FNN Approximation-Based Active Dynamic Surface Control for Suppressing Chatter in Micro-Milling With Piezo-Actuators

In this paper, an active dynamic surface control (DSC) to suppress regenerative chatter in micro-milling with nonlinear piezo-actuators (PZTAs) as active elements has been developed, where the hysteresis effects of two PZTAs are considered. The main features of the proposed approach are: (1) fuzzy neural networks (FNNs) are applied to approximate the unknown functions, including the uncertain dynamics of the high speed cutting system, the unknown bounding functions related to the time-delayed states, and the control errors introduced during the control design procedure; (2) to avoid the development of the adaptation law for each individual weight of the FNNs, the squared 2-norms of the weight vectors are constructed; (3) the utilization of two decreasing smooth performance functions ensures the boundedness of the tracking errors with the prescribed performance; (4) the Prandtl-Ishlinskii (PI) model is employed to depict the hysteresis effect of the active PZTAs and its inverse construction is adopted to mitigate the nonlinear influence; and (5) the Lyapunov-Krasovskii functional is used to cope with the time-delayed effect of chatter in micro-milling, which plays a pivotal role in developing the active control laws. The developed controller with the employments of Lyapunov-Krasovskii functionals, DSC and the adaptive FNN backstepping design can successfully suppress the chatter in micro-milling, guaranteeing all the signals of the closed-loop system are bounded. Simulation results are provided to verify the effectiveness of the proposed control approach.