A Mathematical Means of Spreading Clustered System Roots
CONTROL DYNAMICS CO HUNTSVILLE AL
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The purpose of the study reported upon herein is to investigate the potential existence of a clustering of system poles and zeros in the z-domain. This potential is shown to exist. A means of separating the clustering is proposed by mapping from the complex z-domain onto the complex w-domain. The reason for so doing is to ameliorate computational difficulties that can arise as the result of closely clustered roots. It was shown that such a situation could occur, but that there are design techniques to prevent it. If these fail, an alternate approach is described whereby the system poles and zeros are transformed from the complex z-domain to the complex w-domain. It then is possible to increase the scaling in the w-domain with significant effect in separating the clustered poles and zeros, thereby obviating computational difficulties that might have arisen because of the clustering in the z-domain.
- Numerical Mathematics