This paper presents a direct field-feedback method with an observer for precise control of an eddy-current density (ECD) field induced in an electrically conductive-plate by a set of individually manipulatable currents. The magnetic flux density (MFD) generated by the ECD is measured by an array of MFD sensors, and fed back for compensating external disturbances and time-varying effects of the system parameters and ECD model inaccuracy. For feedback control of the multiple-input and multiple-output (MIMO) distributed-parameter system, a distributed current source (DCS) method is used to formulate the ECD system in state space, where the conductor is discretized into elemental ECD sources as system state variables providing a basis to design the state controller and observer. Based on the observability of the MFD sensing system and the controllability of the EM actuation system, the controller and observer were designed using a pole-placement method. Results illustrating the design concept are presented, demonstrating the feasibility and efficiency of the proposed method; both well-defined and arbitrary EC contours are considered. While illustrated in the context of controlling an EC pattern, the methods presented here provide the essential basis for designing and controlling a distributed-parameter system utilizing the physical fields of the system for state feedback and error compensation with a distributed set of actuators and sensors.

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