System Identification Experiment Solutions

System identification is a crucial research direction in engineering control, with its core objective being the establishment of mathematical models through input-output data. Correlation analysis is a classical identification method, particularly suitable for impulse response identification of linear time-invariant (LTI) systems.

Experimental Background Correlation analysis is based on the Wiener-Hopf equation, which derives the system's impulse response by calculating the cross-correlation function between input and output signals combined with the input signal's autocorrelation function. This method exhibits strong robustness against noise, making it especially suitable for real-world engineering scenarios with significant noise interference.

Experimental Content Input Signal Design: Typically employs white noise or pseudo-random binary sequences (PRBS), as their autocorrelation functions approximate impulse functions, thereby simplifying computations. Data Acquisition: Records system input signals and corresponding output responses, ensuring sampling frequency complies with the Shannon theorem. Correlation Function Calculation: Uses MATLAB's `xcorr` function to compute cross-correlation between input-output signals and autocorrelation of the input signal. Impulse Response Solution: Employs frequency domain transformation or direct matrix solving methods to derive impulse response sequences from correlation functions.

Experimental Extensions Noise Impact Analysis: Compares identification accuracy of impulse responses under different signal-to-noise ratios (SNR) to validate correlation analysis's noise resistance. Model Validation: Contrasts identification results with theoretical impulse responses or verifies model dynamic characteristics through step response analysis.

Key Report Components Complete reports should include experimental principles, algorithmic steps, MATLAB program flowcharts, result curves (e.g., identified vs. theoretical impulse responses), and error analysis. Programs must annotate critical steps, such as cross-correlation computation, matrix inversion implementations, or FFT transformation logic.