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Error Transfer Function



The error transfer function relates an output of error (which is just the output, e(s), from the feedback summation block) to your input commanded value, which we'll refer to as 'e_ref(s)'. To evaluate this for our generic model, where: simply write out the algebraic relationship between desired output (e(s)) and input (e_ref(s)): Then, move all terms in 'e(s)' [output] to one side and all term in 'e_ref(s)' [input] to the other: and the ERTF(s) is:
  • Use the ERTF(s) to evaluate the steady-state response of a closed-loop system. Refer to the lecture notes entitled "Time-domain performance of feedback-controlled systems" (distributed Oct-24-00) for more details. The response to a STEP input is found by evaluating the following for 's=0' (i.e., steady state): The response to a RAMP input is: (Note that the difference is in a multiplied by '1/s'.)

    gonzo@mit.edu page 4 (of 10) 2.010 Tutorial #6, 30-Oct-00