A New Stability Index for Industrial Servo Systems Using Frequency Response Function Considering Measurement Delay and Noise

Designing a controller which achieves a high bandwidth with good stability is an important requirement in industrial servo systems. The frequency response function (FRF) is one of the widely utilized tools, but FRF results are sensitive to measurement delays and measurement noise. This hinders the tuned controller to achieve predicted performance levels. The measurement noise can distort the FRF in whole frequency ranges and has been considered in many previous research efforts; however, the measurement delay has seldomly been considered in the design process. When the measurement delay is not considered, the information in the high-frequency range which is typically related to system resonances can be inaccurate. This paper proposes a new stability index for the FRF which considers the uncertainties from both measurement delay and noise. In the proposed method, the uncertainty bounds of measurement delay and noise are defined and the maximum moving area of FRF data for each frequency is calculated based on these uncertainty bounds. The stability index is defined to check possible encirclements on the Nyquist plot based on the maximum moving area. The proposed stability index is used to tune notch filters in industrial belt-drive systems with wide resonance frequency variations. The experimental results show that the proposed stability index achieves stable tuning performance even in the presence of delay and noise in FRF data.