Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system

Use of the Nyquist Stability Criterion in the Design of Interactive Audio Digital Filters

Interactive audio processing systems sometimes include user-controlled digital filters, whose response is obtained by interpolating between different transfer functions. Audible artifacts produced by these filters are caused by migration across the unit circle of the zeros in their transfer function, depending on the interpolation parameter values. There are cases in which the Nyquist stability criterion for discrete-time systems can turn useful to inspect, and possibly modify the trajectories of such zeros. After a general discussion, two examples are illustrated in which Nyquist stability is used to optimize the response of filters realizing a linear interpolation between two transfer functions