The elements of a feedback system are not complicated: the basic loop structure and a simple controller are all that is required. In fact, all the case studies were completed with nothing more complicated than the generic feedback loop as implemented in the closed_loop() convenience function!

Most controllers, also, were of the generic PID type, although particular situations sometimes called for specially designed controllers. But even those controllers were very simple and did nothing more than calculate an output based on the input while maintaining only minimal internal state.

The natural temptation to build more complicated controllers should probably be resisted in most cases. The feedback principle is not about clever (and complex) algorithms; rather it works with simple components put together in a straightforward fashion. What makes feedback work is that corrective actions are calculated and applied constantly. Because of the iterative nature implied by the feedback scheme, the components and calculations themselves can (and should) be simple.

Given all the details and specific methods to “measure the transfer function” presented in Chapter 8, it is easy to forget that we are really after only a few pieces of basic information:

All the methods presented earlier are just ways to obtain those basic pieces of knowledge about the process in question.

The same can be said for controller tuning. For PID controllers, the controller gains consist of the static gain factor Δu/Δy, which is modified by a factor that takes the dynamic response of the process into account (increasing the gain for sluggish processes, decreasing the gain when there is noticeable delay). Given only those bits of process knowledge, we can find controller gains that will result in a workable closed-loop operation and that can be improved through trial and error in a manual process. The formulas and methods discussed in Chapter 9 are primarily shortcuts for this process.

There are a variety of signals flowing around a control loop: the set-point, the process output, the tracking error, the controller output. Add some additional elements, like actuators or filters, and we are talking about half a dozen individual signals for a basic loop alone! In a nested arrangement, the number of signals multiplies.

It is surprisingly easy to get confused about which signal goes where, and with which sign (plus or minus). If a newly commissioned loop does not seem to work at all, it often helps to trace all signals around the loop and to confirm that the components were indeed wired together correctly. To ensure that the signs are correct it helps to ask, for each component: if the input goes up, should the output go up or down—and what does it actually do?

Most of the case studies showed systems that included a stochastic aspect. In fact, randomness and the uncertainty that it brings about will often be what makes feedback control an attractive proposition in the first place.

In all the case studies, I have taken a “naive” approach to noise. In essence we assumed that we could ignore the randomness, and concentrate only on the deterministic part of the system, on the premise that the noise would “average itself out” over time. In a similar spirit, we have usually shown only a single simulation run for each system with the understanding that the observed behavior is typical and a representative sample from all possible runs. Performing several simulation runs quickly gives one a sense for the magnitude of the variations that can be expected. If greater accuracy is required (in simulations or a production installation), then one can calculate the desired quantity as the average over several experimental runs.

It is a natural impulse to use filters as elements in a control loop to obtain smoother signals. Although that often makes sense, it is not always necessary. Keep in mind that filters slow signals down; therefore what we gain in smoothness via filtering may be lost again because the system now requires greater controller gains. Filters should be used only when they have been shown to be necessary. One should not automatically reach for a filter just because a signal is noisy.

Finally, all the case studies assumed that the noise involved was relatively harmless: possibly of large amplitude but always of finite variance. This is not necessarily so: systems exhibiting noise with a power-law spectrum do exist and always require special treatment.