A 4(n+1)-Dimensional Model Reference Adaptive Control for the Stabilization of any Strictly Proper Minimum Phase Linear Systems with Relative Degree Not Exceeding Two and Dimension Not Exceeding n,
YALE UNIV NEW HAVEN CT DEPT OF ELECTRICAL ENGINEERING
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In a recent paper it was shown that there are smooth, nonlinear, three-dimensional controllers, not incorporating probing signals, which are capable of adaptively stabilizing any single-input, single-output, minimum phase, relative degree two or less linear system of any dimension. Controllers of this type are based on minimal dynamic compensator synthesis. While such controllers are simple in structure they do not have a model-following capability. In this paper we develop a new algorithm based on observer theory, which can adaptively stabilize and achieve model-following as well. The controller, which is a smooth nonlinear dynamical system of dimension 4n1, can adaptively stabilize any physical process with scalar input u and scalar output y, provided the process can be modelled by a strictly-proper, minimum phase, linear system of dimension not exceeding n and relative degree not exceeding two.
- Theoretical Mathematics