Practical experience with unified discrete and continuous–time, multi–input identification for control system design

The paper is concerned with the practical aspects of a unified approach to the identification and estimation of multiple–input, single–output (MISO) transfer function models for both continuous and discrete–time systems. The estimation algorithms considered in the paper are based on the Refined Instrumental Variable (RIV) approach to identification and estimation, where the MISO model denominator polynomials are normally constrained to be equal. Unconstrained RIV estimation presents a more difficult problem and it is necessary to exploit an iterative, back–fitting routine to handle this more general situation. The paper focuses on the practical realization of this back–fitting algorithm, including its initiation from either common denominator MISO or repeated SISO estimation. The rivcdd algorithm for continuous– time model estimation, as implemented in the CAPTAIN Toolbox for Matlab, is then used in three practical examples: first, the modelling of solute transport and dispersion in a water body; secondly, modelling for two control problems, namely a pair of connected laboratory DC motors and a nonlinear wind turbine simulation.