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Bode's Sensitivity Integral
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let ''L'' be the loop transfer function and ''S'' be the sensitivity function. In the diagram, P is a dynamical process that has a transfer function P(s). The controller, C, has the transfer function C(s). The controller attempts to cause the process output, y, to track the reference input, r. Disturbances, d, and measurement noise, n, may cause undesired deviations of the output. Loop gain is defined by L(s) = P(s)C(s). The following holds: :\int_0^\infty \ln , S(j \omega), d \omega = \int_0^\infty \ln \left, \frac \ d \omega = \pi \sum Re(p_k) - \frac \lim_ s L(s) where p_k are the poles of ''L'' in the right half plane (unstable poles). If ''L'' has at least two more poles than zeros, and has no poles in the right half plane (is stable), the equation simplifies to: :\int_0^\infty \ln , S(j \ome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bode Sensitivity Integral Block Diagram
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Bode may refer to: People * Bode (surname) * Bode Miller (born 1977), American skier * Bode Sowande (born 1948), Nigerian writer and dramatist * Bode Thomas (1918–1953), Nigerian politician Geography * Böde, village in Zala County, Hungary * Bode, Iowa, city in Humboldt County, Iowa, United States * Bode, Nepal, city in Bhaktapur District, Nepal * Bode (river), a major river in Saxony-Anhalt, Germany, tributary of the Saale * Bode (Wipper), a small river in Thuringia, Germany, tributary of the Wipper Other * Bode (crater), lunar crater * Bode plot, graph used in electrical engineering and control theory * Bode (fashion brand), American clothing company See also * Bodie (other) * Bodhi The English term enlightenment is the Western translation of various Buddhist terms, most notably bodhi and vimutti. The abstract noun ''bodhi'' (; Sanskrit: बोधि; Pali: ''bodhi''), means the knowledge or wisdom, or awakened intellect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hendrik Wade Bode
Hendrik Wade Bode ( ; ;Van Valkenburg, M. E. University of Illinois at Urbana-Champaign, "In memoriam: Hendrik W. Bode (1905-1982)", IEEE Transactions on Automatic Control, Vol. AC-29, No 3., March 1984, pp. 193–194. Quote: "Something should be said about his name. To his colleagues at Bell Laboratories and the generations of engineers that have followed, the pronunciation is boh-dee. The Bode family preferred that the original Dutch be used as boh-dah." December 24, 1905 – June 21, 1982) was an American engineer, researcher, inventor, author and scientist, of Dutch ancestry. As a pioneer of modern control theory and Electronics, electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research. His synergy with Claude Shannon, the father of information theory, laid the foundations for the technological convergence of the information age. He made important contributions to the design, guidance and control of anti-aircraft systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feedback
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 had 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 ... [...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] |
Pole (complex Analysis)
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. In some sense, it is the simplest type of singularity. Technically, a point is a pole of a function if it is a zero of the function and is holomorphic in some neighbourhood of (that is, complex differentiable in a neighbourhood of ). A function is meromorphic in an open set if for every point of there is a neighborhood of in which either or is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicities of its poles equals the sum of the multiplicities of its zeros. Definitions A function of a complex variable is holomorphic in an open domai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero (complex Analysis)
In complex analysis (a branch of mathematics), a pole is a certain type of singularity (mathematics), singularity of a complex-valued function of a complex number, complex variable. In some sense, it is the simplest type of singularity. Technically, a point is a pole of a function if it is a zero of a function, zero of the function and is holomorphic function, holomorphic in some neighbourhood (mathematics), neighbourhood of (that is, complex differentiable in a neighbourhood of ). A function is meromorphic function, meromorphic in an open set if for every point of there is a neighborhood of in which either or is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicity (mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity (control Systems)
The controller parameters are typically matched to the process characteristics and since the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. One way to characterize sensitivity is through the nominal sensitivity peak M_s: M_s = \max_ \left, S(j \omega) \ = \max_ \left, \frac \ where G(s) and C(s) denote the plant and controller's transfer function in a basic closed loop control system written in the Laplace domain using unity negative feedback. The sensitivity function S, which appears in the above formula also describes the transfer function from external disturbance to process output. In fact, assuming an additive disturbance ''n'' after the output of the plant, the transfer functions of the closed loop system are given by Y(s) = \frac R(s) + \frac N(s) Hence, lower values of , S, suggest further attenuation of the external disturbance. The sensiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
