale industrial prototype system composing of voltage-mode-controlled buck converters.