1 Steady-State Error M. Sami Fadali Professor of Electrical Engineering University of Nevada

2 Error Assume stability for the limit to exist. Steady state practically reached after (3-5)   = largest time constant of the system

3 Error Block Diagram

4 Unity Feedback Error depends on input & type number of system. n th order, type l

5 Step: Position Error Constant

6 Ramp: Velocity Error Constant

7 Parabolic: Acceleration Error Constant

8 Unity Feedback Error

9 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.

10 Percentage Error Expressed as a percentage of the input amplitude. Unaffected by input scaling.

11 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 K p (step) –Type 1, use position error constant K v (ramp) –Type 2, use position error constant K a (parabolic)

12 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.

13 Steady-State Error For unity feedback systems, we can use error constants to calculate e R (  )