Transient Response

Transient Response

1. The time response of a control system consists of transient response and steady-state response

2. Which goes from the initial state to the final state

3. By: Abigail Romero Trejo

   • 1112567

4. Unit-Step Response

   • First Order Systems
     • The smaller the time constant "T", the faster the system response
   • Second Order Systems
     • Standard form of a transfer function
       • Where:
         • = Attenuation
         • Wn= Undamped natural frequency
           • It is the frequency at which the system output would oscillate if the damping were decreased to zero
         • = Damping ratio
         • Wd= Damped natural frequency
     • Underdamped
       • The transient response is oscillatory
       • < 1
       • THe poles are complex conjugates
         • Lie in the left-half s plane
       • 0<
     • = 0
       • The transient response does not die out
     • Critically damped
       • = 1
       • The two poles are equal
     • Overdamped systems
       • >1
       • The two poles are negative real and unequal
     • Performance measures
       • Delay time (td)
         • Time required for the response to reach half the final value the very first time
       • Rise time (tr)
         • Time required for the response to rise from 10% to 90%, 5% to 95% or 0% to 100% of its final value
       • Peak time (tp)
         • Time required for the response to reach the first peak of the overshoot
       • Maximum overshoot (Mp)
         • Maximum peak value of the response curve measured from unity
       • Settling time (ts)
         • Time required for the response curve to reach and stay within a range about the final value of size specified by absolute percentage of the final value (2-5% usually)

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