10 CHAPTER 1. A PRELUDE TO CONTROL THEORY
gear having teeth of a special shape. Attached to the pendulum is a device to
engage the teeth of the gear. For each swing of the pendulum, one tooth of the
gear is allowed to ìescape.î That is what produces the ticking sound of a clock.
One additional job of the escapement gear is to impart just enough energy into
the pendulum to overcome friction and allow it to keep swinging.
Example 1.10 (Unstable system)Aninverted pendulumis an upright
pole with its fulcrum at the base. The objective is to balance the pole in the
upright position by applying the appropriate force at the base. An inverted
pendulum is inherently unstable, as you can observe by trying to balance a pole
upright in your hand (Figure 1.13). Feedback control can be used to stabilize
an inverted pendulum. We will give several examples in later chapters.
Figure 1.13. Balancing inverted pendulum1.4 Alookatcontrollerdesign......................
Synthesizing the above examples of control problems, we can describe a typical
control problem as follows. For a given plantP, it is desirable to control a