Beam control method of a liquid crystal spatial light modulator based on fractional-order active disturbance rejection control

The viscoelasticity and relaxation of liquid crystal molecules make the beam deflection dynamics of the liquid crystal spatial light modulator present a memory effect depending on historical states, which integer-order control cannot characterize, causing sluggish response and poor accuracy. FOPID lacks disturbance observation and compensation capability and can only suppress disturbances passively through error feedback. A fractional-order active disturbance rejection control method is proposed: a fractional-order extended state observer estimates the internal and external disturbances as a total disturbance and compensates them by feed-forward; a Smith predictor cancels the time delay; FOPSO-GWO tunes the controller parameters. It reduces settling time and steady-state error while improving deflection accuracy and robustness.