state observer

In control theory, a state observer is a system that models a real system in order to provide an estimate of its internal state, given measurements of the input and output of the real system. It is typically a computer-implemented mathematical model.
Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback. In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable, it is possible to fully reconstruct the system state from its output measurements using the state observer.

Typical observer model

The state of a physical discrete-time system is assumed to satisfy

where, at time k, is the plant's state; is its inputs; and is its outputs. These equations simply say that the plant's current outputs and its future state are both determined solely by its current state and the current inputs. (Although these equations are expressed in terms of discrete time steps, very similar equations hold for continuous systems). If this system is observable then the output of the plant, , can be used to steer the state of the state observer.
The observer model of the physical system is then typically derived from the above equations. Additional terms may be included in order to ensure that, on receiving successive measured values of the plant's inputs and outputs, the model's state converges to that of the plant. In particular, the output of the observer may be subtracted from the output of the plant and then multiplied by a matrix L; this is then added to the equations for the state of the observer to produce a so-called Luenberger observer, defined by the equations below. Note that the variables of a state observer are commonly denoted by a "hat": and to distinguish them from the variables of the equations satisfied by the physical system.

The observer is called asymptotically stable if the observer error converges to zero when . For a Luenberger observer, the observer error satisfies . The Luenberger observer for this discrete-time system is therefore asymptotically stable when the matrix A − LC has all the eigenvalues inside the unit circle.
For control purposes the output of the observer system is fed back to the input of both the observer and the plant through the gains matrix K.

The observer equations then become:

or, more simply,

Due to the separation principle we know that we can choose K and L independently without harm to the overall stability of the systems. As a rule of thumb, the poles of the observer A − LC are usually chosen to converge 10 times faster than the poles of the system A − BK.

Continuous-time case

The previous example was for an observer implemented in a discrete-time LTI system. However, the process is similar for the continuous-time case; the observer gains L are chosen to make the continuous-time error dynamics converge to zero asymptotically (i.e., when A − LC is a Hurwitz matrix).
For a continuous-time linear system

,

where , the observer looks similar to discrete-time case described above:

.

The observer error satisfies the equation

.

The eigenvalues of the matix A − LC can be made arbitrary by appropriate choice of the observer gain L when the pair [A,C] is observable, i.e. observability condition holds. In particular, it can be made Hurwitz, so the observer error when .

Peaking and other observer methods

When the observer gain L is high, the linear Luenberger observer converges to the system states very quickly. However, high observer gain leads to a peaking phenomenon in which initial estimator error can be prohibitively large (i.e., impractical or unsafe to use).^[1] As a consequence, nonlinear high gain observer methods are available that converge quickly without the peaking phenomenon. For example, sliding mode control can be used to design an observer that brings one estimated state's error to zero in finite time even in the presence of measurement error; the other states have error that behaves similarly to the error in a Luenberger observer after peaking has subsided. Sliding mode observers also have attractive noise resilience properties that are similar to a Kalman filter.^[2][3]

State observers for nonlinear systems

Sliding mode observers can be designed for the non-linear systems as well. For simplicity, first consider the no-input non-linear system:

where . Also assume that there is a measurable output given by

There are several non-approximate approaches for designing an observer. The two observers given below also apply to the case when the system has an input. That is,

.

Linearizable error dynamics

One suggested by Kerner and Isidori^[4] and Krener and Respondek^[5] can be applied in a situation when there exists a linearizing transformation (i.e., a diffeomorphism, like the one used in feedback linearization) such that in new variables the system equations read

The Luenberger observer is then designed as

.

The observer error for the transformed variable satisfies the same equation as in classical linear case.

.

As shown by Gauthier, Hammouri, and Othman^[6] and Hammouri and Kinnaert,^[7] if there exists transformation such that the system can be transformed into the form

then the observer is designed as

,

where L(t) is a time-varying observer gain.

