Introduction: Modeling, Identification, Optimization, and Control

Abstract

Mathematical modeling, simulation, nonlinear analysis, decision making, identification, estimation, diagnostics, and optimization have become major mainstreams in control system engineering. The designer describes physical system dynamics in the form of differential or difference equations, and the comprehensive analysis of complex dynamics systems is performed analytically or numerically solving these equations. To develop mathematical models of the system dynamics, the Newtonian mechanics, Lagrange’s equations of motion, Kirchhoff’s laws, and the energy conservation principles are used. It is evident that one cannot guess models of physical systems and pretend that the assumed models describe real-world systems under consideration. Chapter 2 illustrates that the designer can straightforwardly develop mathematical models of electromechanical systems, as well as their components (actuators, transducers, power converters, electric circuits, and filters) to be simulated and controlled. The development of accurate mathematical models, in the form of differential or difference equations, with a minimum level of simplifications and assumptions is a critical first step because all subsequent steps will be mainly based on the mathematical model used. Model development efforts are driven by the final goal, which is to satisfy the desired system performance as measured against a wide spectrum of specifications and requirements imposed. That is, mathematical models must satisfy the intents and goals for which they were developed, serve the design objectives, be user-friendly and well understood, and so forth.