System Elegant-frequency Characteristics, Wave-sign Diagrams and Stability Criterion

Abstract

Frequency domain method is a crucial technique for analyzing systems in classical control theory, relying primarily on logarithmic frequency characteristics. Characteristic curves generated in semi-logarithmic coordinate systems are typically displayed using a widely recognized chart known as a Bode diagram. However, creating a Bode diagram is an inconvenient process and results in abstract plots. Additionally, incomplete ranges of styles in basic links, along with varying expressions of open-loop frequency characteristics under different forms of feedback, create difficulties in understanding and challenges in application. This paper begins by classifying basic links in detail and constructing gain-phase frequency characteristics from logarithmic frequency characteristics. Then, a functional transformation is applied to plot characteristic curves in a Cartesian coordinate system of linear division, similar to those in a Bode diagram, by which gain-phase frequency characteristics are converted into elegant-frequency characteristics. This approach eliminates difficulties in plotting and understanding of a Bode diagram associated with using a semi-logarithmic coordinate system. On this basis, this paper proposes the concept of loop elegant-frequency characteristics, to solve the problems of misleading and inconvenient applications of open loop frequency characteristics. Elegant-frequency characteristics can facilitate efficient engineering applications, such as analysis, calculation and system correction, and enable the derivation of additional new features, such as wave-sign characteristics and stability criterion, which enhances the frequency domain method and advances the associated knowledge system.

Keywords

• logarithmic coordinate system
• logarithmic frequency characteristic
• bode diagram
• gain-phase frequency characteristic
• elegant-frequency characteristic
• wave-sign pattern