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For example, a temperature-controlled circulating bath has two PID controllers in cascade, each with its own thermocouple temperature sensor. The outer controller controls the temperature of the water using a thermocouple located far from the heater, where it accurately reads the temperature of the bulk of the water.
The Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications. This tuning rule is meant to give PID loops best disturbance rejection. [2]
P&IDs are originally drawn up at the design stage from a combination of process flow sheet data, the mechanical process equipment design, and the instrumentation engineering design. During the design stage, the diagram also provides the basis for the development of system control schemes, allowing for further safety and operational ...
Intuitively, for the k sample intervals during which no fresh information is available, the system is controlled by the inner loop which contains a predictor of what the (unobservable) output of the plant G currently is. To check that this works, a re-arrangement can be made as follows:
For example, the position of a valve cannot be any more open than fully open and also cannot be closed any more than fully closed. In this case, anti-windup can actually involve the integrator being turned off for periods of time until the response falls back into an acceptable range.
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With the present example, if you turn off the hot then (apart from the water actually in flight) the temperature cannot continue to rise, and so PID control is unnecessary. Previously, when talking about the water as it came out of the tap, the example described a 1st order system with a built-in pure time delay.