Interval Modeling and Robust Control of Piezoelectric Microactuators

Microsystems are very sensitive to environmental disturbances (thermal variation, surrounding vibration, micro-objects in contact with them, etc.) and they are often subjected to small degradation or their behaviors are often affected during the functioning. As a result, their parameters often change during the micromanipulation, microassembly, or measurement tasks and the accuracy or even the stability may be lost. For that, robust control laws should be introduced to control them and to ensure the performance. H-infinity and mu-synthesis approaches were the classical robust techniques used to control microsystems. They are undeniably efficient but they lead to high-order controllers that are sometimes inconvenient for real-time embedded systems. In this brief, by the means of interval numbers that are used to characterize the uncertain parameters, we propose a method to synthesize simple controllers ensuring robust performance for microsystems. The controller synthesis is formulated as a set-inclusion problem. The main advantages of the proposed method are the ease of modeling the uncertain parameters thanks to intervals and the simplicity and low-order of the derived controllers. The method is afterwards applied to model and control piezoelectric microactuators and the experimental results show its efficiency. Finally, using the H-infinity technique, we also demonstrate numerically the performance robustness of the closed-loop with the designed controller.