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Topic: Inverted pendulum

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	SEISMOMETER - LoveToKnow Article on SEISMOMETER (Site not responding. Last check: 2007-11-02)
		Very long pendulums (30 to 40 ft.) are less subject to this disadvantage, but on the other hand their installation is a matter of some.,~.
		With pendulums of shorter length say 2 metres, it is necessary to have a multiplication 8o to 100 fold by a double system of very light levers, in order to render the extremely slight tilting of their support perceptible.
		The movements of the apparatus, which when complete should consist of two similar pendulums in planes at right angles to each other, are recorded by means of a beam of light, which, after reflection from the mirror or mirrors, passes through a cylindrical lens and is focussed upon a moving surface of photographic paper.
	71.1911encyclopedia.org /S/SE/SEISMOMETER.htm (2719 words)

	zia >> portfolio >> inverted pendulum (Site not responding. Last check: 2007-11-02)
		Stabilizing the inverted pendulum is the classic controls problem, introduced in the first week of each of the controls and dynamics classes I have taken (2.003, 2.004, 2.010 and 2.151).
		My first work on the inverted pendulum problem was for my undergraduate thesis: "Stabilizing an Inverted Pendulum with its base rotating around a horizontal axis." I extended the classic problem to handle a case where the pendulum base no longer moves in a line.
		The integration of the actual pendulum with the 2.010 lab was unfortunately doomed to failure for many reasons, including a large dead-zone in the drive motor, noisy position and velocity measurements from the existing sensors and a noisy differentiation of the pendulum angle measurement.
	www.mit.edu /people/zcs/portfolio/ip.html (456 words)

	Inverted pendulum -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-02)
		The inverted pendulum is a widely used benchmark for testing control algorithms ((additional info and facts about PID controller) PID controller, (Any network of neurons or nuclei that function together to perform some function in the body) neural networks, (additional info and facts about Genetic algorithm) Genetic algorithms, etc).
		In practice, the inverted pendulum is frequently made of an aluminium strip, mounted on a ball-bearing pivot; the oscillatory force is conveniently applied with a (Fine-toothed power saw with a narrow blade; used to cut curved outlines) jigsaw.
		If the driving point moves in (Periodic motion in which the restoring force is proportional to the displacement) simple harmonic motion, the pendulum's motion is described by the Mathieu equation.
	www.absoluteastronomy.com /encyclopedia/i/in/inverted_pendulum.htm (229 words)

	Inverted Pendulum Balancing Robot
		This problem of balancing an inverted pendulum is of the delicate control subset of problems in the greater field of robotics: it is almost purely mechanical, precluding the need for higher-level planning or behavioral programming that a more complex robot might require.
		This inverted pendulum problem, and more generally the problem of delicate control, is not nearly as broad in scope as that of achieving AI, but is still, in a sense, a relevant and necessary problem to solve.
		Theta is the angle between the pendulum and the horizontal axis, g is the acceleration due to gravity, a is dv/dt, the acceleration of the cart, and L is the length of the pendulum.
	www.cs.hmc.edu /~dodds/projects/RobS03/Mapping/oldindex.html (2399 words)

	Inverted Pendulum
		The pendulum consists of two plastic-coated metal rods mounted with epoxy in a plywood base.
		The coil surrounding the upper pair senses motion of the pendulum.
		I think this could be because the design had a flexible vertical rod rather than a stiff rod with a spring at its base, as in the Colorado School of Mines SENS design.
	www.jclahr.com /science/psn/inverted (322 words)

	CTM Example: Inverted Pendulum Modeling
		The C matrix is 2 by 4, because both the cart's position and the pendulum's position are part of the output.
		The pendulum can be stabilized in an inverted position if the x position is constant or if the cart moves at a constant velocity (no acceleration).
		We emphasize that the purpose of these examples is to demonstrate design and analysis techniques using Matlab; not to actually control an inverted pendulum.
	www.engin.umich.edu /group/ctm/examples/pend/invpen.html (1052 words)

