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

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7.1. Motivation

A control system must satisfy desired performance characteristics (closed-loop time constant, minimal overshoot, etc.) for nominal operating conditions. By nominal, we normally mean that the plant is perfectly described by the model used for control-system design. In reality, a model is never perfect, so controllers must be designed to be robust (to remain stable even when the true plant characteristics are different from the model).

So far we have analyzed the closed-loop characteristic equation (1 + gcgp) for stability, either by directly calculating the roots or by using the Routh array to verify that the roots (closed-loop poles) are negative. There are two problems with this approach:

  1. Although the closed-loop characteristic ...

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