Discrete-Time Optimal Control of Electromagnetic Coil Systems for Generation of Dynamic Magnetic Fields with High Accuracy

Electromagnetic coil systems (ECSs) have been widely used for actuation and motion control of magnetic micro/nanorobots. In this paper, two typical ECSs with different system configurations are developed: One is computer-based and uses servoamplifiers for driving the coils and the other adopts an embedded control system with home-designed circuit boards for driving the coils. For dynamic control of the two types of ECSs, a unified control scheme is proposed with two objectives: 1) to make the output magnetic field converge to the reference without steady-state error; 2) to achieve optimal transient response under tunable requirement of control effort. In the scheme, dynamic models of the two systems are described by a unified state-space form with different dimensions, which are obtained by system identification. Then, a discrete-time optimal controller is designed based on the linear quadratic with integral action method to realize the control objectives. Finally, in order to make the controller applicable to the real ECSs, the time-delayed system states are estimated by utilizing a Kalman filter, and a Smith predictor inspired compensator is designed to compensate for time delay and modeling error. Simulations and experiments using the proposed control scheme are conducted for the two ECSs with three-axis Helmholtz coils, which show the easy adaption of the control approach to different coils. Experimental results validate the significantly improved dynamic performances of the two ECSs, and tracking a three-dimensional dynamic magnetic field with high accuracy is also demonstrated.