NEDL Inverse – Wikipedia

Scheme of an inverse pendulum on a car

The Inverse pendulum Is a pendulum with a focus above the axis. The pendulum is located in its highest point in an unstable rest position. The inverse pendulum is one of the standard tasks of the control technology for the
Stabilization of an unstable control route.

A standard example for an inverse pendulum is a car with an inverse pendulum mounted on it. The pendulum movement can be influenced by the horizontal movement of the car.

The standard task of a linear inverse pendulum can be expanded in its dimension. A possible extension is a second degree of freedom of the axis, another expansion represents an inverse pendulum with several axes and coupled commuting.

Spatial inverse pendulum [ Edit | Edit the source text ]

Spatial Inverses pendulum. The pendulum has two degrees of freedom, the base of the pendulum is movable in the level along two directions (green and blue arrow).

With the spatial inverse pendulum, the axis, for example the car, moves not along a straight, but free on the level. The axis of the inverse pendulum is movable in two directions, the pendulum can therefore tip over in all directions.

The axis now has to be moved in the level of the linear inverse pendulum in the level that it does not tip over. Technical structures could either solve this task through a robot arm with at least two degrees of freedom or a freely movable car.

The task that an artist is on hand when balancing a rod is clear.

The inverse pendulum is located at the highest point in an unstable rest position. The inverse pendulum, viewed as a system, always strives for the state of the slightest total energy. This condition is in a vibration around the stable resting or in it. Small excavations from the unstable resting position mean that the pendulum rod leaves this resting. The necessary energy must then be consistently supplied to the system in order to stay in its unstable resting.

The size to be controlled with an inverse pendulum is the angle

Between pendulum and vertical axis. The angle

is measured continuously and compared with a guide size. The guide size is

which corresponds to the pendulum in its upright position. If there is a deviation between measured size, the actual value, and guide size, the setpoint, a control is carried out to compensate for the actual and setpoint. The control takes place in the inverse pendulum in the above -mentioned design by moving the base point in order to move it under the focus of the inverse pendulum.

The measurement of the angle

usually takes place either via a position sensor or a rotary angle transmitter in the axis of the pendulum. The difference between the target and actual value is translated into a manner for the actuator by a controller.

Applications of the inverse pendulum can be found in various forms in everyday life. An example is the balancing of people and objects, as practiced by artists in acrobatics. An upright person can also be seen as an inverse pendulum: the focus is above the stand area, and body movements bring the pendulum out of balance, so that a countermovement is necessary to restore or maintain it.

Driving on a unicycle can be Drive on an inverse pendulum be interpreted. The Segway Personal Transporter, a single -axle electric motor scooter, takes over the balancing for the driver by means of electronic control.

The GRASSHOPPER sponsorship rocket from the US company SpaceX uses the principle to start and land again.

• Fritz Tröster: Control and control technology for engineers . 2nd Edition. Oldenbourg Verlag, 2005, ISBN 3-486-57681-X.