Control Systems

Question 1

control system (definition)

Answer 1

input –> system –> output

Question 2

what is a Laplace transform?

Answer 2

transforms a function in the TIME domain to the FREQUENCY domain

Question 3

laplace transform input (format) and output (format) - example

Answer 3

input = f(t) (some function of time)
output = F(s) (some function of 's' - complex frequency domain)

Question 4

Laplace transform of 1

Answer 4

1/s

Question 5

Laplace transform of e^-at

Answer 5

1/s+a

Question 6

Why are Laplace transforms necessary/make life easier?

Answer 6

Input in time domain are ODE’s - differential equations. These aren’t fun to work with. The output of a transform, however, is algebraic (in the freq. domain) - much nicer to work with!

Question 7

What is a transfer function?

Answer 7

A Transfer Function is the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions and equilibrium point to be zero.

Question 8

poles of a function

Answer 8

values of ‘s’ that make P(s)/Q(s) = infinity (that is, roots of Q(s) =0)

Question 9

zeros of a function

Answer 9

values of ‘s’ that make P(s)/Q(s) = 0 (that is, roots of P(s) = 0)

Question 10

why are the poles & zeros of a function important?

Answer 10

they determine whether or not a system is stable or unstable

Question 11

poles must be where for system stability?

Answer 11

must be in the left hand plane (negative).

Question 12

Why are poles in the right-hand side of plane unstable?

Answer 12

positive root means the inverse laplace transformce is e^(somepositivenumber), which approaches infinity. If there’s a sign difference, than some approach 0, and the others approach infinity (hence instability).

Question 13

Routh-Hurwitz (concept)

Answer 13

rather than finding roots of high-order polynomials, can observe patterns in coefficents and their sign to determine system stability.

Question 14

With an input of a sine wave, the output of an LTI system:

- amplitude/frequency/ phase will stay the same (which?)

Answer 14

Frequency always stays the same.

Question 15

Concept of bode plot

Answer 15

Say you want to see the frequency output of a system if a particular input is applied. Easy; just graph it. More often then not, though, you want to see a SPECTRUM of outputs. This is where the bode plot comes in.

Question 18

Bode plot layout

Answer 18

Two graphs - one is gain, the other phase - both plotted against frequency. Gain is in decibels (20 log(amplitude) ).

Question 19

closed-loop system (define)

Answer 19

a system involving feedback

Question 20

Poles & zeros of a system (define)

Answer 20

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Control systems, in the most simple sense, can be designed simply by assigning specific values to the poles and zeros of the system.

Question 21

type of a system (define)

Answer 21

number of integrators (feedback loops), where integrator = 1 / s
Therefore type 0 system = 0 integrators

Question 22

List three typical input signals

Answer 22

unit step, ramp & parabolic

Question 23

Transient response (define)

Answer 23

The response from 0 to settling time

Question 24

Steady-state response (define)

Answer 24

The response from settling time onwards

Question 25

Peak time (define)

Answer 25

The time the system response reaches a maximum

Question 26

. Damping factor (define)

Answer 26

The parameter of a second order system which affect the response speed, commonly labeled
as ζ

Question 27

PID controller

Answer 27

A proportional, integral and derivative (PID) controller

Question 28

Phase lead-lag compensators

Answer 28

A compensator/controller which generates both positive and negative phase shift in
frequency response

Question 29

fg

Answer 29

fgg