Chapter 6. Review and Outlook
Before proceeding to practical matters that are directly relevant to applications and implementations, let’s summarize the conceptual foundations of feedback control as we have developed them so far.
The Feedback Idea
The idea behind feedback control is simple:
Constantly compare the actual output to the setpoint; then apply a correction in the correct direction and of approximately the correct size.
The comparison and corrections are performed at runtime. Precisely because feedback relies on runtime observations and adjustments, feedback control is capable of responding to unanticipated disturbances.
Iteration
Feedback is an iterative scheme. That we keep monitoring the output and applying corrections is what makes feedback control feasible. Instead of having to get it “right” in a single step, we need only make things “better” because there is always another chance to fix any outstanding errors.
As a side effect, the ongoing iteration will also make the system robust to change.
Process Knowledge
One benefit of the feedback concept is that it does not require detailed knowledge about the controlled system and its behavior. Only two bits of information are required:
We must be able to identify the correct direction for the application of a corrective action. (In other words, we must know whether increasing the input will end up increasing or decreasing the output. This amount of process knowledge is indispensable.)
In general, we want to apply the largest possible correction that will not make the system unstable, in order to achieve the quickest possible reduction and elimination of the tracking error. This implies that we must be able to estimate the typical size or scale of the system’s response to an input change.)
Although feedback control does not require detailed knowledge about the controlled process, we must have at least enough information to answer the two preceding items in order to apply feedback control successfully. (Incidentally, it is this requirement that makes multidimensional control so hard: obtaining even these insights is extremely difficult if there is more than one control signal involved.)
Avoiding Instability
A system exhibits unstable behavior if it permanently oscillates between over- and undercompensation, without converging to a steady state. In extreme cases of instability, the amplitude of the oscillations increases over time (until the system is destroyed). Instability is usually the result of control actions that are too large.
The “theory” primarily tries to determine how large control actions can be for a given system. The answer depends on the static “scale” of the system’s input/output relation in the steady state and on the dynamic response of the system to an input change. Any form of lag or delay typically has the effect of reducing the magnitude of the corrective action that can be applied in any given moment.
The Setpoint
Feedback control has the effect of reducing the tracking error, which is the difference between the reference value (or setpoint) and the actual process output.
A necessary ingredient for feedback control is the existence of such a setpoint. We must have a notion of a desired value for the tracked metric. If we cannot identify a setpoint and cannot formulate a specific value (or, at least, a range of values) to track, then feedback control is not applicable.
Control, Not Optimization
The setpoint must be a value, not a condition. In particular, it is not possible to specify an extremal condition on the output (such as “the greatest possible success rate” or “the shortest possible response time”).
Feedback must not be confused with an optimization scheme. It has no notion of finding the “best” settings. Instead, feedback is a control mechanism: it will find (and maintain) the appropriate process inputs to produce a specific desired output, even in the presence of changing external conditions.