30 Questions
Which chapter is devoted to the analysis of system transient response?
Chapter 4
What does the order of a system refer to?
The order of the equivalent differential equation representing the system
What are the two responses that make up the output response of a system?
Forced response and natural response
Why does Chapter 4 come before Chapter 5 in the book?
To demonstrate applications of the system representation by evaluating the transient response from the system model
What are the poles of a transfer function?
The values of s that cause the transfer function to become infinite
What are the zeros of a transfer function?
The values of s that cause the transfer function to become zero
What does a pole of the input function generate?
The form of the forced response
What is the time constant of a response?
The time for e^at to decay to 37% of its initial value
Which of the following is the definition of rise time?
The time for the waveform to go from 0.1 to 0.9 of its final value
What is settling time defined as?
The time for the waveform to reach 2% of its final value
What is the transfer function used to calculate the unit step response of a second-order system?
$C(s) = R(s)G(s)$
What is the term used to describe a second-order system response with two real poles and no zeros?
Overdamped
Which of the following best describes the time constant of the exponential decay in a second-order system?
It is equal to the reciprocal of the real part of the system pole
What is the damped frequency of oscillation in an underdamped response?
It is equal to the imaginary part of the poles
What type of response is characterized by a transient response that is a damped oscillation?
Underdamped response
What is the characteristic of a critically damped response?
It is the fastest possible response without overshoot
Which parameter is defined as the time required for the waveform to go from 0.1 of the final value to 0.9 of the final value?
Rise time
Which parameter is defined as the time required to reach the first, or maximum, peak?
Peak time
Which parameter is defined as the amount that the waveform overshoots the steady-state value at the peak time, expressed as a percentage of the steady-state value?
Percent overshoot
Which parameter is defined as the time required for the transient’s damped oscillations to reach and stay within 2% of the steady-state value?
Settling time
Which part of the response remains the same as the poles move to the left?
The frequency
What remains the same for all waveforms in Figure 4.19(c)?
The peak time
What is the relationship between the pole location and the response speed?
The farther the poles are from the origin, the faster the response
What does the percent overshoot remain the same for?
Different waveforms
What is the main focus of the second example?
Design
What does the order of a system refer to?
The number of poles
Which two parameters are associated with second-order systems?
Natural frequency and damping ratio
What is the definition of the damping ratio, ζ?
The ratio of the exponential decay frequency to the natural frequency
What is the relationship between the value of ζ and the type of response obtained?
The lower the value of ζ, the more oscillatory the response
What is the transform of the response, C(s), for the general second-order system of Eq. (4.22) in terms of ζ and ωn?
$C(s) = \frac{\omega_{n}^{2} \cdot (s + \zeta \cdot \omega_{n})},{(s - \zeta \cdot \omega_{n})^2 + \omega_{n}^{2} \cdot (1 - \zeta^2)}$
Test your understanding of underdamped response parameters such as rise time, peak time, percent overshoot, and settling time. This quiz will assess your knowledge of how these specifications are defined and their significance in analyzing waveforms.
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