Robust Interval Luenberger Observer-Based State Feedback Control: Application to a Multi-DOF Micropositioner

Controlling multidegrees of freedom (DOF) micropositioning systems always represents a great challenge because of the high sensitivity to the environment at this scale and the cross-coupling effects present between the different axes. A robust Luenberger observer-based state feedback design using interval analysis and the regional pole assignment technique are introduced to control such systems. This robust control design keeps the same structure of the classical state-feedback with the usual Luenberger observer. However, the syntheses of the observer and the feedback controller are performed by means of interval techniques to find the set of gains that are robust against system uncertainties and that satisfy some predefined performances. For this matter, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation is proposed to find these robust gains. The control approach is validated in simulation and then tested experimentally to control a multi-DOF positioning structure.