Application of Frequency Domain Analysis in Intelligent Control Systems

## 1. Introduction

### 1.1 Research Background
In the field of intelligent control systems, frequency domain analysis is emerging as a crucial method of analysis and is drawing significant attention. With the expanding applications of intelligent control systems, there is a growing demand for enhanced system performance and optimization, making the application of frequency domain analysis increasingly vital.

### 1.2 Research Significance
Frequency domain analysis aids engineers in gaining an in-depth understanding of the system's frequency characteristics, thus guiding system design, optimization, and control strategy formulation. It allows for a better comprehension of the system's dynamic response and stability, which in turn improves the performance and stability of intelligent control systems.

### 1.3 Research Objectives and Summary of Contents
This article aims to explore the application of frequency domain analysis within intelligent control systems, delve into the basic principles and methods of frequency domain analysis, discuss its integration with intelligent control systems, and demonstrate its application effects through case studies. The analysis of relevant theories and practical cases is intended to provide useful insights and methods for the design and optimization of intelligent control systems.

## 2. Fundamentals of Frequency Domain Analysis

As an important theoretical tool in control systems, frequency domain analysis has far-reaching application significance. This chapter will introduce the foundational knowledge of frequency domain analysis, including an overview of frequency domain analysis, the principles of Fourier Transform, and spectral analysis methods. Join us in exploring the core concepts of frequency domain analysis.

## 3. Overview of Intelligent Control Systems

Intelligent control systems, as an essential branch of modern control engineering, have seen significant growth over the past few decades. This chapter will present the fundamental concepts, historical development, and application fields of intelligent control systems, offering a better understanding of the role of frequency domain analysis within these systems.

#### 3.1 Introduction to Intelligent Control Systems
Intelligent control systems refer to the automation of complex systems through the use of artificial intelligence, fuzzy logic, neural networks, and other technologies, ***pared to traditional PID control systems, intelligent control systems are better suited for nonlinear, time-variant, and uncertain systems, enhancing system stability and robustness.

#### 3.2 Development History of Intelligent Control Systems
The roots of intelligent control systems can be traced back to the 1960s, with the rapid development fueled by advancements in computer technology and the rise of artificial intelligence research. From early fuzzy control systems to subsequent neural network control and genetic algorithm optimization, intelligent control systems have continuously evolved and improved.

#### 3.3 Application Fields of Intelligent Control Systems
Intelligent control systems are now widely applied in various sectors, including industrial control, biomedicine, transportation, aerospace, etc. They play a significant role in complex system modeling and optimization, adaptive control, fault diagnosis, and more, providing robust support for enhancing system performance and efficiency.

## 4. Theoretical Basis of Frequency Domain Analysis in Intelligent Control Systems

#### 4.1 Application of Frequency Domain Analysis in System Identification

Within intelligent control systems, frequency domain analysis is critically important in system identification. Analyzing ***mon system identification methods include transfer function model fitting and parameter estimation, in which frequency domain analysis is an indispensable component.

# Example: System Identification using Frequency Domain Analysis
import numpy as np
import matplotlib.pyplot as plt
from scipy import signal

# Ge