Two-Stage and Projection Methods for Closed-Loop Identification Using Generalized Orthonormal Basis Functions

Abstract

This paper proposes a closed-loop identification method based on the construction of generalized orthonormal basis functions (GOBF). It modifies the two-stage and projection methods, which apply a finite impulse (FIR) model structure to the estimation of the closed-loop sensitivity model in the input reconstruction step. In our approach the GOBF construction is applied instead of the FIR model in order to give better approximation of the sensitivity model. With appropriately selected basis functions in which the basis is generated by all-pass functions having poles close to the poles of the system the model structure is in a much more concise representation and the convergence rate can be faster. The paper gives the algorithm of the closed-loop identification method, and it demonstrates the method in a numerical example for an inverted pendulum device.