System Identification Examples with MATLAB Implementation

In the following content, we will provide comprehensive information about system identification. System identification is a methodology that utilizes collected data to understand system behavior. The Recursive Least Squares algorithm, Instrumental Variable method, Augmented Least Squares method, and Bias-Compensation method represent commonly employed approaches for system identification. We will now present detailed explanations of these techniques along with MATLAB programming examples to facilitate better understanding of their practical applications.

The Recursive Least Squares algorithm implements real-time parameter estimation through continuous updating of system parameters as new data becomes available, using a recursive formulation that avoids matrix inversion at each step. The Instrumental Variable method addresses bias issues in standard least squares by introducing correlated but noise-free variables to improve estimation accuracy. The Augmented Least Squares method extends basic least squares by incorporating additional parameters or constraints to handle specific system characteristics. The Bias-Compensation method systematically corrects estimation biases that arise from various noise conditions, ensuring more accurate parameter identification.

Each method will be demonstrated with MATLAB code examples showing key implementation aspects: initialization of parameter vectors, recursive update equations, covariance matrix handling, convergence criteria, and practical considerations for real-world application. The code will illustrate how to structure the algorithms efficiently, handle numerical stability issues, and validate results through simulation studies.