	Java Inverted Pendulum (Site not responding. Last check: 2007-11-02)
		Java Inverted Pendulum was created as a semester project at the University of Zurich in winter 1999.
		The inverted pendulum is classic two-dimensional control problem with the goal to keep a pole vertically balanced.
		Read the documentation to learn about the ideas behind Java Inverted Pendulum, the architecture of the program and the AI techniques that were used.
	homepage.sunrise.ch /mysunrise/jmrodriguez/JInvPendulum (417 words)

	Inverted Pendulum
		While holding the pendulum in the inverted position, the saw is switched on and brought up to speed until the pendulum becomes stable.
		The pivot is pulled down..., etc. Thus the amplitude, frequency, and phase (relative to the pendulum's free motion) of the pivot's vibration all conspire to stabilize the pendulum and keep it near the vertical position.
		Since the pendulum moves with speeds of a few m/sec, it should be directed away from the audience and the operator ought to wear safety goggles as a precaution (the pendulum is press-fit onto the bearing and you can never tell when disaster will strike).
	www.fas.harvard.edu /~scdiroff/lds/OscillationsWaves/InvertedPendulum/InvertedPendulum.html (628 words)

	Inverted Pendulum (Site not responding. Last check: 2007-11-02)
		The rotating inverted double pendulum is (also) an excellent test bed for nonlinear control theory.
		A simple pendulum, made of a rod and a disk at one end, can be made to oscillate in an inverted position on its pivot oscillating at the proper frequency and amplitude.
		Below is a demonstration of an one-stage Inverted Pendulum controlled by a Fuzzy Java Controller generated by...
	www.laboratoryequipment-net.info /laboratory-equipment/inverted-pendulum.html (466 words)

	CTM Example: State-space design for the inverted pendulum
		As you may have noticed if you went through some of the other inverted pendulum examples the design criteria for this example are different.
		However, for an inverted pendulum it is unrealistic to consider just the single output system.
		We are using both outputs (the angle of the pendulum and the position of the cart) to design the observer.
	www.engin.umich.edu /group/ctm/examples/pend/invSS.html (1642 words)

	Double Inverted Pendulum
		This system has two free moving inverted pendulums of different lengths (0.3 m and 0.08 m).
		They are mounted on are cart that is driven by a 24 V motor on the end of the track via a pulley and nylon wire.
		I was able to get it to balance with both of the pendulums (movie), however if I wanted to use the position controller (a knob that you could turn and it would change where the carriage centered itself) it would only work intermittently.
	people.wwc.edu /student/barnsa/projects/dip.htm (534 words)

	Controlling an Inverted Pendulum. An Example of a Digital Feedback Control System. (Site not responding. Last check: 2007-11-02)
		A free swinging pendulum is inverted so the hinge is at the bottom.
		The challenge is to move the bottom of the pendulum back and forth to keep the pendulum from falling over.
		This paper derives all the characteristic equations of motion for an inverted pendulum, all the transfer functions, Bode plots, state space representations, and concludes with an example of controlling a real setup.
	members.cox.net /srice1/pendulum/synopsis.htm (193 words)

	Fuzzy Pendulum Demonstration (Site not responding. Last check: 2007-11-02)
		This is a demonstration of fuzzy logic control using a stationary inverted pendulum with a variable mass on the top of the pendulum and a variable strength motor on the bottom that will try to balance the pendulum.
		In the initial state of operation all of the rules are enabled, a yellow bopper rod will appear from the left and knock the mass to the right whenever the pendulum is balanced (within certain tolerances) and the mass will not be bobbing up and down.
		The cyan colored ball at the bottom of the pendulum is a motor which, when given current, drives the pendulum one way or the other.
	www.iit.nrc.ca /IR_public/fuzzy/FuzzyPendulum.html (1135 words)

