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CONTROL SYSTEMS 27
nal. Such transformations may take the form of scaling (to a different size) or conver-
sion from one signal type to another (like from light values to a voltage signal).
Often, the comparison within the circular symbol is not a simple subtraction.
Sometimes it’s a comparison (bigger or smaller) and the output of the circle represents
either off or on. Thermostats work this way, for example.
Clearly, the system looks like a closed loop. Often, such a system is also referred to
as a closed-loop feedback system. All these terms generally mean the same thing.
Let’s run the first experiment over again a different way as a closed-loop control sys-
tem. Now close your eyes and point again to the object (trying to put your finger right
on the object in your field of vision). Open your eyes again, and see how close you
came. You still didn’t get it right with your eyes closed, but now with your eyes open,
you’ve introducted feedback into the system. With your eyes open, it’s easy for you to
make the correction and get your finger right over the object in your field of vision (see
Figure 2-6).
Notice, the steady state error is now much less. We think the error is actually zero,
but we’ll see shortly that this is rarely the case. Certainly, closed loop control is a bet-
ter solution in terms of accuracy, but it comes at the cost of providing extra control ele-
ments (in this case, vision).

STEADY STATE ERROR

Now that we’ve identified a parameter of interest, let’s look at the math. We can assign
arbitrary variables to represent the signals and control system elements that we have
been talking about (see Figure 2-7).
Looking at the circular arithmetic element (subtraction),
b a d

The actuator is said to have a gain of C. This gain can be immense and the system will
still work. As an example, if a very tiny positive signal takes place at b, then signal d
can be extremely large and positive. Similarly, if a very tiny negative signal is issued at

FIGURE 2-6 The closed-loop control error is smaller with eyes open.