Discretising controllers with slow sampling

A simple approach to digital control design is the local discretisation of an effective continuous-time control law, such as well-tuned PID (proportional-integral-derivative). There are rules of thumb (e.g. the sample rate should be at least 25times the closed-loop bandwidth) that ensure only marginal degradation in performance, but these often require fast and accurate implementations. Low-power microcontrollers, on the other hand, might be slow and have restricted word-length. An approach to discretisation is thus to employ a mixed realisation using an `analogue wrap-around´ in which a proportional signal bypasses the computer and is added to the computer´s digitally-evaluated component. Analysis and simulated examples indicate that this can lead to a significant reduction of the sample rate required for good closed-loop control when compared with the classical methods of Tustin, step- and ramp-invariant transformations