	The rotating inverted pendulum (Site not responding. Last check: 2007-11-02)
		The rotating inverted pendulum is a excellent test bed for nonlinear control theory.
		It is similar to the classic inverted pendulum control experiment, in that we seek a feedback control law that balances Link 2 in its unstable, inverted position.
		This means that the nonlinear controller can move the inverted pendulum (turn Link 1) to a new position faster than a linear controller, as the plots below show.
	www.control.toronto.edu /~bortoff/pendulum.html (241 words)

	ROTATIONAL INVERTED PENDULUM (Site not responding. Last check: 2007-11-02)
		The rotational inverted pendulum is a nonlinear plant that is commonly found in university control laboratories (often, however, it is of the cart-pole variety on a track).
		The inverted pendulum system utilizes two optical encoders to measure the angular position of both joints at each sampling instant.
		The inverted pendulum system allows the user to change the system parameters, or add disturbances, by attaching containers of various size and contents to the end of the pendulum (e.g., in labs on adaptive control a container of bolts or water is added to the end of the pendulum as a disturbance).
	www.ece.osu.edu /~passino/rip.html (322 words)

	Two Stage Inverted Pendulum
		The inner loop is for controlling the first stage pendulum; the outer loop is for controlling the second stage.
		In other words, in a two stage inverted pendulum system, the purpose of the outer loop is to produce an angle for the first stage to follow.
		Control engineers are aware of the difficulty in designing a controller for a two-stage inverted pendulum using conventional approaches.
	www.aptronix.com /fuzzynet/applnote/twostage.htm (1138 words)

	CTMS Example: Frequency Response Control of the Inverted Pendulum Model
		Pendulum should not move more than 0.05 radians away from the vertical.
		To see how this problem was originally set up, consult the inverted pendulum modeling page.
		We will now design an inverted pendulum controller for an impulse force using Nyquist diagrams (we cannot use Bode plots because the system is unstable in open loop).
	www.library.cmu.edu /ctms/ctms/examples/pend/invfr.htm (1255 words)

	Biomechanics of quadrupedal walking: how do four-legged animals achieve inverted pendulum-like movements? -- Griffin et ...
		Inverted pendulum mechanics of the center of mass for dogs walking at a range of speeds.
		is the ratio of fore pendulum mass to the combined mass of both pendulums (equivalent to the fraction of body weight supported by the fore limbs).
		A represents the pendulum phase and mass distribution combination actually used by the dogs, and D represents the phase and mass distribution shown in the hypothetical diagram of Fig.
	jeb.biologists.org /cgi/content/full/207/20/3545 (7199 words)

	Inverted pendulum experiment
		The inverted pendulum is now added to the positioned 'trolley' and the sensor for tilt angle is investigated, together with its interface.
		As a result, when the top of the pendulum is slowly moved from side to side the trolley moves to cause the pendulum to lean 'inwards'.
		One explanation is that by accelerating the trolley to the right, we cause the pendulum to lean to the left which in turn will result in the trolley being moved to the left.
	www.usq.edu.au /course/material/eng3905/MPLAB3.htm (2204 words)

	The Inverted Pendulum: A Singularity Theory Approach - Broer, Hoveijn, Noort, Vegter (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		Abstract: The inverted pendulum with small parametric forcing is considered as an example of a wider class of parametrically forced Hamiltonian systems.
		3 A reversible bifurcation analysis of the inverted pendulum (context) - Broer, Hoveijn et al.
		1 Stability of the inverted pendulum --- a topological explana..
	citeseer.ist.psu.edu /broer98inverted.html (647 words)

	Inverted Pendulum with Delayed Feedback (Site not responding. Last check: 2007-11-02)
		The experiment involves balancing an pendulum in the inverted (upright position), by moving the base of pendulum according to a prescribed control law.
		When the system is disturbed, the pendulum oscillates, but the oscillations eventually die down and the pendulum returns to the vertical position.
		The inverted position is no longer stable and the pendulum oscillates with constant amplitude.
	www.math.uwaterloo.ca /~sacampbe/invpend.html (218 words)