Sliding mode observer

As discussed for the linear case above, the peaking phenomenon present in Luenberger observers justifies the use of a sliding mode observer. The sliding mode observer uses non-linear high-gain feedback to drive estimated states to a hypersurface where there is no difference between the estimated output and the measured output. The non-linear gain used in the observer is typically implemented with a scaled switching function, like the signum (i.e., sign) of the estimated–measured output error. Hence, due to this high-gain feedback, the vector field of the observer has a crease in it so that observer trajectories slide along a curve where the estimated output matches the measured output exactly. So, if the system is observable from its output, the observer states will all be driven to the actual system states. Additionally, by using the sign of the error to drive the sliding mode observer, the observer trajectories become insensitive to many forms of noise. Hence, some sliding mode observers have attractive properties similar to the Kalman filter but with simpler implementation.^[2][3]
As suggested by Drakunov,^[8] a sliding mode observer can also be designed for a class of non-linear systems. Such an observer can be written in terms of original variable estimate and has the form

where:

• The vector extends the scalar signum function to n dimensions. That is,

for the vector .

• The vector has components that are the output function and its repeated Lie derivatives. In particular,

where is the i^th Lie derivative of output function h along the vector field f (i.e., along trajectories of the non-linear system). In the special case where the system has no input or has a relative degree of n, is a collection of the output and its n − 1 derivatives. Because the inverse of the Jacobian linearization of must exist for this observer to be well defined, the transformation is guaranteed to be a local diffeomorphism.

• The diagonal matrix of gains is such that

where, for each , element and suitably large to ensure reachability of the sliding mode.

• The observer vector V(t) is such that

where here is the normal signum function defined for scalars, and denotes an "equivalent value operator" of a discontinuous function in sliding mode.

The idea can be briefly explained as follows. According to the theory of sliding modes, in order to describe the system behavior, once sliding mode starts, the function should be replaced by equivalent values (see equivalent control in the theory of sliding modes). In practice, it switches (chatters) with high frequency with slow component being equal to the equivalent value. Applying appropriate lowpass filter to get rid of the high frequency component on can obtain the value of the equivalent control, which contains more information about the state of the estimated system. The observer described above uses this method several times to obtain the state of the nonlinear system ideally in finite time.
The modified observation error can be written in the transformed states . In particular,

and so

So:

1. As long as , the first row of the error dynamics, , will meet sufficient conditions to enter the e₁ = 0 sliding mode in finite time.
2. Along the e₁ = 0 surface, the corresponding equivalent control will be equal to , and so . Hence, so long as , the second row of the error dynamics, , will enter the e₂ = 0 sliding mode in finite time.
3. Along the e_i = 0 surface, the corresponding equivalent control will be equal to . Hence, so long as , the (i + 1)^th row of the error dynamics, , will enter the e_{i + 1} = 0 sliding mode in finite time.

So, for sufficiently large m_i gains, all observer estimated states reach the actual states in finite time. In fact, increasing m_i allows for convergence in any desired finite time so long as each function can be bounded with certainty. Hence, the requirement that the map is a diffeomorphism (i.e., that its Jacobian linearization is invertible) asserts that convergence of the estimated output implies convergence of the estimated state. That is, the requirement is an observability condition.
In the case of the sliding mode observer for the system with the input, additional conditions are needed for the observation error to be independent of the input. For example, that

does not depend on time. The observer is then

superfluidity

Superfluidity is a phase of matter or description of heat capacity in which unusual effects are observed when liquids, typically of helium-4 or helium-3, overcome friction by surface interaction when at a stage (known as the "lambda point" for helium-4) at which the liquid's viscosity becomes zero. Also known as a major facet in the study of quantum hydrodynamics, it was discovered by Pyotr Kapitsa, John F. Allen, and Don Misener in 1937 and has been described through phenomenological and microscopic theories. In the 1950s Hall and Vinen performed experiments establishing the existence of quantized vortex lines. In the 1960s, Rayfield and Reif established the existence of quantized vortex rings. Packard has observed the intersection of vortex lines with the free surface of the fluid, and Avenel and Varoquaux have studied the Josephson effect in superfluid ⁴He.

Some theories

L. D. Landau's phenomenological and semi-microscopic theory of superfluidity of ⁴He earned him the Nobel Prize in Physics in 1962. Assuming that sound waves are the most important excitations in ⁴He at low temperatures, he showed that ⁴He flowing past a wall would not spontaneously create excitations if the flow velocity was less than the sound velocity. In this model, the sound velocity is the "critical velocity" above which superfluidity is destroyed.
(⁴He has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.) Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the ⁴He called the "condensate".
From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the ⁴He is no longer superfluid.
To explain the early specific heat data on superfluid ⁴He, Landau posited the existence of a type of excitation he called a "roton", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.
Bijl in the 1940s^[1], and Feynman around 1955 ^[2], developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky.
Landau thought that vorticity entered superfluid ⁴He by vortex sheets, but such sheets were shown to be unstable.
Lars Onsager and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex rings.

