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Control Systems: Time Response Analysis and System Characteristics

Learn about time response analysis, transfer functions, poles and zeros effects, system response, and characteristics in control systems. Explore Mason's rule, input types, and system behavior from transient to steady state.

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Control Systems: Time Response Analysis and System Characteristics

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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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