Abstract
The implementation of control algorithms is invariably through the use of embedded microcontrollers rather than the employment of analogue devices. Control algorithms are implemented in either high level or low level language. It is a rare practice to work near the limit given by Shannon's theorem. A useful rule of thumb is to sample the signal at about ten times higher than the highest frequency thought to be present. If a signal is sampled below Shannon's limit, then a lower frequency signal, called an alias may be constructed. It is possible to reconstruct a continuous signal from an ideal sample by the use of a hold device. The z-transform is the principal analytical tool for single-input-single-output discrete-time systems, and is analogous to the Laplace transform for continuous systems. Just as transient analysis of continuous systems may be undertaken in the s-plane, stability and transient analysis on discrete systems may be conducted in the z-plane. The Jury stability test is employed in a similar manner to assess the stability of discrete systems. Digital compensators can also be designed in the z-plane for discrete systems.
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