PID Control Systems.

PID is an enhanced feed back system designed to determine the overall system behaviour. A simple feedback system comprises a single feedback path and is proportional only.

Feedback systems are used to reduce or eliminates errors. In a typical PID installation, we have a set point and the PID feedback systems works to keep the output value equal to the setpoint value. It is possible for the setpoint value to be a changing value, but this can add complication.
An ideal system would have a linear transfer function, zero phase shift and zero delay. Under these conditions, a proportional control is all that is needed.
A real world system commonly has a non linear transfer function (pumping is a classic case) and there can be a considerable delay between the "action" and the "reaction" (measured value). If a purely proportional control is applied under these conditions, there will be overshoot and oscillations and it will not be possible to achieve a stable output over the whole control range.

One way to see the effect of system delay between the input and the output of a system, is to apply a step function. If the response is perfect and there is no dely, the output will accurately track the input with a proportional feedback system..

If there is a delay, then the error signal fed back is the result of an input some time earlier. By the time the controller sees the output at the correct level, it has already increased the drive too much. The net result is that there is an overshoot, followed by an undershoot and effectively a decaying oscillation.

The addition of the proportional feedback reduces the risetime seen on the output, but adds over and undershoot and a decaying oscillation. The output is closer to the required output, so the error is reduced.

The PID controller is a three term controller incorporating a Proportional feedback element (P), an Integral feedback Element (I) and a Derivative feedback element (D).

The Integral element is added to the proportional element to provide a means for eliminating a changing offset in a non linear system, and to slow down the reaction to allow for the time delays in the system. This will reduce the overshoot experienced in the practical proportional control system.

The derivative element is added to provide a means of reducing sudden changes in the output and will provide a faster response to step functions and transients.

Setting up a PID system is a balancing act with all terms interacting. Excessive Integral gain will slow the response rate excessively and may result in the output moving with load changes. Insufficient integral gain will cause the output to overshoot and oscillate around the set point. Excessive derivative gain will result in instability with severe oscillation around the set point. The derivative gain should be used sparingly to improve transient performance, and is best added in only after the proportional and integral gains have been set for best performance. The derivative gain can then be slowly increased to the point of best stability of the output.