Data-driven disturbance compensation for core-type linear motors using TISO-GPR integrated with disturbance observers

An integrated control structure that combines Gaussian process regression (GPR) and a disturbance observer (DOB) is proposed for a core-type linear motor that is affected by patterned disturbance and model mismatch. The conventional controller is a DOB-based feedforward/feedback structure, and the compensation performance is limited by the fixed bandwidth of the Q -filter and the estimation bias that appears under model uncertainty. In addition, the effective frequency is shifted by the motion velocity, and disturbance rejection is degraded under a fixed-bandwidth design. A two-input single-output GPR (TISO-GPR) that uses the position and the velocity as inputs is designed to model a lumped disturbance. A periodic kernel is applied on the position axis to represent the spatial period, and a kernel that reflects the velocity-dependent disturbance component is applied on the velocity axis, where the spatial period is fixed by the device geometry and consistent prediction on the position axis is enabled beyond the training range. The disturbance estimated by the DOB is used for training, and the posterior mean estimate is used as the compensation signal in the feedback loop, which is inserted as an internal feedback compensation signal within the DOB-based structure. A time-domain analysis shows that the compensation is bounded and that a small-gain condition guarantees BIBO stability. Experiments confirm that the proposed method improves the tracking performance and robustness.