Controlled Systems

This chapter is colourful. It jumps back and forth between topics and may, in retrospect, seem like a confused lecture. In this chapter I explain how control works. For that I need a lot of fundamentals. Explaining them all in advance is terribly boring. That is why I introduce the fundamentals whenever I need them. Unfortunately, every structure dies in the process. For precisely this reason, I hope you enjoy reading it, because here you have to think along very alertly and your brain is challenged.

In this chapter you learn how controlled systems are calculated. For this, we classify typical recurring behaviours and analyse how they behave in a control loop.

All systems that behave the same with respect to their input and output quantities are treated the same in control engineering. Fortunately, very different function blocks, such as a gearbox and a lever, can be described with very similar mathematics. Control loops always measure the output quantity and feed it back to the input. Control loops are also very similar to one another in structure.

Control engineering exploits these similarities to derive a general solution. From the general solution of all control loops, we then determine specific solutions for your concrete control loop. You should remember this approach as an engineer. Occasionally you have to solve very similar problems several times in succession.

Let us look at this using the example of a tax return. You can write a tax return completely from scratch every year. But tax returns are very similar from year to year, because the names of the children or the spouse rarely change. The best way to solve the problem is to create a general tax return as a template and adapt it slightly each year. Then you only enter into the general tax return the income and expenses that differ from the template, and you are quickly done.

It can save time to solve the problem once in general and then only feed the general solution with the parameters of the specific problem. Determining the general solution is a lot of work, but you save that many times over later with many specific solutions. This applies all the more, the more similar the problems are.