Control Systems Flashcards
control system (definition)
input –> system –> output
what is a Laplace transform?
transforms a function in the TIME domain to the FREQUENCY domain
laplace transform input (format) and output (format) - example
input = f(t) (some function of time) output = F(s) (some function of 's' - complex frequency domain)
Laplace transform of 1
1/s
Laplace transform of e^-at
1/s+a
Why are Laplace transforms necessary/make life easier?
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!
What is a transfer function?
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.
poles of a function
values of ‘s’ that make P(s)/Q(s) = infinity (that is, roots of Q(s) =0)
zeros of a function
values of ‘s’ that make P(s)/Q(s) = 0 (that is, roots of P(s) = 0)
why are the poles & zeros of a function important?
they determine whether or not a system is stable or unstable
poles must be where for system stability?
must be in the left hand plane (negative).
Why are poles in the right-hand side of plane unstable?
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).
Routh-Hurwitz (concept)
rather than finding roots of high-order polynomials, can observe patterns in coefficents and their sign to determine system stability.
With an input of a sine wave, the output of an LTI system:
- amplitude/frequency/ phase will stay the same (which?)
Frequency always stays the same.
Concept of bode plot
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.
Bode plot layout
Two graphs - one is gain, the other phase - both plotted against frequency. Gain is in decibels (20 log(amplitude) ).
closed-loop system (define)
a system involving feedback
Poles & zeros of a system (define)
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.
type of a system (define)
number of integrators (feedback loops), where integrator = 1 / s
Therefore type 0 system = 0 integrators
List three typical input signals
unit step, ramp & parabolic
Transient response (define)
The response from 0 to settling time
Steady-state response (define)
The response from settling time onwards
Peak time (define)
The time the system response reaches a maximum
. Damping factor (define)
The parameter of a second order system which affect the response speed, commonly labeled
as ζ
