diff --git a/200 Library Papers/doyleFeedbackControlTheory2009.md b/200 Library Papers/doyleFeedbackControlTheory2009.md new file mode 100644 index 000000000..6ff2040ee --- /dev/null +++ b/200 Library Papers/doyleFeedbackControlTheory2009.md @@ -0,0 +1,88 @@ +--- +readstatus: false +dateread: +title: "Feedback Control Theory" +year: 2009 +authors: + + + - "Doyle, John" + + - "A, Francis" + + - "Tannenbaum, Allen" + + +citekey: "doyleFeedbackControlTheory2009" + + + + + + + +--- +# Indexing Information +## DOI +[](https://doi.org/) +## ISBN +[](https://www.isbnsearch.org/isbn/) +## Tags: + + +>[!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! +# Annotations + +>[!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. + +### Imported: 2024-10-12 1:22 pm + + diff --git a/4 Qualifying Exam/3 Notes/Feedback Control Theory.md b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md new file mode 100644 index 000000000..bf57bc1ce --- /dev/null +++ b/4 Qualifying Exam/3 Notes/Feedback Control Theory.md @@ -0,0 +1 @@ +# Chapter 1: \ No newline at end of file diff --git a/4 Qualifying Exam/3 Notes/Robust Control.md b/4 Qualifying Exam/3 Notes/Robust Control.md index 5893e68b8..7be1c9b2a 100644 --- a/4 Qualifying Exam/3 Notes/Robust Control.md +++ b/4 Qualifying Exam/3 Notes/Robust Control.md @@ -2,7 +2,7 @@ ## Where did Robust Control come from? After the beginnings of modern control and the development of optimal control, John Doyle released a paper in 1978 titled [Guaranteed Margins for LQG regulators](doyleGuaranteedMarginsLQG1978a). This is a less than one page paper that basically gave birth to the robust control field, with a three word abstract: "There are none." I'm working out the kinks in this one ([[Basic Feedback Control]]), but essentially the gaussian part of the LQG is what destroys the guaranteed part of the phase and gain margins. The additional estimator involved can really screw with things. - +I should add some context: [[4 Qualifying Exam/3 Notes/Feedback Control Theory]]. # What does Robust Control do? Robust control works with [[What is gain scheduling?]]