Optimal Control of a 3-axis Helmholtz Coils System for Generation of Dynamic Magnetic Field Waveforms with High Accuracy

Tri-axis Helmholtz coils systems have been widely used for actuation and motion control of magnetic microrobots. This paper addresses the dynamic control of a lab-made 3- axis Helmholtz coils system in order to offer precise dynamic actuation for magnetic microrobots. This paper proposes an optimal control scheme based on model predictive control (MPC), and the objective is to improve the tracking performance for different forms of dynamic magnetic fields. In the control scheme, the system dynamics is approximated by a nominal model which is obtained by system identification, and the modeling uncertainties and external disturbances are lumped together and estimated by a disturbance observer (DOB) which provides the control robustness. The high-accuracy dynamic tracking is achieved by implementing a MPC controller based on the nominal system model. To validate the effectiveness of the proposed control scheme, simulations and experiments using the proposed control scheme with control frequency of 25 kHz are conducted on the lab-made 3-axis Helmholtz coils system. The results show significantly improved field generation performances and the system can accurately track different types of field waveforms.