Inverted pendulum system

Design a fuzzy logie eontroller for the inverted pendulum system shown in Figure 10.13 so that the pendulum remains in the vertieal position. 

The inverted pendulum problem is a elassie example of produeing a stable elosed-loop eontrol system from an unstable plant. 

Fig. A1.4 Inverted pendulum control system design using pole placement...

There is also an openloop unstable mechanical system the inverted pendulum. This is the problem of balancing a broom on the palm of your hand. You must keep moving your hand to keep the broom balanced. If you put your brain on manual and hold your hand still, the broom will topple over. So the process is openloop unstable. 

Parametrically Forced Inverted Pendulum The basic example for parametrically excited systems is the inverted pendulum with periodically vibrating suspension (see Fig. 17). The equation of motion for the system reads... 

Bagheri Shouraki and Honda (1998) showed the ability of ALM for stable controlling of dynamic systems such as invert pendulum... 

The VIRGO project is a French/Italian collaboration using a 3-km arm length detector close to Pisa, Italy. The Michelson interferometer is equipped with Fabry-Perot cavities. The seismic attenuation system is the combination of an inverted pendulum for preisolation and a five-stage pendulum cascade (superattemator). The arrangement allows for an extension of the sensitivity band down to 4 Hz. The interferometer is actually under constmction and is expected to be operative in 2002. 

Free pendulums come in two main categories, those where the specimen itself supports an inertia arm and those where the end load is balanced so that there is no tensile stress in the specimen, these are known as inverted torsion pendulums. In either case the sensing of twist is done usually either by an optical system or by an electrical one. 

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