Page 60 - Anatomy of a Robot

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CONTROL SYSTEMS 45
Galloping Gerdie? It shook itself to pieces because the mechanical engineers
missed damping out a resonant mechanical frequency. Talk about a failure to con-
trol damping. See www.ketchum.org/tacomacollapse.html for an interesting treat-
ment of this particular mechanical failure.
More variables This brings up a good point. All along, we have assumed that
both the mass and the friction beneath the mass are fixed with respect to fre-
quency as the position of the mass changes.
If the mass is not solid but has a harmonic resonance in its structure, then the
system will not behave per the model. So be very careful that your robot has a
solid construction and as few resonant mechanical elements as possible. It is
much easier to control the position of a one-pound block of steel than it would
be to control a one-pound bowl of jello.
If the coefficient of friction varies with position, similar problems could occur.
We have to clearly identify all the frictional elements at work within our robot
system. Some will be inherent in the materials (like in the springs). Other fric-
tional elements will be accidental and must be carefully analyzed to make sure
they stay constant with position. Its not wise to allow unspecified frictional ele-
ments to govern our system. To take back control of the design, we can can
deliberately put a frictional element of our choosing into the system. If it is
much larger than the inherent or accidental frictional elements, it will swamp
out their effect as much as possible and make our design more reliable in its
performance.
Stability An entire body of control system theory is devoted to the stability of
systems. We certainly know from the bridge example that it’s important. It’s also
extremely complex in the mathematical theory and we need not go into it here, but
we should look at several pieces of advice. First, we should identify just what
instability is.
Some control systems, if not designed right, can oscillate way too much, upset the
mechanics, and ruin the operation of the robot. These oscillations can stem from
various flaws in the design.
Resonant frequencies As we just mentioned, make sure the mechanics and
other physical elements of the system, such as the frictional components and
spring elements, do not have resonant frequencies. Make sure they behave the
same way across all the frequencies to which the robot will be subjected. One
way to ensure this is to put the system on a mechanical vibrator, as we’ll see later.
Bad selection of the frequency v Sometimes the mechanical system does
have some resonant frequencies within the design. If v is chosen wrong, the
ringing may be way too large and the system may be unstable. Alter v and see
if things calm down. If this helps, then analyze the mechanics again.