Shift and delta operator realizations for digital controllers with finite-word-length considerations

Abstract

This paper addresses implementation issues of digital controllers with finite word length (FWL) considerations. Both the shift and delta operator parameterizations of a general controller structure are considered. A unified formulation is adopted to derive a computationally tractable stability related measure that describes FWL closed-loop stability characteristics of different controller realizations. Within a given operator parameterization, the optimal FWL controller realization, which maximizes the proposed stability related measure, is the solution of a nonlinear optimization problem. Relationship between the $z$-operator and $\delta$-operator controller parameterizations is analyzed, and it is shown that the $\delta$ parameterization has better FWL closed-loop stability margin than the $z$ domain approach under a mild condition. A design example is included to verify the theoretical analysis and to illustrate the proposed optimization procedure.

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