Chapter 10. Implementation Issues
Implementing a feedback loop based on a PID controller involves some low-level choices in addition to the overall concerns about stability and performance.
Actuator Saturation and Integrator Windup
In principle, there is no limit on the magnitude of the controller’s output: when the controller gain is sufficiently large, the controller output u can become arbitrarily large. But it’s a whole different question whether the downstream system (the “plant”) will be able to follow this signal. It may either not have enough “power” to respond to an arbitrarily large input, or we may run into an even more fundamental limitation.
Think of a heated room. Given a high enough setting on the dial, the desired heat output from the central heating system can be very large—quite possibly larger than the amount of heat the heating system can actually produce. But even more dramatic is the opposite scenario in which we select a desired temperature that is lower than the current room temperature. In this case, the best the controller can do is to switch the heat off—there is no way for it to actively lower the temperature in the room (unless it is coupled to an air conditioning unit).
Such limitations always exist. In the case of a pool of compute servers, the maximum number of servers is limited: once they are all online, further demands from the controller will have no effect. At the other extreme, the number of active servers can never fall below zero. And so on.