A non-minimum state space approach to true digital control based on δ-operator models

Previous publications have introduced the concept of `true digital control´ (TDC) and discussed a novel non-minimum state space (NMSS) approach to the identification, estimation and true digital control of dynamic systems described by transfer function models in the backward shift (z^-1) operator. In this paper, the authors show how the same NMSS approach can be applied to systems described by the alternative but related delta (δ) operator transfer function model and introduces the conditions for the controllability of the model. The state variable feedback control law associated with this NMSS model can be defined either for closed loop pole assignment (PA) or optimal linear quadratic control. The former PA control algorithm is developed and applied to a simple second order process. Recursive instrumental variable (IV) procedures for the identification and estimation of δ-operator models are then described and shown to be optimal and sub-optimal generalisations of methods proposed previously for continuous-time systems. Finally, the paper re-visits the simple second order model and presents illustrative simulation results which demonstrate the efficacy of the complete TDC design procedure