Predictive virtual sensor identification for nonlinear MPC: application to a 2-DoF flexible direct-drive robotic arm

Nonlinear Model Predictive Control (NMPC) is a powerful optimal control framework for nonlinear systems, offering high flexibility and performance. NMPC operates by solving an optimal control problem online at each time step, which requires predictive models capable of predicting multiple steps ahead with high accuracy and computational efficiency. Nevertheless, two major challenges limit its practical implementation: first, constructing models that accurately capture complex nonlinear dynamics is difficult; second, the control variables that determine performance can often be measured only in controlled offline experiments using specialized measurement equipment, but not during real-world operation. To address these challenges, this paper proposes Predictive Virtual Sensor Identification (PVSID), which constructs virtual sensors of desired control variables without deriving an explicit detailed physics-based dynamic model, as the predictive models required by NMPC. The effectiveness of the proposed approach is experimentally validated on a two-degree-of-freedom (2-DoF) flexible robotic arm through vibration suppression and high-precision trajectory tracking. The results confirm that PVSID constructs a virtual sensor that captures complex nonlinear dynamics, including flexible-link vibrations, and that NMPC with the PVSID-identified model yields control inputs that suppress these vibrations, resulting in highly accurate tip-position tracking.