Physics · Control Systems
A single-loop control system has a forward-path transfer function G(s) and a feedback-path transfer function H(s). The error signal e(s) is formed at a summing junction from the reference input r(s) and the feedback signal b(s) = H(s)y(s). Which option correctly relates the definition of e(s) to the corresponding closed-loop transfer function T(s) = Y(s)/R(s)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The sign in the denominator of T(s) depends exclusively on the internal sign of G(s).
- 2For both negative and positive feedback cases, T(s) = G(s) / [1 + G(s)H(s)].
- 3If e = r - b, then T(s) = G(s) / [1 + G(s)H(s)]; if e = r + b, then T(s) = G(s) / [1 - G(s)H(s)].✓
- 4If e = r + b, then T(s) = G(s) / [1 + G(s)H(s)]; if e = r - b, then T(s) = G(s) / [1 - G(s)H(s)].
Correct answer
If e = r - b, then T(s) = G(s) / [1 + G(s)H(s)]; if e = r + b, then T(s) = G(s) / [1 - G(s)H(s)].
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