Active Piezoelectric Control of Three-Dimensional Vibration in a Flexible Circular Shaft via a Fuzzy Adaptive PID Algorithm

Flexible circular shafts are critical components for power transmission in engineering systems. However, they are susceptible to complex three-dimensional coupled vibrations under multidirectional excitations, which can compromise operational stability and lead to structural fatigue. To address this issue, this paper presents an active control method for the three-dimensional vibration of a piezoelectrically driven flexible circular shaft via a fuzzy adaptive PID algorithm. The study begins by establishing a dynamic model of the system based on the Euler–Bernoulli beam theory and Lagrange equation. This model forms the foundation for the design of a fuzzy adaptive PID controller. The accuracy of the developed model is then validated through simulations and experiments. Subsequently, active vibration control (AVC) experiments are carried out to evaluate the vibration attenuation effectiveness of various control strategies (including a conventional PID controller as the benchmark for comparison) under different types of excitations applied at the shaft root. The results demonstrate that the proposed active control method has superior control performance, and exhibits excellent vibration suppression performance, especially under bidirectional excitation at the natural frequency, where the vibration suppression ratios in the two orthogonal directions reach 93.03% and 92.09%, respectively.