Page 80 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Closed Loop Controls, Rabbits and Hounds

Unfortunately, the D-term can also induce instability if its effective gain is greater
than unity, and it amplifies system noise. I have found this term to be of some lim-
ited value in temperature control applications, but of much less value at all in con-
trolling servo motors. In fact, purely reactive controls such as PIDs tend in general to
be of limited use with most servo motors.

Predictive controls
The reactive controls we have been discussing are driven entirely by error. This is a
bit like driving a car while looking out the back window. Your mistakes may be ob-
vious, but their realization may come a bit too late. By running controls strictly from
the error signal, we are conceding that an error must occur. Indeed, there will always
be a bit of error, but wouldn’t it be nice if we could guess the required power first,
and only use the remaining error to make up for relatively smaller inaccuracies in
our guess?

Predictive controls do just this. Predictive controls do not care about the error, but
simply watch the rabbit and try to predict the amount of power required to make the
servo track it. Since they watch the rabbit, and are not in the feedback loop, they
are both faster and more stable than reactive controls.

The rabbit term
Looking at the temperature rabbit curve of Figure 5.3, we begin to realize that there
are two relationships between the rabbit and the required power that can be readily
predicted. The first relationship is that for any steady-state temperature, there will
be a certain constant power required to overcome heat loss to the environment and
maintain that temperature. Let’s call this the rabbit term, and in the simplest case it
is the product of the rabbit and the rabbit gain. For a temperature control this is the
amount of power required to maintain any given temperature relative to ambient.
For the drive motor of a robot, this will be the amount of power that is required to
overcome drag and maintain a fixed speed.
The power required may not bear a perfectly linear relationship with the set point
over its entire range. This rabbit gain will vary with factors such as ambient tempera-
ture, but if the operating temperature is several hundred degrees, and the ambient
variation is only say 20 degrees, then this power relationship can be assumed to be a
constant. If the ambient temperature varies more appreciably, we could take it into
account in setting the gain. Note that in some cases the relationship may be too nonlinear

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