MATLAB Code Implementation for System Identification

In the field of system identification, MATLAB provides powerful tools and function libraries to implement various signal generation and system modeling tasks. This article introduces several key signal generation methods and their roles in system identification. ### Generation of M-Sequence M-sequence (Maximum-length sequence) is a pseudo-random binary sequence commonly used as input excitation signals for system identification. Its key characteristic is an autocorrelation function that approximates an impulse function, effectively exciting all frequency bands of a system. In MATLAB implementation, M-sequences can be generated using shift registers with specific feedback logic. This typically requires defining register length and initial states, which can be implemented through bit manipulation operations or using communications toolbox functions like `pnseq`. ### Generation of Inverse M-Sequence Inverse M-sequence is the reversed version of an M-sequence, frequently employed in specific system identification scenarios. It maintains the pseudo-random properties of the original M-sequence but alters the signal's temporal structure, facilitating analysis of system symmetry or nonlinear characteristics. The generation method typically involves generating a standard M-sequence first, then applying array reversal operations using MATLAB's `fliplr` or `flipud` functions. ### Generation of White Noise White noise is an idealized random signal with uniform power spectral density across all frequencies. MATLAB provides built-in functions like `randn` (for Gaussian white noise) and `rand` (for uniformly distributed white noise) for noise generation. White noise serves as an effective input signal for system identification because it uniformly excites all frequency bands of a system, making it particularly suitable for frequency response analysis of linear systems. The noise amplitude and duration can be controlled through function parameters. ### Implementation of System Identification Combining the above signals, the basic workflow for system identification typically includes: Input Signal Generation: Selecting M-sequence, inverse M-sequence, or white noise as excitation signals Data Acquisition: Collecting input-output data through experiments or simulations Model Fitting: Using MATLAB's System Identification Toolbox functions (such as `tfest` for transfer function estimation or `ssest` for state-space model estimation) to approximate system models Validation and Analysis: Comparing model outputs with actual data to verify identification accuracy through functions like `compare` or `resid` These methods find widespread applications in control systems, signal processing, and communication engineering fields.