Inverted pendulum

The inverted pendulum is a pendulum with a focus above the axis. The pendulum is at its highest point in an unstable position of rest. The inverted pendulum is one of the standard tasks of control systems for the stabilization of an unstable control loop.

A standard example of an inverted pendulum is a car with an inverted pendulum mounted on it. The oscillating motion can be controlled by the horizontal movement of the carriage.

Designs

The standard task of a linear inverse pendulum can be extended in its dimensions. One possible extension is a second degree of freedom of the axle a different extension is an inverted pendulum with multiple axes and coupled pendulums dar.

Spatial inverted pendulum

When spatial inverse pendulum moves the axis, so for example the car, not along a straight line, but freely in the plane. The axis of the inverse pendulum is movable in two directions, so the pendulum can tilt in all directions.

The axis must now be analogous to the linear inverse pendulum in the plane be moved in such a way that it does not tilt. Technical building could solve this problem either by a robot arm with at least two degrees of freedom or a freely movable in level car.

Clearly that is the task that meets an artist while balancing a stick on his hand.

Inverted pendulum control as a technical task

The inverted pendulum is located at the highest point in an unstable position of rest. The inverse pendulum considered system always seeks the status of the lowest total power. This state is in an oscillation about the stable rest position or in the latter. Small deflections from the unstable position of rest cause the pendulum rod leaves this rest position. The system then must be the necessary power can be supplied constantly to remain in its unstable position of rest.

The quantity to be controlled in an inverted pendulum is the angle between the pendulum and the vertical axis. The angle is continuously measured and compared with a reference variable. The reference variable, which corresponds to the pendulum in its upright position. Where a deviation between the measured size, the actual value, and the reference variable, the setpoint control is made to align actual and target value. The control is performed in inverse pendulum in the above designs by the movement of the base point in order to move it at the center of gravity of the inverted pendulum.

The measurement of the angle is usually carried out either by a position sensor or a rotary encoder in the axis of the pendulum. The difference between the setpoint and actual value is translated by a controller in a control variable for the actuator.

Applications

Applications of the inverse pendulum can be found in various forms in everyday life. One example is the balancing of people and objects, as practiced by artists in acrobatics. Also, an upright man can be considered as an inverse pendulum: the focus is above the ground and body movements bring the pendulum from the equilibrium, so that a counter-movement is required to restore this or to receive.

Driving on a unicycle can be interpreted as driving on an inverted pendulum. The Segway Personal Transporter, a uniaxial electric scooter, takes over the balancing for the driver by means of electronic control.

The launcher Grasshopper the U.S. company SpaceX, uses the principle to start upright and land again can.