Proportional–Integral–Derivative-Based Learning Control for High-Accuracy Repetitive Positioning of Frictional Motion Systems

Classical proportional-integral-derivative (PID) control is exploited widely in industrial motion systems with dry friction motivated by the intuitive and easy-to-use design and tuning tools available. However, classical PID control suffers from severe performance limitations. In particular, friction-induced limit cycling (i.e., hunting) is observed when integral control is employed on frictional systems that suffer from the Stribeck effect, thereby compromising setpoint stability. In addition, the resulting time-domain behavior, such as rise time, overshoot, settling time, and positioning accuracy, highly depends on the particular frictional characteristic, which is typically unknown or uncertain. On the other hand, omitting integral control can lead to constant nonzero setpoint errors (i.e., stick). To achieve superior setpoint performance for frictional motion systems in a repetitive motion setting, we propose a PID-based feedback controller with a time-varying integrator gain design. To ensure optimal setpoint positioning accuracy, a data-based sampled-data extremum-seeking architecture is employed to obtain the optimal time-varying integrator gain design. The proposed approach does not rely on knowledge on the friction characteristic. Finally, the effectiveness of the proposed approach is evidenced experimentally by application to an industrial nanopositioning motion stage setup of a high-end electron microscope.