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The inverted pendulum was a central component in the design of several early seismometers due to its inherent instability resulting in a measurable response to any disturbance. [8] The inverted pendulum model has been used in some recent personal transporters, such as the two-wheeled self-balancing scooters and single-wheeled electric unicycles.
A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
These equations have been verified by comparison with multiple numeric models derived completely independently. [2] The equations show that the bicycle is like an inverted pendulum with the lateral position of its support controlled by terms representing roll acceleration, roll velocity and roll displacement to steering torque feedback.
Full state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in predetermined locations in the s-plane. [1]
English: Plots illustrating the behaviour of an inverted pendulum mounted on an oscillatory base. The first plot shows the response of the pendulum on a slow oscillation ( ω = 10 {\displaystyle \omega =10} ), the second the response on a fast oscillation ( ω = 200 {\displaystyle \omega =200} ).
A double inverted pendulum is the combination of the inverted pendulum and the double pendulum. The double inverted pendulum is unstable, meaning that it will fall down unless it is controlled in some way. The two main methods of controlling a double inverted pendulum are moving the base, as with the inverted pendulum, or by applying a torque ...
Spherical pendulum: angles and velocities. In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass m moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.
Sometimes the model is built directly starting from known physical equations, for example, in the case of a mass-spring-damper system we know that ¨ = ˙ (). Even assuming that a "complete" model is used in designing the controller, all the parameters included in these equations (called "nominal parameters") are never known with absolute ...