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For the unity feedback control system shown below. R(s) E(s) 100(s +2)(s+6) C(s) +. s(s + 3)(s + 4) If the applied input is unit step signal, what is the steady state error?

For the unity feedback control system shown below. R(s) E(s) 100(s +2)(s+6) C(s) +. s(s + 3)(s + 4) If the applied input is unit step signal, what is the steady state error?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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For the unity feedback control system shown below: \[ \begin{matrix} R(s) & \quad + & \quad E(s) & \quad & \quad & \quad & \quad & C(s) \\ & \quad \circlearrowleft & \quad & \quad & \quad & \quad \left[ \frac{100(s + 2)(s + 6)}{s(s + 3)(s + 4)} \right] & \quad & \\ \end{matrix} \] If the applied input is a unit step signal, what is the steady-state error? **Diagram Explanation:** This is a block diagram of a unity feedback control system. It consists of: - **R(s):** The reference input signal. - **E(s):** The error signal, obtained from the summation of R(s) and the feedback signal. - **Summing Junction:** A point where the reference input R(s) is compared with the feedback to generate an error signal E(s). - **Forward Path Transfer Function:** \(\frac{100(s + 2)(s + 6)}{s(s + 3)(s + 4)}\) - The numerator represents the zeroes (\(s + 2\) and \(s + 6\)). - The denominator represents the poles (at 0, \(-3\), and \(-4\)). - **Feedback Loop:** The system is a unity feedback loop, where the output C(s) is fed back directly to the input to be compared with R(s). The task is to determine the steady-state error when the input is a unit step signal.
Transcribed Image Text:For the unity feedback control system shown below: \[ \begin{matrix} R(s) & \quad + & \quad E(s) & \quad & \quad & \quad & \quad & C(s) \\ & \quad \circlearrowleft & \quad & \quad & \quad & \quad \left[ \frac{100(s + 2)(s + 6)}{s(s + 3)(s + 4)} \right] & \quad & \\ \end{matrix} \] If the applied input is a unit step signal, what is the steady-state error? **Diagram Explanation:** This is a block diagram of a unity feedback control system. It consists of: - **R(s):** The reference input signal. - **E(s):** The error signal, obtained from the summation of R(s) and the feedback signal. - **Summing Junction:** A point where the reference input R(s) is compared with the feedback to generate an error signal E(s). - **Forward Path Transfer Function:** \(\frac{100(s + 2)(s + 6)}{s(s + 3)(s + 4)}\) - The numerator represents the zeroes (\(s + 2\) and \(s + 6\)). - The denominator represents the poles (at 0, \(-3\), and \(-4\)). - **Feedback Loop:** The system is a unity feedback loop, where the output C(s) is fed back directly to the input to be compared with R(s). The task is to determine the steady-state error when the input is a unit step signal.
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