An active micro-vibration isolation system for adaptive vibration suppression using piezoelectric stack actuators is presented, along with the discrete time modelling method, real-time adaptive controller design, and hardware implementation. The system comprises piezoelectric stack actuators, capacitive displacement sensors, power amplifiers, signal conditioners, and a real-time computer. A discrete asymmetric Bouc-Wen model is developed to characterize the nonlinear behavior of the piezoelectric stack actuators. System identification is conducted using an improved particle swarm optimization method, specifically the Hybrid PSO-Jaya algorithm, which sequentially integrates the PSO algorithm with the Jaya algorithm. Additionally, an improved adaptive filtering algorithm employing affine projection, referred to as the FXAPA algorithm, is introduced to facilitate real-time control. The efficacy of the proposed active micro-vibration isolation technology is validated through micro-vibration suppression tests.