Nonlinear frictional disturbances limit the performances of high-precision mechatronics systems. Recently it was shown that nanometric positioning can be achieved only if these disturbances are identified, modelled and compensated for via suitable control approaches. A PID controller, complemented with feed-forward based on the Generalized Maxwell-slip model, allows hence to achieve nanometric positioning but its real-time implementation is difficult, whereas a self-tuning regulator enables nanometric positioning with a marked overshoot. Koopman-based model predictive control (MPC) is applied in this work instead. This approach allows “lifting” the nonlinear dynamics of the considered device into a higher dimensional space where its behaviour can be predicted by a linear system ; the computational complexity of the thus obtained controller is hence comparable to that of equivalent linear controllers. The resulting positioning performances are evaluated numerically in the MATLAB/Simulink environment and compared to those when the mechatronics device is driven by using different controllers. It is thus shown that the Koopman-based MPC virtually eliminates steady state errors, decreases the settling time and results in very small overshoots.
