H Infinity Feedback Control of a Piezoelectric Micromanipulator with Actuator Saturation

This paper presents the hysteresis modeling and precision trajectory control of a piezoelectric micromanipulator with actuator saturation. An improved Prandtl-Ishlinskii (PI) hysteresis model combining the dead zone operator is established, and a hysteresis-based feedforward controller is derived. Then, the system model is decomposed into linear reversible parts and bounded parts. An augmented model using three weight functions is developed, and the
$H_{\infty}$
feedback controller is used to ensure system stability and accuracy. An anti-saturation compensator is designed to avoid possible actuator saturation. The experimental results show that the influence of micromanipulator hysteresis is reduced using feedforward control. The improved PI hysteresis model is feasible. When the reference trajectory is the step, triangular and sinusoidal signals, or even changing the micromanipulator parameters, the
$H_{\infty}$
feedback controller can effectively track the given reference signal with a small relative control error. Additionally, the trajectory tracking standard error decreases from 3.7 (1.6)
$\mu\mathrm{m}$
to 2.1 (1.0)
$\mu\mathrm{m}$
for sinusoidal (triangular) signal at amplitude saturation by using the anti-windup compensator. The experiments verify the validity of the designed
$H_{\infty}$
feedback control strategy with actuator saturation.