Page 78 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Closed Loop Controls, Rabbits and Hounds

than to motor controls, especially in mobile robots where the servo target is con-
stantly being revised.
In motor control applications the speed command often varies so rapidly that the
integral term is of little value in closing the error. For this reason, I do not recom-
mend the integral term in any control where the power will normally go to zero
when the rabbit reaches its destination (such as a position commanded servo on a
flat surface).

In applications where an integral is appropriate, and where the rabbit tends to stay
at set point for extended periods, an integral hold off is usually helpful. This simple bit
of logic watches the rabbit and when its absolute derivative becomes small (the rab-
bit isn’t changing much) it enables the integral term to accumulate. When the rab-
bit is in transition, the integral is held constant or bled off.

Generally, introducing sudden changes into the calculation of the PID (such as dumping the
integral) is not an optimal solution because the effects of such excursions tend to destabilize
the system.

Figure 5.3. A well-tuned PID using only proportional and integral terms

Figure 5.3 shows a well-tuned PID control using only these P and I terms. The total
power, proportional, and integral terms correspond to the scale on the right side of
the graph, while the scale for the rabbit and temperature are on the right.
Notice that the temperature rabbit is an exponential function that approaches the
set point of 250 degrees. The trick here is that while the temperature clearly over-

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