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

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4 Author(s)
Wu, J. ; Inst. of Adv. Process Control, Zhejiang Univ., Hangzhou ; Li, G. ; Istepanian, R.H. ; Chu, J.

The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parametrisations 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 realisations. Within a given operator parametrisation, the optimal FWL controller realisation, which maximises the proposed stability related measure, is the solution of a nonlinear optimisation problem. The relationship between the z-operator and δ-operator controller parametrisations is analysed, and it is shown that the δ parametrisation has a 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 optimisation procedure

Published in:

Control Theory and Applications, IEE Proceedings -  (Volume:147 ,  Issue: 6 )