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

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M16.3. Stability Analysis for Digital Control Systems

For a standard discrete feedback control system, the closed-loop system is stable if the poles of the closed-loop transfer function are all inside the unit circle. The closed-loop transfer function is

so the roots of

must be less than 1 in magnitude.

Example M16.1: Stability of a Discrete Control System

Consider a first-order process, where the output is temperature (°C), the manipulated input is valve position (%), and the time unit is minutes.

If discretized with a sample time of 1 minute, ...

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