Background

Although the phenomenologies of the superfluid states of helium-4 and helium-3 are very similar, the microscopic details of the transitions are very different. Helium-4 atoms are bosons, and their superfluidity can be understood in terms of the Bose statistics that they obey. Specifically, the superfluidity of helium-4 can be regarded as a consequence of Bose-Einstein condensation in an interacting system. On the other hand, helium-3 atoms are fermions, and the superfluid transition in this system is described by a generalization of the BCS theory of superconductivity. In it, Cooper pairing takes place between atoms rather than electrons, and the attractive interaction between them is mediated by spin fluctuations rather than phonons. (See fermion condensate.) A unified description of superconductivity and superfluidity is possible in terms of gauge symmetry breaking.
Superfluids, such as supercooled helium-4, exhibit many unusual properties. (See Helium#Helium II state). Superfluid acts as if it were a mixture of a normal component, with all the properties associated with normal fluid, and a superfluid component. The superfluid component has zero viscosity, zero entropy, and infinite thermal conductivity. (It is thus impossible to set up a temperature gradient in a superfluid, much as it is impossible to set up a voltage difference in a superconductor.) Application of heat to a spot in superfluid helium results in a wave of heat conduction at the relatively high velocity of 20 m/s, called second sound.
One of the most spectacular results of these properties is known as the thermomechanical or "fountain effect". If a capillary tube is placed into a bath of superfluid helium and then heated, even by shining a light on it, the superfluid helium will flow up through the tube and out the top as a result of the Clausius-Clapeyron relation. A second unusual effect is that superfluid helium can form a layer, 30 nm thick, up the sides of any container in which it is placed. See Rollin film.
A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity (the speed of sound in the superfluid) is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized, that is, a superfluid can not spin at certain "allowed" or critical speed values. In simplified terms, if the container is rotated to a certain allowed speed, the superfluid will rotate very quickly along with the container, otherwise, if the speed is too slow, then the superfluid will not move at all, unlike how a normal fluid like water will rotate along with its container from the start. (compare this to the london moment)

Properties

The normal phase of non-zero entropy and superfluid phase of zero entropy coexist. This gives a strange phenomenon of two-fluid model.
A consequence of is that when the two-fluid pass through a capillary, effectively only the superfluid can flow through due to its zero viscosity along the way. This gives a strange situation where we have mass transfer without heat transfer (since there is no entropy transfer)!

Applications

Recently in the field of chemistry, superfluid helium-4 has been successfully used in spectroscopic techniques as a quantum solvent. Referred to as Superfluid Helium Droplet Spectroscopy (SHeDS), it is of great interest in studies of gas molecules, as a single molecule solvated in a superfluid medium allows a molecule to have effective rotational freedom, allowing it to behave exactly as it would in the "gas" phase.
Superfluids are also used in high-precision devices such as gyroscopes, which allow the measurement of some theoretically predicted gravitational effects (for an example see the Gravity Probe B article).
In 1999, one type of superfluid has been used to trap light and slow its speed greatly. In an experiment performed by Lene Hau, light was passed through a Bose-Einstein condensed gas of sodium (analogous to a superfluid) and found to be slowed to 17 m/s (61.2 km/h) from its normal speed of 299,792,458 metres per second in vacuum.^[3] This does not change the absolute value of c, nor is it completely new: any medium other than vacuum, such as water or glass, also slows down the propagation of light to c/n where n is the material's refractive index. The very slow speed of light and high refractive index observed in this particular experiment, moreover, is not a general property of all superfluids.
The Infrared Astronomical Satellite IRAS, launched in January 1983 to gather infrared data was cooled by 720 litres of superfluid helium, maintaining a temperature of 1.6 K (-271.4 ­°C).

