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Control Engineering Basics

In a unity-feedback system the forward transfer function is G(s) = 9/(1 + 2s). Which of the following is the steady-state error for a step setpoint of size 1?

  1. A0
  2. B0.1
  3. CAbout 0.11
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Answer: B. 0.1

For a unity-feedback system, the steady-state error to a step is 1/(1 + Kp), where Kp = G(0) is called the position error constant. Here Kp = 9, so the steady-state error is 1/(1 + 9) = 0.1. In a system whose forward path has no integrator (a type 0 system), raising the gain makes the error smaller but not zero. To bring the error to zero, an integrator is added, for example with PI control.

  • A. The steady-state error becomes zero when the forward path contains an integrator (1/s).
  • B. Correct. The output settles at 0.9, leaving an error of 0.1.
  • C. This is 1/Kp = 1/9. The correct formula is 1/(1 + Kp).
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More Control Engineering Basics questions

  1. In a unity-feedback system with a stable closed loop, the forward transfer function G(s) contains one integrator 1/s (a type 1 system). Which of the following correctly describes the steady-state error?
  2. Which of the following is the condition for a continuous-time linear system to be stable (its impulse response approaches zero with time)?
  3. Which of the following closed-loop systems, given by their characteristic equations, is stable?
  4. A unity-feedback system has the loop transfer function K/(s(s + 1)(s + 2)). Which of the following is the range of K for which the closed-loop system is stable?
  5. Which of the following correctly describes the Nyquist stability criterion?

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