A First Course in FUZZY and NEURAL CONTROL

1.3. STABLE AND UNSTABLE SYSTEMS 9

1.3 Stableandunstablesystems.....................

Stability of an uncontrolled system indicates resistance to change, deterioration,
or displacement, in particular the ability of the system to maintain equilibrium
or resume its original position after displacement. Any system that violates
these characteristics is unstable. A closed-loop system must, aside from meeting
performance criteria, be stable.

Example 1.9 (Stable system)The pendulum is among the most stable of
all systems. No matter what position the ball is placed in, the pendulum tends
toward the vertical ìat restî position, shown in Figure 1.11.

Figure 1.11. Pendulum in motion and at rest

Pendulum clocks have been used to keep time since 1656, and they have not
changed dramatically since then. They were thefirst clocks having a high level
of accuracy, made possible by the fact that the period of a pendulumís swing
is related only to the length of the pendulum and the force of gravity. When

Figure 1.12. Clockís escapement with pendulum

you ìwindî a weight-driven clock, you pull on a cord that lifts the weights. The
weights act as an energy storage device so that the clock can run unattended for
relatively long periods of time. There are also gears that make the minute and
hour hands turn at the proper rates. Figure 1.12 shows an escapement with a