Page 56 - Anatomy of a Robot

02_200256_CH02/Bergren 4/17/03 11:23 AM Page 41
Hang the 250-gram weight, measure the displacement in meters, and then
compute K in newtons per meter. CONTROL SYSTEMS 41
c. Coefficient of friction
ii.First, you must know how friction behaves, since it can get complex. The
friction is greater in our model when the weight is not moving. This is
termed static friction. Once the mass starts to move, the friction decreases
to a lower level as long as the mass continues to move. Think of friction
as a series of microscopic speed bumps. They don’t seem as bumpy if the
weight is moving faster, but if the weight slows to a crawl, the speed
bumps are painful to go over. We’ve all experienced static friction before.
Often, it takes an extra heave-ho to start pushing something, and a bit less
effort to keep it going. Just be aware that system behavior won’t precisely
follow the model if B is greater when the mass is at rest. A couple of web
sites about friction are located at www.iit.edu/ smile/ph9311.html and
www.iit.edu/ smile/ph9104.html.
ii.The coefficient of friction B can be measured in two ways:
Force conversion: Take a spring with a known spring constant K and
use it to pull the weight at a constant velocity dx/dt across the friction
surface. The force exerted by the spring is K x, where x is the
displacement of the spring. At a constant velocity, the spring force
equals the force of friction, which is B dx/dt.
B K x>1dx>dt2

Derivation: We’ll see later how, knowing K and m, we can derive B by
observing the system behavior. This would prove useful when changes
have to be made to either of the three parameters to change system
behavior.
2. Let’s assume we know B, K, and m. We can plug these numbers into the equa-
tion for x(t) and plot the predicted results. The robot should follow the model’s
behavior if the model truly does mimic the design of the robot.
Let’s tackle the second goal.

HOW TO CHARACTERIZE THE ROBOT’S PERFORMANCE
AND KNOW WHICH DESIGN PARAMETERS TO ALTER

Figures 2-12, 2-13, 2-16, and 2-17 were made using Excel spreadsheets. They show the
predicted behavior of the model’s second-order system. The figures were made specif-
ically to show how we can guide the design and make the robot behave the way we want
it to. This, of course, is the third goal, so we’ll postpone that part of the discussion.