Identification of static nonlinearities by sinusoidal excitation with variable DC offsets

Area of Science:

• System identification
• Nonlinear dynamics
• Signal processing

Background:

• Nonlinear systems are often analyzed within Wiener-Hammerstein cascades.
• Selecting appropriate test signals is crucial for accurate system identification.
• Sinusoidal signals with DC offsets are suitable for analyzing static nonlinearities.

Purpose of the Study:

• To develop a method for analyzing static nonlinear systems in Wiener-Hammerstein cascades.
• To derive transfer functions relating DC offset input to higher harmonic outputs.
• To demonstrate system reconstruction using inverse filtering.

Main Methods:

• Utilizing sinusoidal excitation with varying DC offsets.
• Measuring system output at higher harmonics of the input frequency using lock-in techniques.
• Calculating transfer functions from DC offset input to higher harmonic output.
• Applying inverse filtering (deconvolution) for system reconstruction.

Main Results:

• Transfer functions for DC offset to higher harmonics were derived, with emphasis on the first harmonic.
• A simulation demonstrated successful reconstruction of a static nonlinear system via deconvolution.
• The deconvolution method bypasses the small-signal assumption, enhancing measurement precision.

Conclusions:

• Sinusoidal excitation with DC offsets is effective for characterizing static nonlinearities in Wiener-Hammerstein systems.
• The derived transfer functions and deconvolution method allow for accurate system identification.
• This approach improves signal-to-noise ratio and measurement accuracy in practical applications.