Fixed-time observer-based tracking controller for a hysteretic piezoelectric deformable mirror of an adaptive optic...

Area of Science:

• Optics and Photonics
• Control Systems Engineering
• Materials Science

Background:

• Piezoelectric deformable mirrors (DM) offer high accuracy and fast dynamics crucial for adaptive optics (AO) systems.
• Hysteresis in piezoelectric materials degrades AO system performance and precision.
• Complex dynamics of piezoelectric DMs complicate controller design.

Purpose of the Study:

• To design a fixed-time observer-based tracking controller (FTOTC) for piezoelectric DMs.
• To estimate system dynamics and compensate for hysteresis in real-time.
• To ensure precise tracking of actuator displacement references within a fixed time.

Main Methods:

• Development of a novel fixed-time observer-based tracking controller (FTOTC).
• Real-time estimation of hysteresis, avoiding computationally intensive inverse operator methods.
• Stability analysis using two consecutive theorems.

Main Results:

• The FTOTC effectively estimates hysteresis and system dynamics.
• Superior tracking performance and hysteresis compensation demonstrated via numerical simulations.
• Tracking errors converge to zero within a fixed time.

Conclusions:

• The proposed FTOTC offers an efficient and real-time solution for controlling piezoelectric DMs.
• This method overcomes limitations of existing inverse hysteresis operator approaches.
• The controller ensures stable and precise tracking for adaptive optics applications.