文档介绍：LECTURE NOTES
Describing Function Analysis Using MATLAB and Simulink
By Carla Schwartz and Richard Gran
ne of the earliest examples of feedback control is feedback gain for the escapement that will ensure the
the escapement mechanism that provides the pendulum swings at the desired frequency and amplitude.
Oforces required to keep a mechanical clock prop- The results of the analysis are then verified by simulation.
erly synchronized. Many famous mathematicians and physi-
History of Pendulum Clocks
cists analyzed escapements during the 17th and 18th
Timekeepers that use either the sun or water have been
centuries.
built since at least 1400 BC. Sundials provided daylight time
This article puter-aided design tools to develop
keeping, while at night, in some civilizations, water clocks
a describing function analysis of a pendulum clock. We de-
were used. For example, the Egyptians had a “Clepsydra”
sign the escapement as a control system that allows the pen-
(from the Greek kleptei, to steal, and hydor, water) that con-
dulum to provide the required time keeping and, at the same
sisted of a bucket with a hole. When filled with water, the wa-
time, add enough energy to the pendulum to e the ter level was a measure of the elapsed time.
damping caused by friction. The first mechanical clocks appeared in the 13th century,
We use analysis tools in the M