Phase margin

Abstract: Multiloop linear-quadratic state-feedback (LQSF) regulators are shown to be robust against a variety of large dynamical linear time-invariant and memoryless nonlinear time-varying variations in open-loop dynamics. The results are interpreted in terms of the classical concepts of gain and phase margin, thus strengthening the link between classical and modern feedback theory.

Abstract: Power-electronics-based dc power distribution systems, consisting of several interconnected feedback-controlled switching converters, suffer from potential degradation of stability and dynamic performance caused by negative incremental impedances due to the presence of constant power loads. For this reason, the stability analysis of these systems is a significant design consideration. This paper reviews all the major stability criteria for dc distribution systems that have been developed so far: the Middlebrook Criterion, the Gain Margin and Phase Margin Criterion, the Opposing Argument Criterion, the Energy Source Analysis Consortium (ESAC) Criterion, and the Three-Step Impedance Criterion. In particular, the paper discusses, for each criterion, the artificial conservativeness characteristics in the design of dc distribution systems, and the formulation of design specifications that ensure system stability. Moreover, the Passivity-Based Stability Criterion is discussed, which has been recently proposed as an alternative stability criterion. While all prior stability criteria are based on forbidden regions for the polar plot of the so-called minor loop gain, which is an impedance ratio, the proposed criterion is based on imposing passivity of the overall bus impedance. A meaningful simulation example is presented to illustrate the main characteristics of the reviewed stability criteria.

Abstract: This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order PllambdaDmu controllers. It is based on determining a set of global stability regions in the (kp, Ki, Kd)-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.