Robust and guaranteed output‐feedback force control of piezoelectric actuator under temperature variation and input constraints

Abstract This paper addresses the control of manipulation force in a piezoelectric tube actuator (piezotube) subjected to temperature variation and input constrains. To handle this problem a robust output‐feedback design is proposed using an interval state‐space model, which permits consideration of the parameter uncertainties caused by temperature variation. The design method is robust in the sense that the eigenvalues of the interval system are designed to be clustered inside desired regions. For that, an algorithm based on Set Inversion Via Interval Analysis (SIVIA) combined with interval eigenvalues computation is proposed. This recursive SIVIA‐based algorithm allows to approximate with subpaving the set solutions of the feedback gain [ K ] that satisfy the inclusion of the eigenvalues of the closed‐loop system in the desired region, while at the same time ensuring the control inputs amplitude is bounded by specified saturation. The effectiveness of the control strategy is illustrated by experiments on a real piezotube of which the environmental temperature is varied.