in the name of allah the most beneficent the most merciful
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In The Name of Allah The Most Beneficent The Most Merciful. ECE 4545: Control Systems Lecture: Time Response of a System. Engr. Ijlal Haider Uo L , Lahore. Outline. Control Talk Reducing Block Diagrams Signal Flow Graph Reducing Signal Flow Graphs Mason’s Rule. Poles and Zeros.

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Presentation Transcript
outline
Outline
  • Control Talk
  • Reducing Block Diagrams
  • Signal Flow Graph
  • Reducing Signal Flow Graphs
  • Mason’s Rule
poles and zeros
Poles and Zeros
  • The polesof a system are the frequencies where the gain of the system become infinite
  • The zerosof a system are the frequencies where the gain of the system become zero
  • In some systems zeros and poles appears at the same location and hence cancels their response
  • [poles, tzero, pzmap]
transfer function
Transfer Function
  • Transfer function describes how a system responds to input applied
  • Fractional form
    • Proper
    • Improper
    • Strictly proper
  • Roots of denominator are poles
  • Roots of numerator are zeros
test inputs
Test Inputs
  • Impulse
  • Step
  • Ramp
  • Parabolic
  • Step is most common
time response of the system
Time Response of the System
  • Transient Response
  • Steady State
  • Forced Response
  • Natural Response
time response
Time Response
  • Transient response
  • The manner in which system behaves from initial state to the final state
  • Purpose of control systems is to provide a desired response.
  • Steady-state response
  • the manner in which the system output behaves as t approaches infinity
  • Purpose of control system is to provide min error from the set point.
effect of poles and zeros
Effect of Poles and Zeros
  • A pole of the input function generates the form of the forced response (that is, the pole at the origin generated a step function at the output)
  • A pole of the transfer function generates the form of the natural response
  • The zeros and poles generate the amplitudes for both the forced and natural responses
first order system
First Order System
  • First Order System
second order system
Second Order System
  • Two Poles
  • Location of poles determine the response of the system
system characteristics
System Characteristics
  • Rise Time
    • the time for the waveform to go from 0.1 to 0.9 of its final value
  • Settling Time
    • the time for the response to reach, and stay within, 2% (or 5%) of its final value
  • Peak Time
    • the time for the response to reach its first or maximum peak
  • Overshoot
    • the amount that the waveform overshoots the steady state, or final, value at the peak time, expressed as a percentage of the steady-state value
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