89 lines
4.0 KiB
Markdown
89 lines
4.0 KiB
Markdown
---
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readstatus: false
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dateread:
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title: "Feedback Control Theory"
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year: 2009
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authors:
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- "Doyle, John"
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- "A, Francis"
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- "Tannenbaum, Allen"
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citekey: "doyleFeedbackControlTheory2009"
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---
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# Indexing Information
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## DOI
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[](https://doi.org/)
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## ISBN
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[](https://www.isbnsearch.org/isbn/)
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## Tags:
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>[!Abstract]
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>In any system, if there exists a linear relationship between two variables, then it is said that it is a linear system.
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>[!note] Markdown Notes
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>None!
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# Annotations
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>[!attention] Highlight
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> *The book is addressed to students in engineering who have had an undergraduate course insignals and systems, including an introduction to frequency-domain methods of analyzing feedbackcontrol systems, namely, Bode plots and the Nyquist criterion.*
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>
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>[!attention] Highlight
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> *The simplest objective might be to keep y small(or close to some equilibrium point)—a regulator problem—or to keep y − r small for r, a referenceor command signal, in some set—a servomechanism or servo problem.*
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>
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>[!attention] Highlight
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> *Uncertainty arises from twosources: unknown or unpredictable inputs (disturbance, noise, etc.) and unpredictable dynamics.*
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>
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>[!attention] Highlight
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> *Ideally, the model should cover the data in the sense that it should be capable of producingevery experimentally observed input-output pair. (Of course, it would be better to cover not just the data observed in a finite number of experiments, but anything that can be produced by the realphysical system. Obviously, this is impossible.)*
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>
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>[!attention] Highlight
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> *Very rarely is the exogenous input w a fixed, known signal. One of these rare instances is wherea robot manipulator is required to trace out a definite path, as in welding. Usually, w is not fixed but belongs to a set that can be characterized to some degree. Some examples:• In a thermostat-controlled temperature regulator for a house, the reference signal is alwayspiecewise constant: at certain times during the day the thermostat is set to a new value. The temperature of the outside air is not piecewise constant but varies slowly within bounds.• In a vehicle such as an airplane or ship the pilot’s commands on the steering wheel, throttle, pedals, and so on come from a predictable set, and the gusts and wave motions have amplitudesand frequencies that can be bounded with some degree of confidence. • The load power drawn on an electric power system has predictable characteristics.Sometimes the designer does not attempt to model the exogenous inputs.*
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>
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>[!attention] Highlight
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> *transfer function fromreference input r to tracking error e is denoted S, the sensitivity function*
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>
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>[!attention] Highlight
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> *Lemma 1 The 2-norm of Gˆ is finite iff Gˆ is strictly proper and has no poles on the imaginaryaxis; the ∞-norm is finite iff Gˆ is proper and has no poles on the imaginary axis.*
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>
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>[!attention] Highlight
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> *A stronger notion of well-posedness that makes sense when P, C, and F are proper is thatthe nine transfer functions above are proper. A necessary and sufficient condition for this is that1 + PCF not be strictly proper [i.e., PCF(∞) 6= −1].*
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>
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>[!attention] Highlight
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> *Nyquist Criterion Construct the Nyquist plot of PCF, indenting to the left around poles on the imaginary axis. Let n denote the total number of poles of P, C, and F in Res ≥ 0. Then the feedbacksystem is internally stable iff the Nyquist plot does not pass through the point -1 and encircles itexactly n times counterclockwise.*
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>
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>[!attention] Highlight
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> *Define the loop transfer function Lˆ := PˆCˆ. The transfer function from reference input r totracking error e isSˆ :=11 + Lˆ ,called the sensitivity function—*
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>
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>[!quote] Other Highlight
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> *Here we used Table 2.1: the maximum amplitude of e equals the ∞-norm of the transfer function. Or if we define the (trivial, in this case) weighting function W1(s) = 1/ǫ, then the performance specification is kW1Sk∞ < 1.The situation becomes mo*
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>
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> >[!note] Note
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> >Ladies and gentlemen, we got him.
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### Imported: 2024-10-12 1:22 pm
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