---
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