Frequency Domain Analysis of Control Systems with MATLAB: A Deep Dive into Transfer Functions and Bode Plots

# Chapter 1: Fundamental Concepts of Frequency Domain Analysis in MATLAB for Control Systems

Control system design and analysis using frequency domain methods hold a central position in both engineering practice and academic research. Frequency domain analysis is concerned with the response characteristics of systems at different frequencies, which is closely related to the stability and performance of the system. This chapter will introduce the basic concepts and operational methods of frequency domain analysis in MATLAB, laying a solid foundation for subsequent in-depth discussions on transfer functions, Bode plots, and advanced frequency domain analysis techniques.

First, we will briefly describe the basic principles of frequency domain analysis, clarifying its role and importance in control system analysis. Then, using MATLAB, this powerful mathematical software, we will demonstrate how to practically operate and analyze the frequency domain behavior of systems, including the spectral representation of system responses and the plotting of frequency characteristic curves. The depth and breadth of this chapter are intended to enable readers to quickly grasp the core concepts of frequency domain analysis and to proficiently apply these concepts within the MATLAB environment.

# Chapter 2: The Concept of Transfer Functions and Their Implementation in MATLAB

## 2.1 Basic Theories of Transfer Functions

### 2.1.1 System Dynamic Characteristics and Transfer Functions

In control system theory, a transfer function is a mathematical model used to describe the relationship between the input and output of a linear time-invariant system. When the system is affected by external forces (such as electrical signals, forces, etc.), its response behavior, i.e., the output quantities (such as displacement, velocity, voltage, etc.) and input quantities exhibit certain dynamic characteristics. The transfer function can transform these dynamic characteristics from the time domain to the complex frequency domain