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Structural interpretation of matched pole–zero discretisation

Structural interpretation of matched pole–zero discretisation

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The paper deals with matched pole–zero discretisation, which has been used in practice for hand calculations in the digital redesign of continuous-time systems but available only in the transfer-function form. Since this form is inconvenient for characterising the time-domain properties of sampled-data loops and for computerising the design of such systems, a state–space formulation is developed. Under the new interpretation, the matched pole–zero model is shown to be structurally identical to a hold-equivalent discrete-time model, where the generalised hold takes integral part, thus unifying the most widely used discretisation approaches. An algorithm for obtaining the generalised hold function is presented. The hold-equivalent structure of the matched pole–zero model clarifies several discrete-time system properties, such as controllability and observability, and their preservation or loss with a matched pole–zero discretisation. With the proposed formulation, the matched pole–zero, hold-equivalent, and mapping models can now all be constructed with a single schematic model. This is of considerable practical importance in digital redesign, especially with the so-called plant-input mapping methods which use the matched pole–zero discretisation of the closed-loop system, and in digital simulations performed with a block-diagram language.

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