A Luenberger observer-based dynamic compensation strategy was proposed to resolve nonlinear abrupt variations induced by transmission backlash in brushless DC servo systems. A high-fidelity system model with a backlash state identification mechanism was established to enable real-time switching between motor inertia and load models within the observer

thereby achieving online parameter identification and backlash compensation for enhanced servo stability. Furthermore

the observer was utilized to mitigate position sampling delays

and the observed motor speed was introduced to construct a position/velocity dual-loop control architecture

which increased system damping and overcame limitations of conventional single-loop systems. Simulations were conducted for the servo system based on Luenberger observer

and physical verification was carried out on servo platform with STM32F407 as control core. The results demonstrate that the backlash-compensated Luenberger observer effectively overcomes system clearance limitations

suppresses response distortions

significantly reduces step-response overshoot and settling time

broadens system bandwidth

and enhances system stability.