Feed-forward frictional-order proportional–integral–derivative-based feedback control of a piezoactuated microposition stage using an extended unparallel Prandtl

Abstract

In the recent past, it has been observed that flexure-based microposition stages with a large workspace and high motion precision are gaining popularity for performing practical micromanipulation tasks. Thus, a piezoactuated flexible two-degrees-of-freedom micromanipulator integrated with a pair of displacement amplifiers is developed. To enhance the practical positioning performance of the micromanipulator, this paper proposes a feed-forward frictional-order proportional–integral–derivative based feedback control approach to eliminate the undesired resonant mode of a piezoactuated microposition stage to satisfy the accuracy of the system. The control approach is composed of the integration inverse feed-forward compensator, the feedback controller, and the frictional-order proportional–integral–derivative controller. The integration inverse feed-forward compensator with an extended unparallel Prandtl–Ishlinskii model is introduced for addressing the nonlinearity of the piezoactuated microposition stage, leading to an approximately linear system. When all the roots of the system characteristic equation are negative real numbers or have negative real parts, the feedback controller is guaranteed to have tracking stability. Next, a frictional-order proportional–integral–derivative controller is designed to enhance the tracking performance of the microposition stage. Finally, comparative experiments with the conventional proportional–integral–derivative controller are performed, revealing that the practical positioning performance has been increased by nearly 35%. The experimental results demonstrate that the performance with the frictional-order proportional–integral–derivative+feedback controller is improved significantly.

Keywords

Piezoelectric actuators microposition stage extended unparallel Prandtl–Ishlinskii hysteresis compensator feedback controller frictional-order proportional–integral–derivative

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Feed-forward frictional-order proportional–integral–derivative-based feedback control of a piezoactuated microposition stage using an extended unparallel Prandtl–Ishlinskii hysteresis compensator

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