Page 68 - Anatomy of a Robot

02_200256_CH02/Bergren 4/17/03 11:24 AM Page 53
CONTROL SYSTEMS 53
mostat goes over the temperature setting. Then it turns the heat all the way off until
the temperature falls below the temperature setting. It’s expensive and inefficient
(in terms of combustion) to ignite a furnace, and it’s best if it runs for a while once
it is ignited. The net result is that the temperature in the room doesn’t stay at a sin-
gle temperature. Instead, it cycles up and down a degree or two around the setting
on the dial. This action, taken by many control systems, is called hunting. We’ll
talk about hunting shortly (see Figure 2-24).
This hunting action by the heating system is just fine in the design of the ther-
mostat. Humans generally cannot sense, nor are they bothered by, the fluctuations
of temperature about the set point. But consider a light dimmer. If the dimmer
turned the lights on and off five times a second, reading would be rather difficult.
Instead, dimmers turn the light on and off around 60 times a second so the human
eye cannot sense the fluctuations. When you design a system that will have hunt-
ing in the output, be sure you know the requirements.
Mechanical wracking Many mechanical systems have loose parts in them that
will slip and then catch. In the model second-order system, consider what happens if
the weight is mounted to the spring with a loose bolt. As the weight shifts direction,
the bolt comes loose for a while and then catches again. The spring constant actually
varies abruptly with time, and the smooth response of the system is disrupted.
You can model the robot’s performance by considering that the model system will
behave in two different ways. While the bolt is caught, the spring constant is per
design. While the bolt is loose, the spring constant is near 0. If such a mathemat-
ical model is too difficult to chart, you can take the following shortcut. Just fig-
ure on adding the mechanical wracking distance (the distance the weight moves
unconstrained by the bolt) to the overshoot and undershoot. This will make a good
first estimate of its behavior. In practice, try to minimize the mechanical instabil-
ities in the robot.
Digital actuators Many other actuators and sensors tend to be digital. Consider
a solenoid. It’s basically an electromagnet pulling an iron slug into the center of
the magnet. It’s either off or on. The iron slug provides the pull on the second-
order system when the electromagnet is activated (see Figure 2-23).
Effectively, our model of the second-order system is good for predicting the sys-
tem’s behavior since the solenoid behaves like a step input.

HUNTING

We’ve seen in the case of the thermostatic heating control system that the output of the
system will hunt, effectively cycling above and below the temperature set point with-
out ever settling in on the final value (see Figure 2-24).