switch

In electronics, a switch is an electrical component that can break an electrical circuit, interrupting the current or diverting it from one conductor to another.^[1][2] The most familiar form of switch is a manually operated electromechanical device with one or more sets of electrical contacts. Each set of contacts can be in one of two states: either 'closed' meaning the contacts are touching and electricity can flow between them, or 'open', meaning the contacts are separated and nonconducting.
A switch may be directly manipulated by a human as a control signal to a system, such as a computer keyboard button, or to control power flow in a circuit, such as a light switch. Automatically-operated switches can be used to control the motions of machines, for example, to indicate that a garage door has reached its full open position or that a machine tool is in a position to accept another workpiece. Switches may be operated by process variables such as pressure, temperature, flow, current, voltage, and force, acting as sensors in a process and used to automatically control a system. For example, a thermostat is an automatically-operated switch used to control a heating process. A switch that is operated by another electrical circuit is called a relay. Large switches may be remotely operated by a motor drive mechanism. Some switches are used to isolate electric power from a system, providing a visible point of isolation that can be pad-locked if necessary to prevent accidental operation of a machine during maintenance, or to prevent electric shock.

Three pushbutton switches (Tactile Switches). Major scale is inches.

s

Contacts

A toggle switch in the "on" position.

In the simplest case, a switch has two pieces of metal called contacts that touch to make a circuit, and separate to break the circuit. The contact material is chosen for its resistance to corrosion, because most metals form insulating oxides that would prevent the switch from working. Contact materials are also chosen on the basis of electrical conductivity, hardness (resistance to abrasive wear), mechanical strength, low cost and low toxicity^[3].
Sometimes the contacts are plated with noble metals. They may be designed to wipe against each other to clean off any contamination. Nonmetallic conductors, such as conductive plastic, are sometimes used.

Actuator

The moving part that applies the operating force to the contacts is called the actuator, and may be a toggle or dolly, a rocker, a push-button or any type of mechanical linkage (see photo).

Arcs and quenching

When the wattage being switched is sufficiently large, the electron flow across opening switch contacts is sufficient to ionize the air molecules across the tiny gap between the contacts as the switch is opened, forming a gas plasma, also known as an electric arc. The plasma is of low resistance and is able to sustain power flow, even with the separation distance between the switch contacts steadily increasing. The plasma is also very hot and is capable of eroding the metal surfaces of the switch contacts.
Where the voltage is sufficiently high, an arc can also form as the switch is closed and the contacts approach. If the voltage potential is sufficient to exceed the breakdown voltage of the air separating the contacts, an arc forms which is sustained until the switch closes completely and the switch surfaces make contact.
In either case, the standard method for minimizing arc formation and preventing contact damage is to use a fast-moving switch mechanism, typically using a spring-operated tipping-point mechanism to assure quick motion of switch contacts, regardless of the speed at which the switch control is operated by the user. Movement of the switch control lever applies tension to a spring until a tipping point is reached, and the contacts suddenly snap open or closed as the spring tension is released.
As the power being switched increases, other methods are used to minimize or prevent arc formation. A plasma is hot and will rise due to convection air currents. The arc can be quenched with a series of nonconductive blades spanning the distance between switch contacts, and as the arc rises its length increases as it forms ridges rising into the spaces between the blades, until the arc is too long to stay sustained and is extinguished. A puffer may be used to blow a sudden high velocity burst of gas across the switch contacts, which rapidly extends the length of the arc to extinguish it quickly.
Extremely large switches in excess of 100,000 watts capacity often place the switch contacts in something other than air to increase the resistance against arc formation, such as enclosing the switch contacts in a vacuum, or immersing the switch contacts in mineral oil.

Contact arrangements

Triple Pole Single Throw (TPST or 3PST) knife switch used to short the windings of a 3 phase wind turbine for braking purposes. Here the switch is shown in the open position.

