Proportional, Integral & Derivative?

Question

With respect to a pressure, level or temperature system, can someone explain proportional, integral and derivative control with respect to proportional band, repeat per minute etc

Are there any books or websites which give a good explanation?

OK so if there is a PB of 100 (gain of 1) then for every 1% the PV differs from the setpoint the output will increase/decrease by 1%. Adding integral will add another 1% over the time desired i.e after one minute and the error is still present the output will increase/decrease by another 1%. How does derivative fit in to this. Also, is what I am saying above correct?

Answer 1

PID controllers attempt to use the model of a 2'nd order, linear differential equation to control a 'system'. By only looking at the difference between a desired setting and a 'controlled value' one has a control system that applys a 'correcting force' (opening or closing a valve, turning a heating element up higher or lower, ect.) that is proportional to the magnitude of the system error. But this means that small errors are difficult to correct. So one 'integrates' the small error over time so that it becomes a larger error term and allows a correction factor to be made. But it's also possible that applying a correction factor may cause the system to move too far. That is, if the system has any 'inertia' (time lag, thermal mass, momentum, etc.) then the correcting force may not be removed before the system 'overshoots'. Clasically this leads to oscillations in the control system. This means that the time derivative of the error signal should also be used to control the correcting force (this was classically done with 'rate feedback' in analog systems).

The whole subject of control systems and control system theory is both fascinating and kinda deep in places. There are lots of websites that talk about PID controllers, lots of manufacturers of PID controllers have a lot of data and explanations on their sites as well.

Doug

Answer 2

The output of a device is fed back to the input through 3 types of circuits Proportional - An amplifier with a fixed gain Integral - An amplifier that's configured as an Integrator Derivative - An amplifier that's configured as a Differntiator The resultant signal is compaired with the input and produces an error signal that will set the Ouput. When the error signal is zero the output is the required value