Sensaphone SCADA 3000 Users manual - Manual (Page 211)

17-3
Chapter 17: PID Programming
tuning factor Kp. The higher the value of Kp the more influence this parameter has on the con-
troller output.
The integral term is computed by taking the integral of the error over a recent time interval
and multiplying it by the Integral tuning factor Ki. The higher the value of Ki the more influ-
ence this parameter has on the controller output.
The derivative term is computed by taking the derivative of the error signal and multiplying it
by the Derivative tuning factor Kd. The higher the value of Kd the more influence this param-
eter has on the controller output.
When the tuning factors are set correctly the system will maintain the set point without taking
too long and without excessive overshoot or undershoot. If the current error is large, has been
sustained for some time, or is changing rapidly, the algorithm will attempt to make a large cor-
rection by generating a large output. Conversely, if the feedback has matched the set point for
some time, the algorithm will leave the output value alone.
Tuning
While this sums up the way you set the PID control algorithms, it doesn’t really express the
most difficult element of PID—and that is tuning. Your objective is to set the Kp, Ki, and Kd
factors so that their weighted sum produces a controller output that steers the process variable
in the desired direction but in such a way as to eliminate any error.
Setting all three tuning constants to large numbers might seem to solve this problem by ensur-
ing an aggressive response to changes; however such a setup will at the very least cause a wild
pendulum of cause and effect, and at the worst actually move the process variable further from
the setpoint than before. Setting the tuning constants too conservatively, on the other hand,
might not allow enough correction to fix one error before a new one appears. The properly
tuned controller exists somewhere between these two extremes. While it recognizes and cor-
rects an error quickly and aggressively, it doesn’t overcompensate and throw the system into an
unending loop of too much and too little.
The thing to understand is that there is no single answer except to say that the best tuning of a
PID controller will depend on how the process responds to that controller’s corrective efforts.
Processes that react instantaneously and predictably need no control feedback at all. If you turn
on a wall switch, your ceiling light comes on. A set amount of electricity arrives to power the
illumination. No feedback is required. However, the amount of electricity available for you to
draw upon must remain relatively constant throughout the day or your lights and appliances
will suffer from potentially problematic surges and blackouts as power rises and falls. In a per-
fectly tuned system, compensation would be instantaneous. As that isn’t possible—the shifts
aren’t precisely predictable—you see occasional (and hopefully very brief) brownouts during
the “lag” between the network’s increased need for power and the controller’s response to that
need.
In a slow process with a long lag time before the process responds to the controller’s efforts,
the proportional term will come into play to keep the output high or low until the error is
eliminated. This will cause a cumulative error over time and the integral term comes into play;
in fact, in a slowly changing process, it will come to dominate. The controller generates output
based on the history of accumulating errors, and the variable overshoots the setpoint, causing
an error in the opposite direction. If that integral tuning constant is not excessive, then this
rebound error will be minimal, and the variation will decrease as this error is added to the orig-
inal. The derivative term will add its share to the controller output then, based on the deriva-
tive of this oscillating error signal—the back and forth between uncorrected and over-corrected
states. The proportional term will rise and fall as the error diminishes toward a steadier state.