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Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a furnace that is either completely on or completely off. Most common residential thermostats are bang–bang controllers. The Heaviside step function in its discrete form is an example of a bang–bang control signal. Due to the discontinuous control signal, systems that include bang–bang controllers are variable structure systems, and bang–bang controllers are thus variable structure controllers.
In optimal control problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches from one extreme to the other (i.e., is strictly never in between the bounds), then that control is referred to as a bang–bang solution.
Bang–bang controls frequently arise in minimum-time problems. For example, if it is desired for a car starting at rest to arrive at a certain position ahead of the car in the shortest possible time, the solution is to apply maximum acceleration until the unique switching point, and then apply maximum braking to come to rest exactly at the desired position.
A familiar everyday example is bringing water to a boil in the shortest time, which is achieved by applying full heat, then turning it off when the water reaches a boil. A closed-loop household example is most thermostats, wherein the heating element or air conditioning compressor is either running or not, depending upon whether the measured temperature is above or below the setpoint.
Bang–bang solutions also arise when the Hamiltonian is linear in the control variable; application of Pontryagin's minimum or maximum principle will then lead to pushing the control to its upper or lower bound depending on the sign of the coefficient of u in the Hamiltonian.[1]
In summary, bang–bang controls are actually optimal controls in some cases, although they are also often implemented because of simplicity or convenience.
Mathematically or within a computing context there may be no problems, but the physical realization of bang–bang control systems gives rise to several complications.
First, depending on the width of the hysteresis gap and inertia in the process, there will be an oscillating error signal around the desired set point value (e.g., temperature), often saw-tooth shaped. Room temperature may become uncomfortable just before the next switch 'ON' event. Alternatively, a narrow hysteresis gap will lead to frequent on/off switching, which is often undesirable (e.g. an electrically ignited gas heater).
Second, the onset of the step function may entail, for example, a high electrical current and/or sudden heating and expansion of metal vessels, ultimately leading to metal fatigue or other wear-and-tear effects. Where possible, continuous control, such as in PID control, will avoid problems caused by the brisk state transitions that are the consequence of bang–bang control.
{{cite book}}: ISBN / Date incompatibility (help)Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a furnace that is either completely on or completely off. Most common residential thermostats are bang–bang controllers. The Heaviside step function in its discrete form is an example of a bang–bang control signal. Due to the discontinuous control signal, systems that include bang–bang controllers are variable structure systems, and bang–bang controllers are thus variable structure controllers.
The Big Bang is a physical theory that describes how the universe expanded from an early state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, the redshift of galaxies and the large-scale structure of the universe. The observed uniformity of the universe, which leads to the horizon and flatness problems, is explained through cosmic inflation: a phase of accelerated expansion during the earliest stages. Detailed measurements of the expansion rate of the universe place the cosmic inflation at an estimated 13.787±0.02 billion years ago, which is considered the age of the universe. A wide range of empirical evidence strongly favors the Big Bang model, which is now widely accepted. Extrapolating this cosmic expansion backward in time using the known laws of physics, the models describe an extraordinarily hot and dense primordial universe. The original Big Bang model extrapolated the universe back towards a Big Bang singularity. However, the modern view incorporates inflationary cosmology, whereby the universe emerged out of inflation in a supercooled state. This was followed by a reheating event that converted the energy that drove inflation into a hot and dense plasma, initiating the hot Big Bang. As the universe expanded, it cooled sufficiently to allow the formation of subatomic particles, and later atoms. These primordial elements—mostly hydrogen, with some helium and lithium—then coalesced under the force of gravity aided by dark matter, forming early stars and galaxies. Measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to a concept called dark energy. The concept of an expanding universe was introduced by the physicist Alexander Friedmann in 1922 with the mathematical derivation of the Friedmann equations. The earliest empirical observation of an expanding universe is known as Hubble's law, published in work by physicist Edwin Hubble in 1929, which discerned that galaxies are moving away from Earth at a rate that accelerates proportionally with distance. Independent of Friedmann's work, and independent of Hubble's observations, in 1931 physicist Georges Lemaître proposed that the universe emerged from a "primeval atom", introducing the modern notion of the Big Bang. In 1964, the CMB was accidentally discovered. Over the next few years measurements showed this radiation to be uniform over directions in the sky and the shape of the energy versus intensity curve, both consistent with the Big Bang models of high temperatures and densities in the distant past. By the late 1960s most cosmologists were convinced that the competing steady-state model of cosmic evolution was incorrect. There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. These include the unequal abundances of matter and antimatter known as baryon asymmetry, the detailed nature of dark matter surrounding galaxies, and the origin of dark energy.
In physical cosmology, Big Bang nucleosynthesis (also known as primordial nucleosynthesis, and abbreviated as BBN) is a model for the production of light nuclei (including, but not limited to, 2H, 3He, 4He, and 7Li) during the first ~20 minutes of the evolution of the universe. The predictions of BBN rely on a combination of thermodynamic arguments and measurements of rates of nuclear reactions that are expected to be active in the early universe. Refined models tend to agree well with observations of these light element abundances. The model is one of the key concepts in standard cosmology. Elements heavier than lithium are instead created in appreciable amounts at later times via stellar nucleosynthesis, through the formation, evolution and death of stars.
Chitty Chitty Bang Bang is the vintage racing car which is featured in the book, musical film and stage production of the same name. Writer Ian Fleming took his inspiration for the car from a series of aero-engined racing cars built by Count Louis Zborowski in the early 1920s, christened Chitty Bang Bang. The original Chitty Bang Bang's engine was from a Zeppelin dirigible. The name reputedly derived either from the sound it made whilst idling, or from a bawdy song from World War I. Six versions of the car were built for the film and several replicas have subsequently been produced. The version built for the stage production holds the record for the most expensive stage prop ever used.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.