A pair of contacts is said to be "closed" when current can flow one to the other. When the contacts are separated by an insulating air gap, an air space, they are said to be 'open', and no current can flow at typical voltages.
Switches are classified according to the arrangement of their contacts in electronics. Electricians installing building wiring use different nomenclature, such as "one-way", "two-way", "three-way" and "four-way" switches, which have different meanings in North American and British cultural regions as described in the table below.
Some contacts are normally open (Abbreviated "n.o." or "no") until closed by operation of the switch, while others are normally closed ("n.c. or "nc") and opened by the switch action.
A switch with both types of contact is called a changeover switch. These may be "make-before-break" which momentarily connect both circuits, or may be "break-before-make" which interrupts one circuit before closing the other.
The terms pole and throw are also used to describe switch contact variations. A pole is a set of contacts and terminals that are connected to a single circuit. A throw is one of two or more positions that the switch can adopt. A single-throw switch has one position that closes contacts, a double-throw switch has two position, and so on.
These terms give rise to abbreviations for the types of switch which are used in the electronics industry such as "single-pole, single-throw" (SPST) (the simplest type, "on or off") or "single-pole, double-throw" (SPDT), connecting either of two terminals to the common terminal. In electrical power wiring (i.e. House and building wiring by electricians) names generally involving the suffixed word "-way" are used; however, these terms differ between British and American English and the terms two way and three way are used in both with different meanings.

Electronics specification and abbreviation	Expansion of abbreviation	British mains wiring name	American electrical wiring name	Description	Symbol	IEC 60617
SPST	Single pole, single throw	One-way	Two-way	A simple on-off switch: The two terminals are either connected together or not connected to anything. An example is a light switch.
SPDT	Single pole, double throw	Two-way	Three-way	A simple changeover switch: C (COM, Common) is connected to L1 or to L2.
SPCO SPTT, c.o.	Single pole changeover or Single pole, centre off or Single Pole, Triple Throw			Similar to SPDT. Some suppliers use SPCO/SPTT for switches with a stable off position in the centre and SPDT for those without.[citation needed]
DPST	Double pole, single throw	Double pole	Double pole	Equivalent to two SPST switches controlled by a single mechanism
DPDT	Double pole, double throw			Equivalent to two SPDT switches controlled by a single mechanism: A is connected to B and D to E, or A is connected to C and D to F.
DPCO	Double pole changeover or Double pole, centre off			Equivalent to DPDT. Some suppliers use DPCO for switches with a stable off position in the centre and DPDT for those without.
		Intermediate switch	Four-way switch	DPDT switch internally wired for polarity-reversal applications: only four rather than six wires are brought outside the switch housing; with the above, B is connected to F and C to E; hence A is connected to B and D to C, or A is connected to C and D to B.

Switches with larger numbers of poles or throws can be described by replacing the "S" or "D" with a number or in some cases the letter "T" (for "triple"). In the rest of this article the terms SPST, SPDT and intermediate will be used to avoid the ambiguity in the use of the word "way".

Biased switches

A biased switch is one containing a spring that returns the actuator to a certain position. The "on-off" notation can be modified by placing parentheses around all positions other than the resting position. For example, an (on)-off-(on) switch can be switched on by moving the actuator in either direction away from the centre, but returns to the central off position when the actuator is released.
The momentary push-button switch is a type of biased switch. The most common type is a "push-to-make" (or normally-open or NO) switch, which makes contact when the button is pressed and breaks when the button is released. Each key of a computer keyboard, for example, is a normally-open "push-to-make" switch. A "push-to-break" (or normally-closed or NC) switch, on the other hand, breaks contact when the button is pressed and makes contact when it is released. An example of a push-to-break switch is a button used to release a door held open by an electromagnet.

Special types

Switches can be designed to respond to any type of mechanical stimulus: for example, vibration (the trembler switch), tilt, air pressure, fluid level (the float switch), the turning of a key (key switch), linear or rotary movement (the limit switch or microswitch), or presence of a magnetic field (the reed switch).

Mercury tilt switch

The mercury switch consists of a drop of mercury inside a glass bulb with 2 contacts. The two contacts pass through the glass, and are connected by the mercury when the bulb is tilted to make the mercury roll on to them.
This type of switch performs much better than the ball tilt switch, as the liquid metal connection is unaffected by dirt, debris and oxidation, it wets the contacts ensuring a very low resistance bounce-free connection, and movement and vibration do not produce a poor contact. These types can be used for precision works.
It can also be used where arcing is dangerous (such as in the presence of explosive vapour) as the entire unit is sealed.

