Abstract
Model reference adaptive control system (MRACS) has become a high perfectible control system with many researches since the presentation by Monopoli. The problem of disturbance elimination and stability have been solved partially, but researches on nonlinear MRACS are not sufficient. There is no research on nonlinear MRACS of which the global stability is guaranteed. This paper shows the design of nonlinear MRACS and the proof of the global stability with using classification of norm for nonlinear functions. The MRACS of this paper has the construction as the combined system of nonlinear model following control system and exponential decay adjustable law by Kreisselmeier. The global stability can be proved with using classification to separate the nonlinear index into three cases (0≤γ<1, 1≤γ<2, 2≤γ) and solving the differential inequality for positive function analytically from the fact that parameter errors decay exponentially. As gradually γ is large, the nonlinear becomes difficult, so additive conditions to the controlled system increase. The MRACS of this paper is not only nonlinear but also multi-input and multi-output. Furthermore it is proved that the condition of strictly positive real is satisfied for stable nonminimum realizations of transfer function. We show the effectiveness of the design of this paper from numerical simulations for no disturbance and with disturbances.
