Hello all,

just want to verify that I have an understanding of what each function does. Please correct me if I am wrong.

Proportional Gain: Basically the multiplication factor between input and output. The higher the (kP) the larger the output is compared to the input.
(example: kP = 5: For ever 1% of input change, the output changed by 5%)

Integral (Reset): Ok, I am not to sure about this one. As I understand it, Integral take the difference between the setpoint and error and adds/subtracts it from the output signal to eliminate offset. The higher the (kI), the more resets per minute, the slower the process variable will get to SP, but it gets there under greater control and stability. The lower the number, the faster it will get to the final SP, but the greater the chance for overshoot.

Derivative (Rate): Again, as I understand it, Derivate changes the output signal in proportion to the change of the slope of the process variable. The higher the (kD) the faster it will get to setpoint and stabalize, but it will take longer to stabilize.

I am not sure about the Derivate definition or the Integral definition so any help is greatly appreciated. I have read a lot about them, but would like examples please.

Thank you.

 

A PID controller output depends on the error between the process variable PV and a target value or set point SP.

The output of a proportional control element is proportional to the error, with the proportionality constant given by the gain K. You may also find some older controllers where the action of the proportional element is defined using "proportional band" PB - this is the % change in error needed to give 100% change in output, and can be calculated from PB = 100/K.

The integral control element gives an output that changes at a rate dependent on the error. The relationship between the change in output and the error is given either by the reset rate in repeats per minute, or the integral action time IAT given in minutes per repeat. The "repeat" in these definitions is in terms of a step change in error in a PI controller - there will be a step change in output = K x error change, followed by a ramp in the output due to the integral. The IAT is the time taken for the integral ramp component to a step change in error to match the initial proportional step change in output.

The derivative term gives a steady component in the controller output which is proportional to the rate of change of error - if the error is fixed, there is no derivative output component. The derivative term is described in terms of the controller response to a RAMP input (as opposed to the step input for proportional and integral) as the derivative action time or DAT. In a PD controller with a ramp change in input of X % per minute, the output will consist of a step, followed by a ramp due to the proportional element of k X %/minute. The DAT is the time needed for the proportional response ramp to build up to the same magnitude as the initial derivative step.

So for a PID controller with a gain of 2, IAT of 5 minutes, and DAT of 0.5 minutes, the output will be:

for a step change in error of 2 %:
a proportional step of 2 x 2 = 4%, followed by a ramp with a rate of 4 % in 5 minutes. The derivative component in the output will theoretically be an infinitely large spike at the time of the change with nothing after: in practice it is effectively zero.

For a ramp change in error of 1.5 % per minute:
the proportional element will be a ramp at 2 x 1.5 = 3 % per minute.
the derivative term will develop an initial step of 3 x DAT = 3 x 0.5 = 1.5 %
the integral term will be a parabola (integral of a ramp). The equation for this term as a function of time is k/(2xIAT) x r x t^t, where r is the ramp rate in error.

Hope that helps,

Bruce.