Resonance Suppression Based on Improved BFGS Notch Filter and Simplified Linear Triangular Model for Double-Inertia Servo Control

To address the defects of the traditional adaptive notch filter, a parameter self-tuning notch filter based on an improved Broyden–Fletcher–Goldfarb–Shanno and a simplified linear triangular model (SLTM) is proposed in this article. A three-parameter notch filter with high flexibility is first used to suppress the resonance of the double-inertia servo system. Then, based on the partial form dynamic linearization data model methodology, an equivalent partial derivative with time-varying properties, in which the SLTM consisting of three parameters of physical significance is utilized to describe the system, is designed to highly approximate the gradient value from the system output to the system input. Additionally, in order to improve the global optimization performance of the IBGS-based notch filter parameter self-tuning, a modified Hessian matrix with a gradient-correcting factor is proposed to correct the search direction, and meanwhile, an extended secant equation incorporating the last three iterations is designed by using the chain rule to improve the convergence speed. Finally, by minimizing the cost function, the notch filter parameters can be online tuned to suppress the resonance for realizing high-precision servo control. Simulation and experimental results are presented to testify the availability of the proposed method.