Chapter 5 Flashcards
in an overdamped system, the poles of the characteristic equation are:
a. two distinct real roots
b. complex conjugates
c. repeated real roots
d. both at the origin
a. two distinct real roots
for a step response, the rise time is shortest when the system is:
underdamped, overdamped, critically damped, marginally stable?
underdamped
for a first order system with constant (tau) how long does it take for the system to reach approximately 98%
4τ
which of the following statements is true for the impulse response of an underdamped second order system?
- the response has a peak followed by oscillations
- the response reaches a steady-state value instantly
- the response is independent of damping
- the response has no initial peak
- the response has a peak followed by oscillations
a first order system subjected to a ramp input will have a steady state error that is:
a. proportional to the slope of the input
b. zero
c. infinite
d. equal to the time constant
a. proportional to the slope of the input
a second order system with ζ> 1 is classified as:
overdamped
for an undamped second order system with ζ=0, the impulse response is:
a. a pure sinusoidal oscillation
b. a decaying exponential function
c. a constant step function
d. a linear ramp function
a. a pure sinusoidal oscillation
if ζ=0.7 in a second order system, which of the following statements is correct?
a. the response has slight oscillations before settling
b. the system is unstable
c. the response is overdamped
d. the response has no overshoot
a. the response has slight oscillations before settling
if the damping ratio (ζ) is equal to one, the system response is:
critically damped
which process input is commonly use to determine the steady state gain of a process? step, ramp, sinusoidal, impulse
step
which damping ration (ζ) produces the fastest step response without oscillations?
1, 0.2, 0.7, 2?
1
a lightly damped second order system subjected to a sinusoidal input will exhibit:
a. high amplification at the resonant frequency
b. no response
c. a step like response
d. an exponential decay
a. high amplification at the resonant frequency
for an impulse imput, the response of an overdamped second order syetm:
a. show no oscillations and settles quicky
b. shows oscillations with overshoot
c. settles in finite time with no oscillations
d. does not reach steady state
c. settles in finite time with no oscillations
for a second order system the peak overshoot depends on:
a. the damping ratio
b. the natural frequency
c. the time constant
d. the input magnitude
a. the damping ratio
the response of a first order system to a ramp input R(t) = At is
a. a delayed ramp response
b. an exponentially decaying function
c. a sinusoidal oscillation
d. a constant steady state value
a. a delayed ramp response
consider a first order system with a time constant of 2 seconds and a gain of 3. what is the output after 2 seconds in response to a unit step input?
1.90, 2.90, 3.90. 3
1.90
a step input is characterized by:
A step input is a sudden and sustained change.
for a second order system with ζ=1, the sinusoidal steady state response will:
a. have no oscillatory amplification
b. have no resonance peak
c. show continuous oscillations
d. be unpredictable
b. have no resonance peak
which of the following process inputs is commonly used to test the transient response of a first order system?
a. step input
b. sinusoidal input
c. exponential input
d. random input
a. step input
which parameter in a second order system determines the degree of oscillation?
a. damping ratio
b. steady state gain
c. time constant
d. natural frequency
a. damping ratio
a ramp can be mathematically represented as:
a. a linear function of time
b. a constant value for all time
c. an oscillating function
d. a sudden, infinite spike at a single point in time
a. a linear function of time
which of the following second order system responses has the fastest rise time but may oscillate?
underdamped
overdamped
critically damped
unstable
underdamped
which standard process input produces a linear increase in output for an integrating process? ramp, step, sinusoidal, impulse
ramp
what happens when ζ = 0 in a second order system?
a. system exhibits sustained oscillations
b. system is overdamped
c. system does not respond
d. system becomes stable
a. system exhibits sustained oscillations
a second order system differs from a first order system because it has:
a. one additional state variable
b. a higher order derivative in the characteristic equation
c. more than one time constant
d. all that is mentioned
d. all that is mentioned
which of the following best describes the effect of increasing damping (ζ) in the step response of a second order system?
a. reduced overshoot
b. increased oscillations
c. faster rise time
d. increased resonance
a. reduced overshoot
a second order system has a ωn=2 rad/s and damping ratio = 0.5. what is the time to first peak (tp)?
a. 3.14 s
b. 1.57 s
c. 0.79 s
d. 2.22 s
tp= π/ωn = 1.57 s
an integrating process has a transfer function g(s) = 1/s. a step input of magnitude 4 is applied. what is the output after 5 seconds?
a. 4
b. 25
c. 20
d. 10
y(t) = 4t = 4*5 = 20
if a second-order underdamped system has a damping ratio of 0.4 and its maximum overshoot is 25%, what is the natural frequency (wn), given a settling time ts=8s (for 2% criterion)?
a. 1.25 rad/s
b. 1.0 rad/s
c. 1.6 rad/s
d. 0.5 rad/s
ts=4/(ζωn);
ωn=4/(8∗0.4)=4/3.2=1.25 rad/s
a level tank is an integrator with a gain of K = 0.1m/min * (L/min)^-1. if a constant inflow of 10 L/min is added and no outflow exists, what is the water level after 3 minutes?
a. 3
b. 5
c. 2
d. 1
3
the overshoot is measured as 16.3%. what is the damping ratio?
a. 0.58
b. 0.7
c. 0.22
d. 0.85
ln(Mp)=−πζ√(1−ζ^2)
close to 0.58
a second-order system has a damping ratio of 0.3 and wn= 4 rad/s. what is the settling time using 2% criterion?
a. 4 s
b. 3 s
c. 2.5 s
d. 3.33 s
ts=4/(ζωn)
d. 3.33 s
for a system with τ = 10s and K = 2, how long will it take for the output to reach 95% of the final value after a unit step input?
a. 30s
b. 10 s
c. 20 s
d. 40 s
95% = 3τ
a. 30s
a first order system has a time constant τ = 5 min and gain K = 2. if a step change of magnitude 3 is applied, what is the output after 1 time constant?
a. 4.55
b. 3.79
c. 2.16
d. 5.0
63.2% = τ
b. 3.79
a first order system has a time constant τ= 5min and gain K=2. if a step change of magnitude 3 is applied, what is the final value of the output?
a. 2
b. 6
c. 3
d. 5
K * step change = 2 * 3 = 6
b. 6
given a second order system with G(s)=25/(s^2 + 6s + 25)
what is the natural frequency?
a. √ 20
b. 6
c. 5
d. 25
ωn = √25 = 5 rad/s
