A model predictive control for a multi-axis piezo system: Development and experimental validation

This paper presents a Model Predictive Control (MPC) strategy for a triaxial piezoelectric actuators (PAs) system. PAs systems require appropriate controllers to guarantee fast and high-precision positioning performances avoiding effects of non-linearities. Typically, commercial systems provide integrated Proportional-Integral (PI) controllers guarantying to maintain system stability in the presence of uncertainty and disturbance. MPC owes its success to the ability of optimally regulate multivariable systems through the minimization of a Quadratic Programming (QP) problem subjected to prescribed constraints. Alternatively, unconstrained MPC eliminates constrains from the problem, reducing the number of operations elapsed to compute the solution. The aim of this work is to design an unconstrained MPC for a 3-DOF PA replacing PI controllers to improve control performances by a smaller increase of required computational effort. The system is described by a Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) model, experimentally identified by the open-loop real plant response. Effectiveness of the proposed method is validated by simulation tests and experiments on the real system, comparing MPC with PI controllers tuned to guarantee common PA stability requirements.