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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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M16.6. Summary

The unit circle plays the same role in discrete-time systems that the real line does in continuous-time systems. A zero outside the unit circle causes the same performance limitations that an RHP zero causes for continuous systems. It is possible, however, for a continuous-time system with no RHP zero to have a discrete zero that is outside the unit circle, if the continuous-time system has a relative order of 3 or higher.

Discrete-time models with zeros outside the unit circle must be factored into the bad stuff for discrete IMC controller design. This procedure is similar to continuous-time models, where RHP zeros must be factored into the bad stuff. The main difference between continuous and discrete systems is that even zeros ...

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