Nonlinear disturbance observer-based distributed event-triggered control of piezoelectric deformable mirrors

Piezoelectric Deformable Mirrors (PDM), serving as critical components in adaptive optics (AO) systems, play a pivotal role in real-time correction of dynamic wavefront aberrations induced by atmospheric turbulence. However, during high-precision wavefront correction processes employing anti-interference closed-loop control strategies, piezoelectric actuators are subjected to high-frequency driving signals, accelerating performance degradation consequently compromises the service longevity of PDM systems. This study proposes a hybrid disturbance rejection control strategy that integrates a nonlinear disturbance observer (NDOB) with an adaptive event-triggered mechanism. The strategy achieves real-time disturbance estimation and compensation via NDOB, while establishing an event-triggering function based on Lyapunov stability theory to derive stability-guaranteed thresholds. By monitoring disturbance estimation residuals in real-time, the control law is activated only when system instability is detected, effectively addressing the critical issue of redundant actuation frequency in conventional disturbance compensation schemes. Simulation results demonstrate that this method significantly reduces the redundant control frequency of the actuator while maintaining the wavefront fitting accuracy under bounded periodic external disturbance conditions. Under the same operating conditions, the control frequency of the PDM is reduced to 1.79% of conventional methods, thereby extending its operational lifespan.