We may show this mathematically, by breaking the “ideal” equation up into three different parts, each one describing its contribution to the output (∆m):Īs you can see, all three portions of this PID equation are influenced by the gain (K p) owing to algebraic distribution, but the integral and derivative tuning parameters (τ i and τ d ) act independently within their own terms of the equation. Increasing K p in this style of PID controller makes the P, the I, and the D actions equally more aggressive. Here, the gain constant (K p ) is distributed to all terms within the parentheses, equally affecting all three control actions. Ideal PID ControllerĪn alternate version of the PID equation designed such that the gain (Kp ) affects all three actions is called the Ideal or ISA equation: If the controller’s PID equation uses Kp as a factor in all three modes, the technician need only adjust K p to re-stabilize the loop. If the controller’s PID equation takes the parallel form, the technician must adjust the P, I, and D tuning parameters proportionately. Note : An example of a case where it is better for gain (K p ) to influence all three control modes is when a technician re-ranges a transmitter to have a larger or smaller span than before, and must re-tune the controller to maintain the same loop gain as before. We may show the independence of the three actions mathematically, by breaking the equation up into three different parts, each one describing its contribution to the output (∆m):Īs you can see, the three portions of this PID equation are completely separate, with each tuning parameter (K p, τ i, τ d ) acting independently within its own term of the equation. However, there are times when it is better to have the gain parameter affect all three control actions (P, I, and D) (Note) At first, this may seem to be an advantage, for it means each adjustment made to the controller should only affect one aspect of its action. In the parallel equation, each action parameter (K p, τ i, τ d ) is independent of the others. The equation used to describe PID control so far in previous articles is the simplest form, sometimes called the parallel equation, because each action (P, I, and D) occurs in separate terms of the equation, with the combined effect being a simple sum: It should be noted that more variations of PID equation exist than these three, but that these are the three major variations. Some controllers offer the choice of more than one equation, while others implement just one. For better or worse, there are no fewer than three different forms of PID equations implemented in modern PID controllers: the parallel, ideal, and series.
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