To tackle the nonlinear characteristics and multi-axis decoupling control challenges of piezoelectric micro-motion stages, we propose a modified pigeon-inspired optimization algorithm(PIO) that incorporates a dynamic mutual learning(DML) strategy. Additionally, an experimental study is conducted to integrate fractional order proportional-integral-derivative(FOPID) control with the DMLPIO-FOPID control strategy. Initially, we perform a mechanical analysis of the piezoelectric micro-motion stage to approximate its nonlinear behavior through linearization techniques. Subsequently, a dynamically opposing learning population is established based on the dynamic mutual learning strategy to enhance the optimization efficacy of the pigeon-inspired optimization algorithm. Furthermore, we introduce a delay identification method utilizing sparse regression algorithms to compensate for hysteresis inverting models associated with piezoelectric micro-motion stages. Finally, an experimental platform is developed for testing the designed controller on piezoelectric micro-motion stages. The experimental results demonstrate that the DMLPIO-FOPID controller outperforms four evaluation function optimization tests by an average margin of 19.28% and 20.73% compared to fruit fly optimization and traditional pigeon-inspired optimization strategies, respectively. Moreover, it achieves minimal mean square deviation and shortest convergence time during three-axis testing of piezoelectric micro-motion stages, indicating that the DMLPIO-FOPID control approach significantly enhances precision in controlling these systems.