Application of discrete derivative method with a new frequency mapping technique for adaptive-notch-filter based vibration control in industrial servo systems

This paper presents an application of a discrete derivative method with a new frequency mapping technique for adaptive-notch-filter (ANF) based resonance suppression in an actual industrial servo system. An ANF includes a frequency estimator which estimates the frequency of input signal in real time. A new discrete derivative method, which utilizes a modified bilinear transform, was recently developed to improve the frequency estimation performance of ANF and applied to computer simulation cases. The frequency estimation performance in steady state is improved, especially in high frequency ranges by using this derivative method. However the previous method can cause large estimation errors when estimated frequency varies rapidly. This paper develops a new frequency mapping technique which compensates for the frequency warping of the modified bilinear transform, and applies it with the discrete derivative method to implement an ANF. This method shows improved frequency estimation performance even when the estimated frequency varies rapidly. Numerical simulations are performed for the cases which an adaptation gain, the amplitude of an input signal, or the frequency of an input signal is high, respectively. Note that the rapid change of estimated frequency occurs in these cases. Experiments using an industrial servo system are also performed to show the improved frequency estimation performance of the developed ANF.