Knife switch

Knife switches consist of a flat metal blade, hinged at one end, with an insulating handle for operation, and a fixed contact. When the switch is closed, current flows through the hinged pivot and blade and through the fixed contact. Such switches are usually not enclosed. The parts may be mounted on an insulating base with terminals for wiring, or may be directly bolted to an insulated switch board in a large assembly. Since the electrical contacts are exposed, the switch is used only where people cannot accidentally come in contact with the switch.
The knife and contacts are typically formed of copper, steel, or brass, depending on the application. Fixed contacts may be backed up with a spring. Several parallel blades can be operated at the same time by one handle.
Knife switches are made in many sizes from miniature switches to large devices used to carry thousands of amperes. In electrical transmission and distribution, gang-operated switches are used in circuits up to the highest voltages.
The disadvantages of the knife switch are the slow opening speed and the proximity of the operator to exposed live parts. Metal-enclosed safety disconnect switches are used for isolation of circuits in industrial power distribution. Sometimes spring-loaded auxiliary blades are fitted which momentarily carry the full current during opening, then quickly part to rapidly extinguish the arc.

Intermediate switch A DPDT switch has six connections, but since polarity reversal is a very common usage of DPDT switches, some variations of the DPDT switch are internally wired specifically for polarity reversal. These crossover switches only have four terminals rather than six. Two of the terminals are inputs and two are outputs. When connected to a battery or other DC source, the 4-way switch selects from either normal or reversed polarity. Intermediate switches are also an important part of multiway switching systems with more than two switches (see next section).

Light switches

In building wiring, light switches are installed at convenient locations to control lighting and occasionally other circuits. By use of multiple-pole switches, control of a lamp can be obtained from two or more places, such as the ends of a corridor or stairwell.

Power switching

When a switch is designed to switch significant power, the transitional state of the switch as well as the ability to stand continuous operating currents must be considered. When a switch is in the on state its resistance is near zero and very little power is dropped in the contacts; when a switch is in the off state its resistance is extremely high and even less power is dropped in the contacts. However when the switch is flicked the resistance must pass through a state where briefly a quarter (or worse if the load is not purely resistive) of the load's rated power is dropped in the switch.
For this reason, most power switches (most light switches and almost all larger switches) have spring mechanisms in them to make sure the transition between on and off is as short as possible regardless of the speed at which the user moves the rocker.
Power switches usually come in two types. A momentary on-off switch (such as on a laser pointer) usually takes the form of a button and only closes the circuit when the button is depressed. A regular on-off switch (such as on a flashlight) has a constant on-off feature. Dual-action switches incorporate both of these features.

A diagram of a dual-action switch system

Inductive loads

When a strongly inductive load such as an electric motor is switched off, the current cannot drop instantaneously to zero; a spark will jump across the opening contacts. Switches for inductive loads must be rated to handle these cases. The spark will cause electromagnetic interference if not suppressed; a snubber network of a resistor and capacitor in series will quell the spark.

Contact bounce

Contact bounce (also called chatter) is a common problem with mechanical switches and relays. Switch and relay contacts are usually made of springy metals that are forced into contact by an actuator. When the contacts strike together, their momentum and elasticity act together to cause bounce. The result is a rapidly pulsed electrical current instead of a clean transition from zero to full current. The effect is usually unimportant in power circuits, but causes problems in some analogue and logic circuits that respond fast enough to misinterpret the on-off pulses as a data stream^[4].
Sequential digital logic circuits are particularly vulnerable to contact bounce. The voltage waveform produced by switch bounce usually violates the amplitude and timing specifications of the logic circuit. The result is that the circuit may fail, due to problems such as metastability, race conditions, runt pulses and glitches.
The effects of contact bounce can be eliminated by use of mercury-wetted contacts, but these are now infrequently used because of the hazard of mercury release. Contact circuits can be filtered to reduce or eliminate multiple pulses. In digital systems, multiple samples of the contact state can be taken or a time delay can be implemented so that the contact bounce has settled before the contact input is used to control anything.

Electronic switches

Since the advent of digital logic in the 1950s, the term has spread to a variety of digital active devices such as transistors and logic gates whose function is to change their output state between two logic levels or connect different signal lines, and even computers, network switches, whose function is to provide connections between different ports in a computer network.^[5] The term 'switched' is also applied to telecommunications networks, and signifies a network that is circuit switched, providing dedicated circuits for communication between end nodes, such as the public switched telephone network. The common feature of all these usages is they refer to devices that control a binary state: they are either on or off, closed or open, connected or not connected.