A general controller-based dynamic linearized model-free adaptive control and its application to PMLSM

In this paper, the controller-based dynamic linearized model-free adaptive control methods are further extended and improved based on existing works for the tracking of a class of unknown nonlinear non-affine discrete-time systems. In particular, the full form dynamic linearized data model and controller are both involved in the control system design, which includes the special cases of compact form and partial form dynamic linearized data models and controllers from existing works. Then the proposed model-free adaptive control approach is developed using the simplified Newton-type optimization method with the integration of existing adaptive estimation algorithms for model parameters. Finally, the ultimate boundedness of the tracking error is analyzed under less stringent conditions than existing works by combining the added mathematical induction with the theory of Geršgorin discs and the contraction mapping principle. The proposed approach is data-driven since only the underlying system's input-output data are used in controller design. The example of a permanent magnet linear synchronous motor demonstrates the effectiveness and potential applications of the proposed approach.