On determining the model structure of a nonlinear feedback control law for a model following nonlinear system

Abstract

The authors present a methodology to determine the model structure of a nonlinear feedback control law so that when it is applied to a model following nonlinear system with predominant nonlinearities, such as industrial robots, it will cause the output of the model following system to follow the output of the referenced model accurately. The proposed algorithm starts with a control sequence for the nonlinear plant which is equal to the control sequence for the model. This control sequence is updated iteratively, taking into consideration a library of nonlinear vector-valued functions associated with the dynamic equations of the nonlinear plant. The essential feature of the technique is that it recursively generates a sequence of projection matrices to be used as mapping transformation operators so that the original vector-valued functions become conjugate directions. This leaves the original nonlinear dynamic equations intact and allows the n-term nonlinear control law to be assembled in n selections from the library.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>