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The argument of the paper is the embedded model control that was developed and tested in the course of past years. The first aim of the method is to equalize implementation and design, which is obtained by explicitly including the design model as the core of the control unit: hence the name of embedded model. After four basic modelling axioms, the paper concentrates on the model error properties, concerning the plant-to-model discrepancies revealed by their output difference. Properties lead to a first theorem: the central error theorem. The theorem asking for model error reduction, the model error causes are investigated and partly included in the embedded model. Residuals will be treated in the Part II of the paper.