Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback

In this paper two measuring techniques are presented for measuring the Higher Order Sinusoidal Input Describing Functions (HOSIDF) of a non-linear plant operating in feedback. The HOSIDF relate the magnitude and phase of the harmonics of the periodic response of a non-linear system to the magnitude and phase of the sinusoidal excitation. In a controlled system the harmonics generated by the non-linear system will be fed back to the input changing the sinusoidal excitation into a harmonic excitation. The first method applies linear techniques to compensate the bias caused by the harmonic components in the excitation signal. The second method uses a modified repetitive control scheme to suppress the harmonic components in the excitation signal. The effectiveness of both methods is tested in simulations of a mass subjected to Coulomb friction, Stribeck-effect and hysteresis in the pre-sliding regime. The friction forces are modeled with the modified Leuven friction model. The results are compared with the HOSIDF simulated under open loop condition. Both methods prove able to produce reliable results.