Control Systems Flashcards

1
Q

transfer function

A

used to represent systems with one input function and one output function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

feedback system

A
  • output signal is returned as input in a feedback loop
  • basic system consists of
  • -> dynamic unit
  • -> feedback unit
  • -> pick-off pint
  • -> summing point
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Closed- Loop Feedback Systems

A

X(s) is the input transfer function
Y(s) is the output transfer function
The overall transfer function (also called closed-loop gain or control ratio)

T(s) = Y(s)/X(s) is the transfer function of the overall feedback system

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Closed Loop Feedback Systems continued

A

Each unit has an associated transfer function:
G(s) is the forward transfer function
H(s) is the reverse transfer function (or feedback gain). When H(s)=1 it is called unity feedback

The loop transfer function (also called loop gain or open loop gain) +G(s)H(s) is the gain after going around the loop one time

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

block diagram

A
  • can represent a physical system
  • with transfer functions, can be used to describe and clarify complex relationships of causes and effects throughout a dynamic system
  • can be simplified into a single block operation

In a block diagram,

  • interconnected black boxes (cascaded blocks) represent functions
  • each block represents and describes a portion of the system
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

block diagram of a linear system

A

typically consists of four components

  • signal
  • block (with transfer function)
  • summing point
  • pick-off-point
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

simplifying block diagrams

A

a block diagram can be simplified using a mathematical system of rules known as a block diagram algebra

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

unity feedback system

A
  • feedback loop has value of H(s) = 1
  • open-loop transfer function is G(s)H(s)=G(s)
  • unstable if feedback is positive
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

for a step input

A
  • often called DC input, because it is like switching a DC source on or off
  • steady-state response obtained by substituting zero for s everywhere in transfer function, then multiplying by magnitude of step
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

for a sinusoidal input

A
  • steady-state response obtained by substituting jw for s everywhere in transfer function T(s) <–> T(jw)
  • output has same frequency as input
  • transforms Laplace transform transfer function into the frequency domain, which is physically meaningful
  • frequency domain analyzed with Bode diagrams
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

steady-state error, ess

A
  • determine long-term performance of a system
  • values will always be zero, infinity or a constant
  • ideally errors e(t) and ess both equal zero
  • always nonzero for pure gain sytems
  • can be near zero for integrating
  • depends on type of input R(s) and system type
  • found from the final value theorem
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

pole of a transfer function

A
  • a value of s that makes the denominator of G(s) zero (pole values are system eigenvalues)
  • therefore makes G(s) infinite
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

zero of a transfer function

A
  • a value of s that makes the numerator of G(s) zero

- therefore makes G(s) zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

poles and zeros

A
  • need not be real or unique

- can be imaginary and repeated within function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

pole-zero diagram

A

a plot of poles and zeros in the s-plane, a rectangular coordinate system with real and imaginary axes

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Bode Plot

A
  • a graphical representation of the response of a control system in the frequency domain
  • gives a visual way to assess control system stability
  • if the input is a steady-state sinusoid at frequency w, the gain plot shows the gain of the system
17
Q

horizontal axis

A

logarithmic, allowing many orders of magnitude in a single plot

18
Q

magnitude (vertical axis)

A

plotted in decibels, allowing many orders of magnitude in a single plot
–> terms that are products can be added, and terms that are quotients can be subtracted

19
Q

single zero plot

A

this is normalized plot of log (w/z) versus 20 log I 1+jw/z I

20
Q

root-locus diagram

A

a plot in the s-plane that shows the location of the poles of the closed-loop transfer function for all values of the system gain constant, K, if the open-loop transfer function G(s) H(s) is known

21
Q

asymptotes

A
  • the number of asymptotes is the number of poles, n, minus the number of zeros, m
22
Q

position-integral-derivative (PID) controller

A

can control the output a system based on a combination of

  • position of the input
  • integral of the input
  • derivative of the input
23
Q

lead or lag compensator

A
  • common control component placed in a feedback circuit
  • improves frequency response of control system
  • also used to
  • -> reduce stead-state error
  • -> reduce resonant peaks
  • -> improve system response by reducing rise time
24
Q

Routh criterion

A
  • the poles of a transfer function determine whether the control system is stable
  • for the system to be stable, poles must be in the negative real section of the s-plane
25
Q

Routh test

A

an efficient method of testing the denominator of a closed-loop transfer function for real positive poles

26
Q

state variable models

A
  • a system with an nth order differential equation can be represented as n first-order differential equations in a matrix-vector form
  • state variable models use linear algebra to solve differential equations and so are useful for computer solutions
  • a state variable can be used for a control system, expressing input and output as separate equations using a dummy variable