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A new efficient controller structure with maximum stability robustness is derived. This structure can be considered as an improved version of the ρ-realisation recently proposed by the authors. It is shown that the optimised structure can improve the stability performance more effectively with the extra freedom introduced and outperform both the optimal ρ-realisation and the fully parametrised optimal realisation significantly.
The stability robustness problem of a discrete-time feedback system, where the digital controller is implemented with finite word length, is investigated. Based on a polynomial operator approach a new sparse controller realisation, called ρ-realisation, is derived. The problem of finding optimal ρ-realisations is solved. A numerical example is given, which shows that the optimised structure outperforms the fully parametrised optimal realisation.
The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parameterisations 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 parameterisation, 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 parameterisations is analysed, and it is shown that the δ parameterisation 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.
The problem of digital controller structures and the effect of finite-word-length (FWL) implementation on the closed-loop stability of digital feedback control systems is addressed. A framework is presented to derive two lower stability bounds for a closed-loop system, which are controller structure dependent, and then to solve the optimal FWL controller structure problem by maximising one of these lower bounds. This yields an improved method to design optimal finite-precision controller structures with better numerical accuracy and closed-loop stability characteristics. Comparisons using numerical examples from two digital controller structures demonstrate that the procedure proposed for the more efficient measure yields an improved finite controller realisation with combined lower bits and higher lower stability bounds.