Based on Lyapunov stability theory, the adaptive law of single-input and single-output controlled plant and the model reference adaptive control system (MRACS) with signal synthesis form are studied in a unified format. This study proposes an MRAC design method that takes states from the model using only the input and output measured values of the controlled plant when the derivatives of various orders of the controlled plant are not measurable. By adopting the method of taking states from the model, this paper not only solves the problem of the plant’s states being unmeasurable but also significantly enhances the system’s disturbance rejection capability. The effectiveness of the method was verified through digital simulations, showing that the controlled plant output can better follow the reference model output, indicating that this approach has greater application value.
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