English
Menu

Control Engineering Basics

When a step of size 2 was applied to a first-order system, the output finally settled at 6 and reached about 63% of its final value 0.4 s after the input. Which of the following is the transfer function of this system?

  1. A3/(1 + 0.4s)
  2. B3/(1 + 2.5s)
  3. C6/(1 + 0.4s)
Show answer and explanation

Answer: A. 3/(1 + 0.4s)

The steady-state gain is the final output divided by the input size: 6 ÷ 2 = 3. The time a first-order step response takes to reach about 63% (1 − e^(−1)) of its final value is the time constant, so T = 0.4 s. The transfer function is therefore G(s) = 3/(1 + 0.4s). In this way, a first-order model can be built easily from the final value and the rise time of a step response.

  • A. Correct. A steady-state gain of 3 and a time constant of 0.4 s.
  • B. This puts 2.5, the reciprocal of the time constant, as the coefficient of s. The coefficient of s is the time constant itself.
  • C. This uses the final output 6 directly as the gain. It must be divided by the input size 2.
Practice this topic Back to topic

Related calculators

PID step response simulatorSee the step response and control effort for a plant and your P, I and D gainsBode plot calculatorDraw magnitude and phase plots from a transfer function and find phase and gain margins

Books on Control Engineering Basics Ad

As an Amazon Associate I earn from qualifying purchases.

More Control Engineering Basics questions

  1. Which of the following is the range of the damping ratio ζ for which the step response of the second-order system G(s) = ωn²/(s² + 2ζωn s + ωn²) overshoots the final value and approaches it while oscillating?
  2. Which of the following is the correct pair of natural angular frequency ωn and damping ratio ζ for the second-order system with the transfer function G(s) = 25/(s² + 4s + 25)?
  3. A step is applied to a second-order system (standard form without zeros) with a damping ratio ζ = 0.5. Which of the following is closest to the overshoot (the maximum excursion beyond the final value, as a fraction of the final value)?
  4. Which of the following is the settling time, until the step response of the system G(s) = 25/(s² + 4s + 25) stays within ±2% of its final value, estimated with the approximation ts ≈ 4/(ζωn)?
  5. A second-order system without zeros has its poles at s = −σ ± jωd. Which of the following correctly describes how the step response changes when only ωd is increased while σ is kept the same?

Comparisons in this topic