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.

Imbalanced vibration is an urgent yet challenging problem in active magnetic bearings (AMBs) rotor manufacturing due to the rotor mass imbalance effect. The virtue of active control in AMB systems lies in enabling substantial online mitigation of imbalanced vibrations. However, in practice, due to the lack of speed sensors in most of the existing AMB-rotor systems, efficient rotational speed feedback is still on the way. As a remedy, this article proposes a rotational speed sensor-free synchronous signal processor (SSP) with the double inputs:$x$- and$y$-axes direction displacement measurements of radial AMBs. The proposed SSP is capable of estimating the rotational speed and accordingly generating synchronous signals of the imbalanced vibrations by filtering noise in both directions. Such signals are afterward implemented as a feedforward compensator for eliminating the periodical imbalance effects. With the assistance of the Lyapunov theory, the conditions of the proposed SSP method together with the feedforward imbalance compensator are derived to guarantee the stability of the closed-loop AMB-rotor system. Extensive experimental results substantiate the effectiveness and superiority of the proposed SSP method in terms of imbalanced vibration suppression.

Chatter is a typical kind of unstable dynamics often encountered in machining processes, which often results in overcut and rapid tool wear. Hence, chatter phenomenon worsens the surface quality and reduces productivity in milling systems as well. Recent years have witnessed a surging industrial demand of high quality and high efficiency machining. Specifically, for low radial immersion milling situation, large depth of cuts is inevitably needed so as to increase the machining efficiency. To fulfill such a task, this paper develops a robust active control method to mitigate the chatter dynamics of low radial immersion milling processes. The present approach increases the axial depth of cuts, and the improvement is inversely proportional to the radial immersion ratio. Finally, case studies are conducted to show the substantially enlarged stable region in the stability lobe diagram (SLD) spanned by spindle rotational speed and axial depth of cut. Thus, the method can be expected to improve the efficiency of milling processes.