Discretization of nonlinear models using a modified Carleman linearization technique

A modification of the Carleman linearization procedure (1932) is proposed for discretizing nonlinear dynamic models for digital control applications. Neglected terms of a truncated Taylor series are approximated as linear combinations of kept terms. The process involves a series of adjustable parameters which are determined via optimization. Integration of the resulting linear model over a sampling period yields an analytic discrete-time model. Excellent discrete models of low orders are obtained in a study involving the nonlinear model of an isothermal continuous stirred tank reactor. The technique displays improved accuracy over a standard Carleman approach of the same order.