|
Hall Circles
Hall circles (also known as M-circles and N-circles) are a graphical tool in control theory used to obtain values of a closed-loop transfer function from the Nyquist plot (or the Nichols plot) of the associated open-loop transfer function. Hall circles have been introduced in control theory by Albert C. Hall in his thesis. Construction Consider a closed-loop linear control system with open-loop transfer function given by transfer function G(s) and with a unit gain in the feedback loop. The closed-loop transfer function is given by T(s) = \frac . To check the stability of ''T''(''s''), it is possible to use the Nyquist stability criterion with the Nyquist plot of the open-loop transfer function ''G''(''s''). Note, however, that only the Nyquist plot of ''G''(''s'') does not give the actual values of ''T''(''s''). To get this information from the G(s)-plane, Hall proposed to construct the locus of points in the ''G''(''s'')-plane such that ''T''(''s'') has constant magnitude and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist Grid
Nyquist may refer to: *Nyquist (surname) *Nyquist (horse), winner of the 2016 Kentucky Derby *Nyquist (programming language), computer programming language for sound synthesis and music composition See also *Johnson–Nyquist noise, thermal noise *Nyquist stability criterion, in control theory **Nyquist plot, signal processing and electronic feedback *Nyquist–Shannon sampling theorem, fundamental result in the field of information theory **Nyquist frequency, digital signal processing **Nyquist rate, telecommunication theory **Nyquist ISI criterion, telecommunication theory *6625 Nyquist, a main-belt asteroid *Nyquist filter, a filter used in television systems *Enquist Enquist is a surname of Swedish origin which may refer to: * Jan Enquist, Swedish rear admiral * Jeff Enquist, American soccer player * Lynn W. Enquist, American professor in molecular biology * Oskar Enquist, Imperial Russian vice admiral of Swedi ... * Nyqvist (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-loop Transfer Function
A closed-loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the plant under control. Overview The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop transfer function is shown below: The summing node and the ''G''(''s'') and ''H''(''s'') blocks can all be combined into one block, which would have the following transfer function: : \dfrac = \dfrac G(s) is called feedforward transfer function, H(s) is called feedback transfer function, and their product G(s)H(s) is called the Open loop transfer function. Derivation We define an intermediate signal Z (also known as error signal) shown as follows: Using this figure we write: : Y(s) = G(s)Z(s) : Z(s) =X(s) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist-plot
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane singularities must be known). As a result, it can be applied to systems defined by non-rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplanes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nichols Plot
The Nichols plot is a Plot (graphics), plot used in signal processing and control theory, control design, named after American engineer Nathaniel B. Nichols.Allen Stubberud, Ivan Williams, and Joseph DeStefano, ''Shaums Outline Feedback and Control Systems'', McGraw-Hill, 1995, ch. 17 Use in control design Given a transfer function, : G(s) = \frac with the closed-loop transfer function defined as, : M(s) = \frac the Nichols plots displays 20 \log_(, G(s), ) versus \arg(G(s)). Loci of constant 20 \log_(, M(s), ) and \arg(M(s)) are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency \omega is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - 20 \log_(, G(s), ) versus \log_(\omega) and \arg(G(s)) versus \log_(\omega) ) - are plotted. In control system, feedback control design, the plot is useful for assessing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer Function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for each possible input. They are widely used in electronics and control systems. In some simple cases, this function is a two-dimensional graph (function), graph of an independent scalar (mathematics), scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory. The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locus (mathematics)
In geometry, a locus (plural: ''loci'') (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.. In other words, the set of the points that satisfy some property is often called the ''locus of a point'' satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be ''located'' or may move. History and philosophy Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was considered as an entity on which a point may be located or on which it moves. Thus a circle in the Euclidean plane was defined as the ''locus'' of a point that is at a given dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circles Of Apollonius
The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection. The main uses of this term are fivefold: # Apollonius showed that a circle can be defined as the set of points in a plane that have a specified ''ratio'' of distances to two fixed points, known as foci. This Apollonian circle is the basis of the Apollonius pursuit problem. It is a particular case of the first family described in #2. # The Apollonian circles are two families of mutually orthogonal circles. The first family consists of the circles with all possible distance ratios to two fixed foci (the same circles as in #1), whereas the second family consists of all possible circles that pass through both foci. These circles form the basis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nichols Chart
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithms
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
