Closed-Loop Control of a Helmholtz Coil System for Accurate Actuation of Magnetic Microrobot Swarms

Magnetic microrobot swarms have attracted lots of research interests in the robotics field. Since the remote actuation of swarm can be affected by the accuracy of the external magnetic field, electro-magnetic systems capable of generating precise magnetic fields have great value. In this work, we propose a closed-loop control scheme for 3-axis Helmholtz coil system to improve the field generation performance. Each coil is connected to and driven by a commercial servo amplifier, and the mathematical model of the system is obtained by the sweeping frequency method. With the identified model, a current controller based on the model predictive control (MPC) is presented, the states of the system and the lumped disturbance are observed by a 4th-order super-twisting sliding mode observer (STSMO) for control input calculation and disturbance compensation. To evaluate the effectiveness of the proposed control scheme, we conduct experiments on a lab-made 3-axis Helmholtz coil system. Results indicate that the bandwidth of the system can be increased to 50 Hz, and the settling time can be reduced to 0.9 ms and 0.83 ms for the outer coil and middle coil, respectively. Moreover, rotating fields with different frequencies are generated with and without the proposed scheme to actuate magnetic vortex-like microswarms. The swarm deforms to an ellipse with shape ratio equals to 0.45 as the frequency increases in the open-loop condition, in contrast to which with the proposed control scheme shows a more accurate and controllable circular pattern.