Steady-State Error

1
Steady-State Error

• M. Sami Fadali
• Professor of Electrical Engineering
• University of Nevada

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Error

• Assume stability for the limit to exist.
• Steady state practically reached after (3-5)?
• ? largest time constant of the system

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Error Block Diagram
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Unity Feedback
nth order, type l

• Error depends on input type number of system.

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Step Position Error Constant
6
Ramp Velocity Error Constant
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Parabolic Acceleration Error Constant
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Unity Feedback Error
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Input Amplitude Scaling

• Error is scaled if input is scaled.
• Table for unity feedback assumes unit input.
• For amplitude A ?1, multiply all error
  expressions by the input amplitude A.

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Percentage Error

• Expressed as a percentage of the input amplitude.
• Unaffected by input scaling.

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Unity vs. Nonunity Feedback

• Nonunity feedback get the steady-state error
  using the closed-loop transfer function T(s).
• Unity feedback use system type and error
  constants.
• Type 0, use position error constant Kp (step)
• Type 1, use position error constant Kv (ramp)
• Type 2, use position error constant Ka (parabolic)

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Error Due to Disturbance

• Output due to disturbance is ideally zero.
• All output due to disturbance is error.
• The total error includes tracking error and
  error due to disturbance.
• For linear systems, use superposition.

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Steady-State Error

• For unity feedback systems, we can use error
  constants to calculate eR(?)