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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. 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

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  1. In The Name of Allah The Most Beneficent The Most Merciful

  2. ECE 4545:Control Systems Lecture:Time Response of a System Engr. Ijlal Haider UoL, Lahore

  3. Outline • Control Talk • Reducing Block Diagrams • Signal Flow Graph • Reducing Signal Flow Graphs • Mason’s Rule

  4. 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]

  5. 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

  6. Test Inputs • Impulse • Step • Ramp • Parabolic • Step is most common

  7. Time Response of the System • Transient Response • Steady State • Forced Response • Natural Response

  8. 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.

  9. System Response

  10. 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

  11. First Order System • First Order System

  12. Second Order System • Two Poles • Location of poles determine the response of the system

  13. 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

  14. Thank You!

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