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| readstatus | dateread | title | year | authors | citekey | |||
|---|---|---|---|---|---|---|---|---|
| false | Feedback Control Theory | 2009 |
|
doyleFeedbackControlTheory2009 |
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[!Abstract] In any system, if there exists a linear relationship between two variables, then it is said that it is a linear system.
[!note] Markdown Notes None!
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[!attention] Highlight 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.
[!attention] Highlight 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.
[!attention] Highlight Uncertainty arises from twosources: unknown or unpredictable inputs (disturbance, noise, etc.) and unpredictable dynamics.
[!attention] Highlight 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.)
[!attention] Highlight 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.
[!attention] Highlight transfer function fromreference input r to tracking error e is denoted S, the sensitivity function
[!attention] Highlight 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.
[!attention] Highlight 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].
[!attention] Highlight 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.
[!attention] Highlight Define the loop transfer function Lˆ := PˆCˆ. The transfer function from reference input r totracking error e isSˆ :=11 + Lˆ ,called the sensitivity function—
[!quote] Other Highlight 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
[!note] Note Ladies and gentlemen, we got him.