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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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In the name of allah the most beneficent the most merciful
In The Name of Allah The Most Beneficent The Most Merciful


Ece 4545 control systems lecture time response of a system

ECE 4545:Control Systems Lecture:Time Response of a System

Engr. Ijlal Haider

UoL, Lahore


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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