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 at the pivot point between the two pendulums. [1]
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger.
In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.
An inertia wheel pendulum is a pendulum with an inertia wheel attached. It can be used as a pedagogical problem in control theory. This type of pendulum is often confused with the gyroscopic effect, which has completely different physical nature.
The Furuta pendulum, or rotational inverted pendulum, consists of a driven arm which rotates in the horizontal plane and a pendulum attached to that arm which is free to rotate in the vertical plane. It was invented in 1992 at Tokyo Institute of Technology by Katsuhisa Furuta and his colleagues. It is an example of a complex nonlinear oscillator of interest in control system theory. The pendulum is underactuated and extremely non-linear due to the gravitational forces and the coupling arising from the Coriolis and centripetal forces. Since then, dozens, possibly hundreds of papers and theses have used the system to demonstrate linear and non-linear control laws. The system has also been the subject of two texts.
A tuned mass damper (TMD), also known as a harmonic absorber or seismic damper, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure. They are frequently used in power transmission, automobiles, and buildings.
Walking is one of the main gaits of locomotion among legged animals. Walking is typically slower than running and other gaits. Walking is defined by an 'inverted pendulum' gait in which the body vaults over the stiff limb or limbs with each step. This applies regardless of the unusable number of limbs—even arthropods, with six, eight, or more limbs, walk.
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
An electric unicycle is a self-balancing personal transporter with a single wheel. The rider controls the speed by leaning forwards or backwards, and steers by twisting the unit using their feet. The self-balancing mechanism uses gyroscopes and accelerometers in a similar way to that used by the Segway PT.
A power inverter, or inverter, is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC).
Active noise control (ANC), also known as noise cancellation, or active noise reduction (ANR), is a method for reducing unwanted sound by the addition of a second sound specifically designed to cancel the first.
A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.
An escapement is a mechanical linkage in mechanical watches and clocks that gives impulses to the timekeeping element and periodically releases the gear train to move forward, advancing the clock's hands. The impulse action transfers energy to the clock's timekeeping element to replace the energy lost to friction during its cycle and keep the timekeeper oscillating. The escapement is driven by force from a coiled spring or a suspended weight, transmitted through the timepiece's gear train. Each swing of the pendulum or balance wheel releases a tooth of the escapement's escape wheel, allowing the clock's gear train to advance or "escape" by a fixed amount. This regular periodic advancement moves the clock's hands forward at a steady rate. At the same time the tooth gives the timekeeping element a push, before another tooth catches on the escapement's pallet, returning the escapement to its "locked" state. The sudden stopping of the escapement's tooth is what generates the characteristic "ticking" sound heard in operating mechanical clocks and watches. The first mechanical escapement, the verge escapement, was invented in medieval Europe during the 13th century, and was the crucial innovation which lead to the development of the mechanical clock. The design of the escapement has a large effect on a timepiece's accuracy, and improvements in escapement design drove improvements in time measurement during the era of mechanical timekeeping from the 13th through the 19th century.
In physics, complex harmonic motion is a complicated realm based on the simple harmonic motion. The word "complex" refers to different situations. Unlike simple harmonic motion, which is regardless of air resistance, friction, etc., complex harmonic motion often has additional forces to dissipate the initial energy and lessen the speed and amplitude of an oscillation until the energy of the system is totally drained and the system comes to rest at its equilibrium point.
Power electronics is the application of solid-state electronics to the control and conversion of electric power.
A derrick is a lifting device composed at minimum of one guyed mast, as in a gin pole, which may be articulated over a load by adjusting its guys. Most derricks have at least two components, either a guyed mast or self-supporting tower, and a boom hinged at its base to provide articulation, as in a stiffleg derrick.
The term unicycle is often used in robotics and control theory to mean a generalised cart or car moving in a two-dimensional world; these are also often called "unicycle-like" or "unicycle-type" vehicles. This usage is distinct from the literal sense of "one wheeled robot bicycle".
A Ranger is an inverting pendulum ride first manufactured by HUSS Machinenfabrik in 1981. Many of the design elements were later used in the HUSS Rainbow, and the term 'Ranger' has become synonymous with inverting pendulum rides. It was the first inverting swing ride designed since Lee Eyerly's Loop-O-Plane and set the standard for many other attractions using the inverting pendulum ride system, such as the Rainbow, the Kamikaze (ride), and the Inverter.
Pendulum rides are amusement rides based on the motion of a fixed pendulum. The configuration of the ride consists of a gondola, arm, and an axle. One end of the arm is fitted with a passenger-carrying gondola, while the other is attached to the axle. On some models, the arm extends beyond the axle and is fitted with a heavy counterweight. The counterweight is often used when the gondola swings through an inversion. In addition to swinging back and forth, some designs incorporate rotating gondolas and may send riders through a complete inversion. Pendulum rides are propelled by one of two methods: a series of DC motors driving the axle, or wheels at the base of the station pushing the gondola as it swings by.
Standing, also referred to as orthostasis, is a human position in which the body is held in an upright ("orthostatic") position and supported only by the feet. Although seemingly static, the body rocks slightly back and forth from the ankle in the sagittal plane. The sagittal plane bisects the body into right and left sides. The sway of quiet standing is often likened to the motion of an inverted pendulum.
The El Cajón Dam, officially known as Central Hidroeléctrica Francisco Morazán, is a hydroelectric power plant located in Western Honduras. The dam impounds the Comayagua River, which derives its large volume from two large tributaries, the Humuya River and the Sulaco River. El Cajón is a double arch dam, which uses parabolic geometry in horizontal and vertical axises to spread the weight of the impounded water to canyon walls which act as buttresses. Overall, the dam is the fifth highest dam in the Americas and the 16th highest in the world, as well as the highest arch dam in the western hemisphere, and the sixth highest worldwide.
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