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

Engr. Ijlal Haider

UoL, Lahore

Outline
• Control Talk
• Reducing Block Diagrams
• Signal Flow Graph
• Reducing Signal Flow Graphs
• Mason’s Rule
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 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
• Impulse
• Step
• Ramp
• Parabolic
• Step is most common
Time Response of the System
• Transient Response
• Forced Response
• Natural 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.
• 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
• 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
Second Order System
• Two Poles
• Location of poles determine the response of the system
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