|
Hautus Lemma
In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Belevitch-Hautus test or PBH test, can prove to be a powerful tool. A special case of this result appeared first in 1963 in a paper by Elmer G. Gilbert, and was later expanded to the current PBH test with contributions by Vasile M. Popov in 1966, Vitold Belevitch Vitold Belevitch (2 March 1921 – 26 December 1999) was a Belgian mathematician and electrical engineer of Russian origin who produced some important work in the field of electrical network theory. Born to parents fleeing the Bolsheviks, he ... in 1968, and Malo Hautus in 1969, who emphasized its applicability in proving results for linear time-invariant systems. Statement There exist multiple forms of the lemma: Hautus Lemma for controllability The Hautus lemma for controllability says that given a square matrix \mat ... [...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 sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Time-invariant
In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response of the system to an arbitrary input can be found directly using convolution: where is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication, as is frequently employed by the symbol in computer languages). What's more, there are systematic methods for solving any such system (determining ), whereas systems not meeting both properties are generally more difficult (or impossible) to solve analytically. A good example of an LTI system is any electrical circuit consisting of resistors, capacitors, inductors and linear amplifiers. Linear time-invariant system theory i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space
A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space. Definition In the theory of dynamical systems, the state space of a discrete system defined by a function ''ƒ'' can be modeled as a directed graph where each possible state of the dynamical system is represented by a vertex with a directed edge from ''a'' to ''b'' if and only if ''ƒ''(''a'') = ''b''. This is known as a state diagram. For a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elmer G
Elmer is a name of Germanic British origin. The given name originated as a surname, a medieval variant of the given name Aylmer, derived from Old English ''æþel'' (noble) and ''mær'' (famous). It was adopted as a given name in the United States, "in honor of the popularity of the brothers Ebenezer and Jonathan Elmer, leading supporters of the American Revolution." The name has declined in popularity since the first decades of the 20th century and fell out of the top 1,000 names used for American boys in 2009. However, it continues in use for newborn boys in the United States, where 154 boys born there in 2021 received the name. The name is common in the United States and Canada. Notable people with the name include: Mononym * Eilmer of Malmesbury (or Elmer), 11th-century English Benedictine monk * In the amateur radio subculture, an ''Elmer'' is a mentor to a newcoming amateur radio operatorThe term first appeared in the March, 1971 issue of ''QST'' magazine's "How's DX" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vasile M
The male name Vasile is of Greek origin and means "King". Vasile is a male Romanian given name or a surname. It is equivalent to the English name Basil. As a given name As a surname *Cristian Vasile (1908–1985), Romanian tango-romance singer *Nicolae Vasile (born 1995), Romanian professional footballer *Niculina Vasile (born 1958), former Romanian high jumper * Radu Vasile (1942–2013), Romanian politician and Prime Minister *Ștefan Vasile (born 1982), Romanian Olympic canoer Places *Pârâul lui Vasile, a river in Romania * Valea lui Vasile, a river in Romania * Vasile Aron (Sibiu district) See also * Vasiliu (surname) * Vasilescu (surname) * Vasilievca (other) * Vasile Alecsandri (other) * Vasileuți Vasileuți is a commune in Rîșcani District, Moldova Moldova ( , ; ), officially the Republic of Moldova ( ro, Republica Moldova), is a Landlocked country, landlocked country in Eastern Europe. It is bordered by Romania to the west ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitold Belevitch
Vitold Belevitch (2 March 1921 – 26 December 1999) was a Belgian mathematician and electrical engineer of Russian origin who produced some important work in the field of electrical network theory. Born to parents fleeing the Bolsheviks, he settled in Belgium where he worked on early computer construction projects. Belevitch is responsible for a number of circuit theorems and introduced the now well-known scattering parameters. Belevitch had an interest in languages and found a mathematical derivation of Zipf's law. He also published on machine languages. Another field of interest was transmission lines, where he published on line coupling. He worked on telephone conferencing and introduced the mathematical construct of the conference matrix. Early life Belevitch was born 2 March 1921 in Terijoki, Karelia, now incorporated into Russia, but at the time part of Finland. Belevitch's parents were Russian and his mother was an ethnic Pole. They were attempting to flee fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Controllable
Controllability is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied. The following are examples of variations of controllability notions which have been introduced in the systems and control literature: * State controllability * Output controllability * Controllability in the behavioural framework State controllability The state of a deterministic system, which is the set of values of all the system's state variables (those variables characterized by dynamic equations), completely describes the system at any given ... [...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 sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
