System Mathematical Models and Model Identifications

In this chapter, we discussed most popular mathematical models for most often used systems in our world. In Sect. 4.2, various mathematical models for most popular physical systems are introduced and analyzed, which include the mechanical rotational system, electrical circuit system, and electromechanical system. Following this introduction, the relationship between the step response and the poles of a system is analyzed, and a discussion about the time-domain specifications for step responses is given. Some important properties related to system models, such as final value theorem, steady-state errors, stability, and linear approximation of physical systems, are discussed in Sect. 4.4. Some popular and powerful MATLAB functions provided by the Control System Toolbox are introduced in detail since these functions are helpful and useful for the system modeling and conversion operations. The discussion about system identifications is provided in Sect. 4.5. Some popular and important identification methods provided by MATLAB® System Identification Toolbox are discussed in Sect. 4.6. A case study is provided in Sect. 4.7 to show users how to practically perform the identification process for a typical DC motor using the MATLAB® System Identification ToolboxTM. The QEI and PWM modules in TM4C123GH6PM MCU system are also introduced in this section since we need to use these modules to interface the motor amplifiers and motor optical encoders to build and collect the real data required by the identification process.