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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