Mathematical Models of Dynamic Physical Systems

Abstract

Abstract The design of modern control systems relies on the formulation and analysis of mathematical models of dynamic physical systems. Physical systems are represented by connecting the terminals of pure elements in patterns that approximate the relationships among the properties of component devices. The element laws and system relations together constitute a complete mathematical description of a physical system. There are two fundamental approaches to the analysis of linear, time‐invariant systems. Transform methods use rational functions obtained from the Laplace transformation of the system I/O equations. State‐variable methods use the vector state and output equations directly. Simulation is almost always carried out with the assistance of computing equipment. Four methods can be used to construct a phase portrait: (1) direct solution of the differential equation, (2) the graphical method of isoclines, (3) transformation of the second‐order system into an equivalent first‐order system, and (4) numerical solution using simulation.