Discussion on the effects of proportional and integral terms in PID control
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Hello everyone! I’ve been reading about the tuning of PID parameters recently, and it was mentioned that when making a step change in the setpoint: 1. If only proportional action is involved, then this proportional action will cause a sudden change in the output ； 2. If only integration is present, then the output will not undergo a step change. The first sentence is easier to understand, but the second one is not so easy. Why doesn’t the integral effect cause a step change in the output? My understanding is that there still is a step change in the output, and it starts from that point, after which the output increases or decreases. I hope to exchange ideas with all the experts here.
Assuming that only the PI effect is present, and the PV and SV values are equal, i.e., E=0, then the change in output is 0. If a step test is performed on SV at this time, then E changes. In the case of an incremental PID algorithm, under proportional action, the change in output is Kd*(E(n) – E(n-1)) = kd*E(n). Similarly, under integral action, the change in output is KI*E(n). If KI is greater than Kd, then the effect of integral action can even be greater than that of proportional action.
The existing control laws do not have pure integration; they only have proportional-integral or proportional-integral-derivative control. Under proportional-integral control, when a step change occurs, the output jumps first, and starting from this point, the output then increases or decreases.
In practical applications, integration and proportion are used together, that is, the proportional-integral action. Pure integration does not cause a step change in the output, because the output of integration is a straight line whose slope depends on the integration rate. In proportional-integral control, when there is a step change in the error, the step change (vertical increase) in the controller’s output is the result of the proportional action; starting from this point, the output then increases or decreases gradually, which is the result of the integral action.