Hysteresis

Hysteresis, and hysteresis (Greek hysteros " afterwards, later " ), characterizes a - relative to the input size - variant delayed behavior of an output variable. Generally speaking, it is a system behavior, in which the output does not depend only on the independent variable input, but also on the previous state of the output variable. The system can therefore - depending on the previous history - take the same input one of several possible states.

This behavior is typical for either material ( ferromagnetism ) or, for example, is impressed with the two-position controller or the three-position controller. The system shows path dependence.

Hysteresis occurs in many natural and technical processes and control processes and is thus an essential concept of control theory and cybernetics. The term hysteresis was coined by Sir James Alfred Ewing.

• 2.1 Two -point controller
• 2.2 Hard and soft hysteresis curve

Hysteresis effects

Technology

• Hysteresis ferromagnet: The magnetization of a ferromagnet is dependent not only of the externally applied field strength, but also of the time cycle of the magnetization curve. This Hysteresevorgang can be well illustrated by the history of the hysteresis curve or hysteresis loop. A complete traversing the hysteresis curve is called hysteresis.
• Hysteresis in pulp
• Materials Technology: The elastic-plastic deformation behavior of a material is subject to hysteresis. Upon application in the stress-strain diagram is obtained, a hysteresis loop.
• Cybernetics and Control Engineering: Two point controller possess inherent in a hysteresis behavior.
• Logic circuits / interfaces: Schmitt triggers are threshold switch and generate slowly running processes exact logic signals
• Measurement: the hysteresis of indicating instruments is also called hysteresis. It is due to mechanical inaccuracies such as game and or friction, for example, in supporting the gauges ago.
• Hysteresis layer arrangements: a servo motor, for example, works as a mechanical actuator to control circuits, such as the rudder of an aircraft. It generates and then holds a certain opening angle, and controls to also against external forces ( such as turbulence ) by target -actual comparison. To avoid control oscillations due to mechanical play ( permanent, alternating countermeasures smallest deviations, flutter), a hysteresis loop is necessary. For this purpose, depending constructed or programmed by the accuracy of the actual sensors and of the mechanical precision, a delayed reaction to a desired deviation.
• Hysteresis in pacemaker controls: pacemakers have a hysteresis- response. Typically, a certain lower rate ( " required frequency " ) is programmed, for example, 60 beats per minute. The pacemaker normally engages when the pulse rate of the patient drops below the required rate and stimulates the heart muscle with 60 pulses per minute. If you program the other hand, the hysteresis, the pacemaker only jumps at a lower frequency ( min-1, for example, 50), but then stimulated with the intervention frequency (eg, 60 min -1).
• Rheology: The flow behavior of non-Newtonian thixotropic fluids is also spoken by hysteresis. It is the change in viscosity, i.e., the reduction in the toughness of such fluid under the influence of a constant shear rate, depending on the length of exposure. With increase in the length of exposure by the shearing of the hysteresis effect is increasingly irreversible.

Physics recognizes three forms of damping, that is, three different processes that can occur in the material and lead to the formation of a loop loss. Creep leads to relaxation processes, which one of these three forms form ( Relaxationsdämpfung ). Characteristic of such processes is the independence of the attenuation of the amplitude, and the function of the frequency of the input signal. Both ends of the frequency interval, the attenuation is zero. The same applies to the resonance damping. It differs from the Relaxationsdämpfung in that the resonance frequency of the dynamic modulus is smaller than for all other frequencies. In contrast, attenuation and modulus are frequency independent in the hysteresis, but generally involves. amplitude- dependent.

• Marine: Here, hysteresis phenomenon that a yaw movement continues unchanged for the case of a change of the rudder deflection, and rudder angle before it follows the rudder.
• In liquid crystals run phase changes in the form of a hysteresis curve.
• Ferroelectrics have an analog electrical hysteresis behavior of magnetic hysteresis
• In mobile communications process between the two base stations is also used a hysteresis in the hand-off. The special feature here is that the hysteresis is assigned a value: a mobile user should switch the base station when the broadcast signal of the current base station is worse than -55 dBm, with a hysteresis of 5 dB. This means that the subscriber to change only the base stations which are at least -50 dBm or better reception.
• Soil Physics: When saturation and drainage of soils, the relationship between pore water pressure (suction ) and degree of saturation (or water content) is hysteretic. This can be adjusted to a water content of different soil water tension and vice versa. In many cases the water content is higher than for the wetting process when a drainage operation at the same suction pressure. An explanation is provided by the pore structure of natural soils with their wide pore size distribution. The drainage operation can be large pores, which are surrounded by smaller, only drained when the suction is able to dewater the small pore. Conversely, large pores prevent wetting of adjacent smaller pores until the suction pressure is reached that can wet the large pores. According to this model, hysteresis seems to occur mainly in sandy soil, while in clay, no significant effect was found.

Economics

In economics, as in economics, called hysteresis about the reaction of the market to external influences, a (price) system does not return to its original state when it decays.

Mathematics

In dynamic systems, the hysteresis refers to a phenomenon of backward bifurcation.

