使用幅频特性的频域辨识虚拟仿真实验设计

Design of a Virtual Simulation Experiment for Frequency Domain System Identification Using Amplitude-Frequency Characteristic

摘要: 当前“自动控制原理”、“现代控制理论”等控制理论课程中数学建模主要使用机理分析方法，导致学生对系统辨识的理解不深刻。本文以一阶和二阶系统的频域辨识为例，设计了基于幅频特性的频域辨识仿真实验。该实验使用Powerlib模块组中的模块在Simulink中搭建了RC和RLC电路仿真模型，通过电路仿真得到幅频特性，使用线性最小二乘技术推导了基于幅频特性的传递函数模型参数的数学表达式。该仿真实验有利于学生正确理解和掌握频域辨识的原理和过程，为正确使用控制理论进行控制系统分析与设计打下基础。

Abstract: At present, mathematical modeling within control theory courses, including “Principles of Automatic Control” and “Modern Control Theory”, predominantly employs mechanism analysis methodologies. This approach often results in students having a superficial understanding of system identification concepts. By taking the frequency domain identification of first-order and second-order systems as illustrative examples, a simulation experiment for frequency domain identification, based on amplitude-frequency characteristic, is meticulously designed. Within this experimental framework, RC and RLC circuit simulation models are constructed in Simulink utilizing modules from the Powerlib module set. Through circuit simulation, amplitude-frequency characteristic data are systematically acquired. Subsequently, employing linear least squares techniques, the mathematical expressions for the parameters of the transfer function model, derived from the amplitude-frequency characteristic, are rigorously formulated. This simulation experiment significantly enhances students’ comprehension and mastery of the principles and processes inherent in frequency domain identification. Furthermore, it establishes a solid foundation for students to accurately employ the control theory in the analysis and design of control systems.