	Educational Control Products - Control Systems - Inverted Pendulum Accessory
		ur inverted pendulum accessory is a cost effective way to enhance your laboratory's capability.
		Our ECP Inverted pendulum (Model 505) is a stand-alone system with unique dynamic characteristics (right half plane zeros and poles).
		The Pendulum Accessory (A51) described on this page is based on the classical inverted pendulum model and adds on to other stand-alone ECP systems using their actuators, base feedback, and electronics.
	www.ecpsystems.com /controls_pendassc.htm (310 words)

	Microrobot NA - Inverted Pendulum (Site not responding. Last check: 2007-11-02)
		However, it is limited in that it only moves in one dimension, while your hand could move up, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pendulum works.
		Just like the broom-stick, an Inverted Pendulum is an inherently unstable system.
		The Inverted Pendulum is essential in the evaluating and comparing of various control theories.
	www.microrobotna.com /pendulum.htm (135 words)

	simple inverted pendulum problem/ optimal control
		If it blows up starting at small angles, there must be at ==least one in the right half of the s plane.
		= = = of course it's unstable, it's an inverted pendulum.
		of course it's unstable, it's an inverted pendulum.
	www.ee-one.com /new-5817801-4307.html (2135 words)

	Control of An Inverted Pendulum With the Help Of
		A fuzzy controller, a conventional variable structure controller, and a region-wise affine fuzzy controller are compared for the control of an inverted pendulum.
		The system to be controlled is the classical inverted pendulum system described in Figure 1 [10].
		The performance and interests of the control was shown through the control of an inverted pendulum and compared to variable structure control and fuzzy control.
	www.ici.ro /ici/revista/sic2000_1/art05.html (2276 words)

	Fuzzy Controller for an Inverted Pendulum (Site not responding. Last check: 2007-11-02)
		A red ball is attached to the pendulum on top of the roller cart.
		The goal of the controller is to use a motor to keep the pendulum in balance and the roller cart at the center at all times.
		The X and Theta values, displayed on the window, are respectively the cart distance from the center and angle of the pendulum from the vertical direction (both should be close to 0.00).
	www.aptronix.com /fuzzynet/java/pend/pendjava.htm (132 words)

	UIUC RTSL Inverted Pendulum Controller
		We created a demo in which we use camera sensors in complement with potentiometer sensors on the cart to balance an inverted pendulum.
		We were able to successfully control the pendulum and utilize the extra network bandwidth for other real-time communications on the same shared channel using the proposed protocol.
		Control of the inverted pendulum was done using two switchable remote cameras for the cart's position and one potentiometer on the cart for the rod angle.
	pertsserver.cs.uiuc.edu /~mcaccamo/IPC (780 words)

	2.12 Example. A cart and an inverted pendulum
		The problem of balancing a pendulum mounted on a cart is a classic and intriguing problem.
		The cart must be moved using the force u(t) so that the pendulum remains in the upright position and the cart returns to the origin as t
		The differential equations describing the motion of the system may be obtained by writing the sum of forces in the horizontal direction and the sum of the moments about the pivot point.
	www.cs.ut.ee /~toomas_l/linalg/matlabap/control/control12.html (413 words)

	Freeware World Team - Inverted Pendulum
		This program graphically models a difficult-to-believe phenomenon; if you jiggle the pivot of an upside-down pendulum up and down fast enough, the pendulum remains upside-down.
		It may be impossible to spot a regular pattern from the actual motion - a Limit Cycle for instance.
		There is no Limit Cycle for the Inverted Pendulum, but the parameters are confined to defined values for the entire duration of the motion.
	www.all4you.dk /FreewareWorld/Inverted_Pendulum-25328.html (193 words)

	B442 Inverted Pendulum
		for the inverted pendulum has been implemented on a Xilinx XC4003E prototype board.
		The print head was stripped from the carriage and replaced by a bearing mounted rod (wooden arrow shaft).
		There is also a small hole drilled in the metal disk that is sensed with an infrared sensor.
	www.cs.indiana.edu /csg/hardware/B442_inv_pend/picts.html (169 words)

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