In a complex modern plant like e.g. a large Power Station, many variable quantities have to be adjusted moment by moment. These would include the rates at which air and fuel enter the boiler, the temperatures and pressures that exist in different parts of the plant or the level of water in the boiler, to name only a few.
A control system takes the place of perhaps many human operators in automatically setting the positions of each of the devices, like dampers and valves, which adjust each of these "controlled variables".
To do this, each variable is measured, moment by moment, by a 'measuring element' and the latest value is sent to a controller. Another value, called the 'set point' (the ideal value for that variable for the way the plant has to be run at that time) is compared to the measured value in the controller and the error between these is used to produce an an output signal from the controller which tells the appropriate device to open or close in such a way as to reduce the error and so return the variable to a value closer to the ideal. The process itself becomes the last link in a 'closed loop' of elements including the measuring element, the controller and the final control element (the valve or damper). This way of controlling so as to reduce the error is called 'negative feedback'
An individual controller may be used, by itself, to control an individual variable (with a human operator to adjust the set point if necessary) but a number of controllers will often work together when more than one variable has to be changed at the same time. To do this, another controller (a 'master controller') measuring an overall variable, like steam pressure or the power output from the boiler, can be used to automatically adjust the set points of a mumber of other controllers together. Then as more steam or more power output is required from the boiler, the set point sent to each of these individual controllers will alter accordingly for the new running conditions. This way of automatically adjusting the set points of 'slave' controllers by a 'master controller' is called 'cascade control'.
Control is not always easy and so time or rate elements often have to be built into the controller's strategy to prevent the controller from making the plant behave in an unstable way. Instability in control can be caused or made worse by (for instance) making a valve or a damper move open and closed too quickly.
'Proportional Control' (gain) adjusts how far the valve or damper or other controlling device moves for a given measured error but this type of control alone cannot remove the error completely, even in steady-state conditions;
'Integral' control (time) can be added to Proportional action, to increase the controller's output slowly over a set time. This will finally reduce the error to zero as long as the plant is running steadily enough;
'Derivative' control (rate) can be added to Proportional action to increase the controller's output very fast whenever the error is changing at a fast rate. This allows the controller to cope with sudden but short-lived changes in the measured variable.
Estimating the amount of Proportional, Integral and Derivative actions required for any controller is called 'loop tuning' and can be achieved by calculation but often requires the controller to be tried out in practise on real plant conditions before ideal 'PID' settings are found.