As an Electrical Engineer at Union College in 1965, this was my senior year project. I had nine months to apply classical control
system theory (Laplace transforms, Bode
plots, Nyquist criterion, Root Locus, etc.)
to analyze the problem and then build a
For computation, I had my slide rule
and the privilege to use the first computer
ever to arrive at Union College: the IBM
1620. A marvel of the age, it clocked at
100 kHz, and boasted a 20K nib memory
(a nib is four bits) — all for only $65,000.
My primary resource for electrical and
mechanical components was a basement
full of WWII surplus goodies; many from
the B- 29 gunnery control system. My 28V
“cart” drive motor originally fed bullets to
one of the two machine guns in one of
the four turrets spread around the B- 29. I
powered this motor with an amplidyne:
an electromechanical motor generator
pair that could amplify 20 mA from a
vacuum tube into 2 k W to drive the
motor that rotated a gun turret.
Decades ago, the first really
important application of the inverted
pendulum problem was stabilizing a
rocket on its thrust vector. Today, with the
availability of inexpensive gyroscope and
accelerometer chips, stabilized inverted
pendulums are very common; most
notably, the Segway, balance boards, and
self-balancing toys like the MIP and
Mipasaur from Wowee.
Stabilizing an inverted pendulum is a favorite and
much discussed control theory problem for roboticists.
The basic idea is illustrated in Figures 1 and 2.
Simply put, the problem is to drive the robot base
forward or backward in such a manner as to prevent
the inverted pendulum design from falling over. In this
article, we’ll explore the math and science behind this
seemingly simple task.
46 SERVO 12.2017
Figure 2. Balancing a glass of
wine without getting tipsy!
Figure 1. An
connected by a free
pivot to a motor
driven robot base.