Dynamics Modeling and Synchronized Model Predictive Control for a Fabry-Perot Spectrometer

Three piezoelectric actuators (PEAs) are assembled in a Fabry–Perot spectrometer (FPS) to adjust the spacing between two optical plates. The measurement of the FPS requires that the actuated optical plates move in parallel with nanometer resolution. To meet this requirement, the motion of the three PEAs should be controlled synchronously. Thus, the challenging tasks in control of the Fabry–Perot (F–P) system lie in two aspects: control of each PEA precisely at the nanometer level and control of the three PEAs to achieve a synchronized motion. To this end, a novel dynamic model is first proposed to describe the inherent hysteresis effect and the system dynamical behaviors in the F–P system. Based on the proposed model, an inversion-based synchronized model predictive control (SMPC) design is developed. The experimental results validate the proposed control scheme.