|
Fractional-order Integrator
A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative (usually called a differintegral) of an input. Differentiation or integration is a real or complex parameter. The fractional integrator is useful in fractional-order control where the history of the system under control is important to the control system output. Some industrial controllers use fractional-order PID controllers (FOPIDs), which have exceeded the performance of standard ones, to the extent that standard ones are sometimes considered as a special case of FOPIDs. Fractional-order integrators and differentiators are the main component of FOPIDs. Overview The differintegral function, :_a \mathbb^q_t \left( f(x) \right) includes the integer order differentiation and integration functions, and allows a continuous range of functions around them. The differintegral parameters are ''a'', ''t'', and ''q''. The parameters ''a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Integrator
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an important part of many engineering and science, scientific applications. Mechanical integrators are the oldest type and are still used for metering water flow or electrical power. Electronic analogue integrators, which have generally displaced mechanical integrators, are the basis of analog computers and charge amplifiers. Integration can also be performed by algorithms in digital computers. Mechanical integrators One simple kind of mechanical integrator is the disk-and-wheel integrator. This functions by placing a wheel on and perpendicular to a spinning disk, held there by means of a freely spinning shaft parallel to the disk. Because the speed at which a part of the disk turns is proportional to its distance from the center, the rate at whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Leakage (electronics)
In electronics, leakage is the gradual transfer of electrical energy across a boundary normally viewed as insulating, such as the spontaneous discharge of a charged capacitor, magnetic coupling of a transformer with other components, or flow of current across a transistor in the "off" state or a reverse-polarized diode. In capacitors Gradual loss of energy from a charged capacitor is primarily caused by electronic devices attached to the capacitors, such as transistors or diodes, which conduct a small amount of current even when they are turned off. Even though this off current is an order of magnitude less than the current through the device when it is on, the current still slowly discharges the capacitor. Another contributor to leakage from a capacitor is from the undesired imperfection of some dielectric materials used in capacitors, also known as ''dielectric leakage''. It is a result of the dielectric material not being a perfect insulator and having some non-zero conducti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fourier Series
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always Convergent series, converge. Well-behaved functions, for example Smoothness, smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Signal Analysis
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the '' Bell System Technical Journal''. The paper laid the groundwork for later developme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
RC Ladder
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The two most common RC filters are the high-pass filters and low-pass filters; band-pass filters and band-stop filters usually require RLC filters, though crude ones can be made with RC filters. Natural response The simplest RC circuit consists of a resistor with resistance and a charged capacitor with capacitance connected to one another in a single loop, without an external voltage source. The capacitor will discharge its stored energy through the resistor. If is taken to be the voltage of the capacitor's top plate relative to its bottom plate i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Opamp
An operational amplifier (often op amp or opamp) is a DC-coupled electronic voltage amplifier with a differential input, a (usually) single-ended output, and an extremely high gain. Its name comes from its original use of performing mathematical operations in analog computers. By using negative feedback, an op amp circuit's characteristics (e.g. its gain, input and output impedance, bandwidth, and functionality) can be determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op amp itself. This flexibility has made the op amp a popular building block in analog circuits. Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standard integrated circuit op amps cost only a few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost over . Op amps may be packaged as components or used as elements of more complex integrated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Feedback Impedance
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: History Self-regulating mechanisms have existed since antiquity, and the idea of feedback started to enter economic theory in Britain by the 18th century, but it was not at that time recognized as a universal abstraction and so did not have a name. The first ever known artificial feedback device was a float valve, for maintaining water at a constant level, invented in 270 BC in Alexandria, Egypt. This device illustrated the principle of feedback: a low water level opens the valve, the rising water then provides feedback into the system, closing the valve when the required level is reached. This then reoccurs in a circular fashion as the water level fluctuates. Centrifugal governors were used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Capacitor
In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term still encountered in a few compound names, such as the '' condenser microphone''. It is a passive electronic component with two terminals. The utility of a capacitor depends on its capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed specifically to add capacitance to some part of the circuit. The physical form and construction of practical capacitors vary widely and many types of capacitor are in common use. Most capacitors contain at least two electrical conductors, often in the form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, or an electrolyte. The nonconductin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Integrator Circuit
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In optics, high-pass and low-pass may have different meanings, depending on whether referring to the frequency or wavelength of light, since these variables are inversely related. High-pass frequency filters would act as low-pass wavelength filters, and vice versa. For this reason, it is a good practice to refer to wavelength filters as ''short-pass'' and ''long-pass'' to avoid confusion, which would correspond to ''high-pass'' and ''low-pass'' frequencies. Low-pass filters exist in many different forms, including electronic circuits such as a ''hiss filter'' used in audio, anti-al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Round-off Error
In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits), one of the goals of numerical analysis is to estimate computation errors. Computation errors, also called numerical errors, include both truncation errors and roundoff errors. When a sequence of calculations with an input involving any roundoff error are made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate. In short, there are two major facets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Differintegral
In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/ integration operator. Applied to a function ƒ, the ''q''-differintegral of ''f'', here denoted by :\mathbb^q f is the fractional derivative (if ''q'' > 0) or fractional integral (if ''q'' So, \frac = \mathcal^\left\ which generalizes to \mathbb^qf(t) = \mathcal^\left\. Under the bilateral Laplace transform, here denoted by \mathcal and defined as \mathcal (t)=\int_^\infty e^ f(t)\, dt, differentiation transforms into a multiplication \mathcal\left frac\right= s\mathcal (t) Generalizing to arbitrary order and solving for \mathbb^qf(t), one obtains \mathbb^qf(t)=\mathcal^\left\. Representation via Newton series is the Newton interpolation over consecutive integer orders: \mathbb^qf(t) =\sum_^ \binom m \sum_^m\binom mk(-1)^f^(x). For fractional derivative definitions described in this section, the following identities hold: :\mathbb^q(t^n)=\fract^ :\mathbb^q(\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Analog Device
Analog devices are a combination of both analog machine and analog media that can together measure, record, reproduce, receive or broadcast continuous information, for example, the almost infinite number of grades of transparency, voltage, resistance, rotation, or pressure. In theory, the continuous information in an analog signal has an infinite number of possible values with the only limitation on resolution being the accuracy of the analog device. Analog media are materials with analog properties, such as photographic film, which are used in analog devices, such as cameras. Example devices Non-electrical There are notable non-electrical analog devices, such as some clocks (sundials, water clocks), the astrolabe, slide rules, the governor of a steam engine, the planimeter (a simple device that measures the surface area of a closed shape), Kelvin's mechanical tide predictor, acoustic rangefinders, servomechanisms (e.g. the thermostat), a simple mercury t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
