The modulus optimum (MO) criterion can be used for analytical design of the PID controller for linear systems with dominant dead time. However, although the method usually gives fast and non-oscillating closed-loop responses, in the case of large dead time the stability margin gets reduced and even non-stable behavior can be observed. In this case a correction of the settings is needed to preserve the stability margin. We describe and compare two methods of design of the PID controller based on the MO criterion that for the stable first-order systems with dead time preserve the stability margin, trying to keep maximum of the performance of the original MO settings.
The Magnitude Optimum (MO) tuning method for PID controllers, applied on stable and non-oscillating plants, usually gives fast tracking responses and offers very good process output disturbance-rejection performance, even if the process contains significant dead time. On the other hand, when an exogenous disturbance affects the process indirectly, for example, via the plant input, slow disturbance rejection responses may be obtained. The paper proposes a way of removing this problem by means of adding two first-order filters into the control loop, without modifying the controller parameters. The filter parameters are determined so that the disturbance lag is partially compensated and the stability margin properties of the MO tuning are preserved.
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