Signal Design for Multi-input System Identification

Abstract

For the identification of multi-input systems, the utilisation of sets of signals which are uncorrelated with one another allows the effects of the individual inputs to be easily decoupled at the system output. The theory behind the design of sets of uncorrelated signals is explained. This includes Hadamard-modulated signals and signals with a zippered spectrum. The latter may be designed using multisine signals or pseudorandom signals. An application example on a simulated thermoelectric system is presented. An alternative approach using the phase-shifting design is then described. In this approach only one signal is generated and phase-shifted versions of this signal are applied to the multiple inputs. Finally, the identification of ill-conditioned processes is discussed. The problem of ill-conditioning is caused by the singular values having widely differing magnitudes. The method of virtual transfer function between inputs for the identification of ill-conditioned systems is explained. Its effectiveness is illustrated on a simulated multizone furnace.