Page 104 - Analog Circuit Design Art, Science, and Personalities

Jim Roberge

system raises the temperature of the controlled surface about 25 "C above ambient
by means of a resistance heater. The feedback signal is developed by a thermistor,
and thermal dynamics are dominated by a 0.1 inch thick aluminum spreader plate
separating the heater from the controlled surface. The disturbance rejection of the
systcm depends on its isolation from ambient temperature variations and its loop
parameters.
Another experimental setup allows students to design several different types of
servomechanisms. The mechanical portion of this system consists of a DC motor
with an integral tachometer geared to a potentiometer used for position feedback.
Additional inertia can be attached to the motor shaft. The electronics is designed so
that a velocity or a position loop can be easily implemented, using either forward-
path or feedback compensation. A wide range of compensation parameters can he
selected via potentiometers and plug-in components to reduce assembly anxiety
for non-EE students.
The third setup consists of a lightweight "cartooii" of an airplane. The elevator
angle and the pitch angle of the aircraft are driven by positioning servomechanisms
(actually the type used for model plane control). Several plug-in analog-computer-
type boards simulate the pitch dynamics of different aircraft, including one that is
unstable in pitch. (The mock-up is, of course, only used to give a visual indication
of the response to various commands applied via a joystick.) The object here is to
design an autopilot that simplifies the task of "flying" the "airplane."
The basic approach, using any of the experimental setups, is to first characterize it
using appropriate measurements. For example. the dynamics of the thermal system
are described by a diffusion equation and thus cannot bc accurately represented by a
small nr.tmbcr of poles and zeros. Its transfer function is measured over the lrequency
range of interest using a Hewlett-Packard 3562A dynamic signal analyzer. Alterna-
tively, the servomechanism can be accurately modeled after important parameters
have been experimentally determined.
After characterization of the fixed elements, closed-loop performance is predicted
and measured for several configurations. Finallyl compensators that meet speci tied
closed-loop objectives are designed and tested.
The laboratory work is structured as a sequence of short weekly assignments that
closely paraliel and reinforce classroom presentations. As in the case of thc active-
circuits subject. evaluation of laboratory performance is based in large par1 on the
results of a student-teaching assistant interview.
You may wonder why I spend so much time describing a course that is basically
one on classical servomechanisms in a book for analog circuit designers. I remind
you of my belief that this general material is the most important single topic a circuit
designer can know. It is easier to teach this material using relatively slow systems
than high speed electronic ones. because the slower systems are easier to model
accurately. Once the basic ideas are well understood in a servomechanism context,
they are readily transferred to purely electronic tems. Finally, servomechanisms
are fun to work with. (Consider the two-pendulum problem, for example.)
'Jhc graduate course, which is taught every other year, has a "family and friends"
type enrollment: since I generally require that participants have taken both of the
undergraduate courses and done well in them. I occasionally will waive the pre-
requisites. such as in the case of a person who has had extensive experiences as a
practicing circuit designer. Some of my colleagues feel that this requirement unfairly
discriminates against M.I.T. graduate students who did their undergraduate work
elsewhere. if this is the case. at least I came by my prejudices naturally, since I ain
completely inbred at M.I.T. (In actualityl most new graduate students who are inter-

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