Physiology

In physiology is a hysteresis, inter alia, to find in the rest stretching curve of the lung. This refers to the fact that the volume of the lungs decreases more slowly with a decrease in intrapulmonary pressure when it has increased in a pressure increase.

The reason for this can be seen in the reorganization of the molecules of the surfactant factor during the respiratory cycle.

Thermal hysteresis proteins (THP ) result in animals, such as fish to a cryoprotectant. When reinforced THP are present in the body fluid, there is a thermal hysteresis in the formation of ice. The body fluid freezes, for example, at -5 ° C, thawed but only at 0 ° C again. This is not done by increasing the molar concentration in the extracellular fluid, but by the fact that the binding of THP on the ice crystals prevents further formation of ice.

Hydrology

During the flood event of a river at the same water level, the flow and the average flow velocity is different depending on whether the flood wave just coming or going. At the rising of the water level increases the water level gradient, so that the slope force, the mean flow velocity and hence the flow rate. At the expiration of the flood wave on the other hand reduces this gradient, so flow rate and flow decrease accordingly. The higher and shorter the flood wave, the more marked the noticeable hysteresis.

Examples to explain

Two-point controller

The two-position controller is a typical example. In the graph, the origin ( an input variable ) is usually applied on a horizontal axis, the effect of ( output ) on the vertical axis.

As an example, the unfolding of the rear spoiler is used in a car: This " damper " is to be run at low speed and extended above 80 km / h to increase the force of the rear wheels. If the car is traveling in a column whose speed constantly fluctuates between 78 km / h and 83 km / h and the constant extension and retraction would take the spoiler mechanism unnecessary. This is avoided by a hysteresis- switching behavior. The picture to the cause - the speed - plotted on the horizontal axis and set the two switching points for the two-point controller:

• Above 80 km / h, extended upper line on the hysteresis curve.
• Below 60 km / h retracted, lower line on the hysteresis curve.

On the vertical axis of the associated spoiler position is marked.

The condition of the rear spoiler at the switching points lying between the speeds can be read on the vertical axis and depends on the speed from prehistory, that is the direction from which the picture shows the speed on the hysteresis curve tapers:

• Was the car before faster, he stays extended until the car slower than 60 km / h.
• Was the car before slower, he remains retracted until the car faster than 80 km / h.

Hard and soft hysteresis curve

The hard and soft hysteresis is explained in the following on magnetism. The three images show the hysteresis curves of a permanent magnet with hard hysteresis curve, which has a high coercivity and high remanence and transformer iron cores (see also: dynamo sheet ) that hold and soft a small coercivity and different strong inclinations, magnetic shear, and remanences and hard hysteresis curves representing, however, in contrast to a permanent magnetic material having a small coercive force.

A single white district of a ferromagnetic substance having a steep, nearly in the middle vertically extending, hard hysteresis bistable behavior - an effect which was used in the early years of the computer technology, for storing bits in a core memory. In ferromagnetism in a rectangular die-cut sheet metal transformer between these white areas are indeed in the rolling direction of the output sheet, but for example, in an M- cut in only two legs low to the magnetic field direction. However, since the magnetic flux must also run through leg, in which the orientation of Weis ' domains is not in magnetic flux direction and therefore have a sloping curve, there are a total of millions of " switches " ( white areas ) used to be in their orientation magnetic field direction are different. The sum of all these almost vertical and inclined hysteresis curves is the "soft" and inclined hysteresis curve in the image in the center right. In a toroidal transformer, however, the orientation of all white between districts is by rolling in the direction of magnetic flux, which is a steep runs, hard (total) hysteresis curve results. The Ummagnetisierungsenergie here is the smallest, which corresponds to the smallest area within the hysteresis curve. Therefore One then speaks of hard cores with a rectangular hysteresis curve steep runs, but also how the turnout curve, just before the core saturation with a bow, in which turns almost horizontal. There are - depending on the number of magnetic flux in the direction oriented, white between districts in relation to the transverse thereto, - special phenomena:

• Only when the piece of iron was demagnetized, the starting point is at A. The blue curve segment from A through B to C is also called " virgin " curve or " virgin curve ".
• One can use an electromagnet to magnetize to a point B in one direction and then - proceed to the red curve up to the point M - by reversing the polarity of the electromagnet. Then only a few white districts were changed in their orientation. The vertical distance to the horizontal axis, indicates how many areas were affected. It says something about the flux density.
• You can also go from A to C or to D or to E - that depends on how strong the electromagnet. Between C and E all - white districts are oriented parallel, then one speaks of saturation. A further increase of the coil current only increases marginally the magnetic flux in the iron.
• When the electromagnet is switched off, it can return to F. F Whether just as high as C or a little or even much lower, depending on the remanence. This depends on the design, including the (residual ) air gap.
• If the polarity of the electromagnets around and slowly increased the voltage-time area, we managed to point G. The iron piece has been demagnetized, as long as the opposing field is applied. For this purpose, the coercivity of the core had to be overcome in the electromagnet. After turning the opposite field, the magnetization as an elastic spring is running again to zero A man only gets the previous value F. when the modulation of the hysteresis curve in small steps or continuously, reduced by an ever umpolendes and smaller and smaller counter-field ( demagnetization ).