Time-delay Cooperative Control of Circumferential Yarn Implantation System for 3D Braiding Machine Using Novel Nonlinear Adaptive Gains

To achieve accurate and fast cooperative trajectory tracking performance of circumferential yarn implantation system for 3D braiding machine under complicated uncertainties, a new time-delay cooperative control (TDCC) is proposed using novel nonlinear adaptive gains. The proposed TDCC consists of three terms, which are the time-delay estimation (TDE) and fractional-order nonsingular terminal sliding mode (FONTSM) dynamics and designed nonlinear adaptive gains. The TDE is applied to obtain the lumped system dynamics in a concise form, while the FONTSM is designed based on a newly proposed relative-coupling error dynamic to assure high cooperative control performance. Afterwards, novel nonlinear adaptive gains are designed to further enhance the control under measurement noise and lumped uncertainties. Enjoying a novel nonlinear structure, the proposed adaptive gains can effectively suppress the noise effect when the performance is satisfactory; and they still have the ability to ensure adaptive performance greatly when the control tends to degrade. Thanks to above three parts, our TDCC is model-free, precise and robust. Stability is proved using Lyapunov method. Comparative experiments were conducted using a designed circumferential yarn implantation system with three RGVs. The results show that our TDCC provides better performance over the latest two TDC methods, where the root-mean-square error (RMSE) of the RGVs are maximum of 90% and 75% of the other two TDC methods, respectively, and the maximum absolute error (MAE) are maximum of 91.2% and 80.5%, respectively. The RMSE and MAE of the RGVs with payload increase by a maximum of 11.1% and 13.3%, respectively under our TDCC. The results validate the effectiveness of the proposed method.