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A new type of model free adaptive control (MFAC) method, including MFAC scheme designs with the compact-form-dynamic-linearization-based controller (CFDLc) and partial-form-dynamic-linearization-based controller (PFDLc), is presented for a class of discrete-time SISO nonlinear systems. The proposed method is a pure data-driven control method since the controller is independent of the model of the controlled plant, and controller parameter tuning is merely based on the measured I/O data of the controlled plant in closed loop. Differing from the MFAC prototype, the proposed method uses the dynamic linearization approach not only on ideal controller but also on the plant. The stability of the CFDLc-MFAC and PFDLc-MFAC is guaranteed by rigorous theoretical analysis, and the effectiveness is evaluated on simulation examples and a three-tank liquid control experimental system.