Stabilizing a Class of Periodical Time-Delay Milling Systems by Adaptive Active Control Method

Periodical time-delay scenario is often encountered in industrial manufacturing processes. However, the presence of time delays and periodical coefficients brings challenges to controller design and system analysis, which thereby hinders the performance improvement of such systems. In this work, the dynamics of milling systems are transformed into a time-invariant finite-dimensional uncertain model described by Fourier series and Padé approximation. An adaptive active control law is accordingly designed to stabilize such complex dynamics. With the assistance of LaSalle–Yoshizawa theorem, conditions are derived to guarantee sufficiently large stability regions of the corresponding closed-loop system. A numerical case study is conducted on a standard two degrees of freedom milling perturbation system to substantiate the superiority of the proposed adaptive active control technique in terms of enlarged stable operational regions.