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Questions and Answers
Closed-loop control systems should have which of the following properties
Closed-loop control systems should have which of the following properties
- All of the choices (correct)
- Good regulation against disturbances
- Low sensitivity to changes in the plant parameter
- Desirable responses to commands
The slope of the asymptotic plot at very low (w<<1) and high (w>>10)
frequencies are, respectively
The slope of the asymptotic plot at very low (w<<1) and high (w>>10) frequencies are, respectively
- At low frequency: slope = 0 dB/dec and at high frequency: slope = -40 dB/dec (correct)
- At low frequency: slope = 20 dB/dec and at high frequency: slope = 20 dB/dec
- At low frequency: slope = -20 dB/dec and at high frequency: slope = -20 dB/dec
- At low frequency: slope = 0 dB/dec and at high frequency: slope = 40 dB/dec
A feedback system is shown in the figure:
Block diagram with blocks 8/(s+2), 1/s, and 0.125s
A feedback system is shown in the figure: Block diagram with blocks 8/(s+2), 1/s, and 0.125s
- 4 / s(s + 1) (correct)
- 2 / s(s + 2)
- 2 / s(s + 2)^2
- 22/ s(s + 2)^2
When the number of poles is equal to the number of zeroes, how many
branches of root locus tends towards infinity
When the number of poles is equal to the number of zeroes, how many branches of root locus tends towards infinity
The signal flow graph shown in the figure has
*Signal flow graph with a yin/yang half symbol
The signal flow graph shown in the figure has *Signal flow graph with a yin/yang half symbol
The open-loop transfer function of a unity feedback control system is:
G(s) = 1/(s+2)^2
The closed-loop transfer function will have poles at
The open-loop transfer function of a unity feedback control system is: G(s) = 1/(s+2)^2 The closed-loop transfer function will have poles at
As compared to a closed-loop system, an open-loop system is
As compared to a closed-loop system, an open-loop system is
In the signal flow graph shown in the figure, the value of the C/R ratio is
*Graph with circular loop and check towards the output
In the signal flow graph shown in the figure, the value of the C/R ratio is *Graph with circular loop and check towards the output
The characteristic equation for a closed loop system is s^4 + as^3 + bs^2 +
cs + K = 0. For the system to be stable
The characteristic equation for a closed loop system is s^4 + as^3 + bs^2 + cs + K = 0. For the system to be stable
The characteristic equation for a feedback system is s^5 + 2s^4 + 8s^3 +
16s^2 + 16s + 16 = 0. The system is
The characteristic equation for a feedback system is s^5 + 2s^4 + 8s^3 + 16s^2 + 16s + 16 = 0. The system is
For Nyquist contour, the size of radius is _______
For Nyquist contour, the size of radius is _______
When there is a vanishing row in the Routh array for a characteristic equation,
there is a possibility of
When there is a vanishing row in the Routh array for a characteristic equation, there is a possibility of
The input to the controller is the
The input to the controller is the
A system with more than one input variable or more than one output variable
is known by what name?
A system with more than one input variable or more than one output variable is known by what name?
A single-input, single-output system has the state variable representation
x = | 0 1 | | 1 |
|-5 -10 | x + | 0 | u
y = | 0 10 | x
The transfer function of the system T(s) = Y(s) / U(s) is
A single-input, single-output system has the state variable representation x = | 0 1 | | 1 | |-5 -10 | x + | 0 | u y = | 0 10 | x The transfer function of the system T(s) = Y(s) / U(s) is
For the characteristic equation of a system s^5 + s^4 + 2s^3 + 2s^2 + s + 1 =
0
For the characteristic equation of a system s^5 + s^4 + 2s^3 + 2s^2 + s + 1 = 0
The principles of homogeneity and superposition are applied to
The principles of homogeneity and superposition are applied to
Consider the following statements regarding the advantages of closed-loop
negative feedback control systems over open-loop systems
- The overall reliability of the closed-loop systems is more than that of
open-loop system.
- The transient response in the closed-loop system decays more quickly than
in open-loop system.
- In an open-loop system, closing of the loop increases the overall gain of
the system
- In the closed-loop system, the effect of variation of component parameters
on its performance is reduced
Consider the following statements regarding the advantages of closed-loop negative feedback control systems over open-loop systems
- The overall reliability of the closed-loop systems is more than that of open-loop system.
- The transient response in the closed-loop system decays more quickly than in open-loop system.
- In an open-loop system, closing of the loop increases the overall gain of the system
- In the closed-loop system, the effect of variation of component parameters on its performance is reduced
According to Nyquist stability criterion, where should be the position of all
zeros of q(s) corresponding to s-plane
According to Nyquist stability criterion, where should be the position of all zeros of q(s) corresponding to s-plane
The sum of the gains of the feedback paths in the signal flow graph below is
Signal flowgraph that looks like three half-circles in series with paths a, b, c,
f, e, d
The sum of the gains of the feedback paths in the signal flow graph below is Signal flowgraph that looks like three half-circles in series with paths a, b, c, f, e, d
The characteristic equation for a closed loop system is s^3 + as^2 + bs + K =
0 . The marginal value of K is
The characteristic equation for a closed loop system is s^3 + as^2 + bs + K = 0 . The marginal value of K is
In polar plots, what does every point represent w.r.t magnitude and angle?
In polar plots, what does every point represent w.r.t magnitude and angle?
Important modern applications of control systems include which of the fol
lowing?
Important modern applications of control systems include which of the fol lowing?
The difference between the reference input and the feedback signal is the
The difference between the reference input and the feedback signal is the
The transmission path from the summing point to the controlled output c
The transmission path from the summing point to the controlled output c
For the system shown in the given figure the transfer function X(s)/F(s) is
*Translational system with hanging spring attached to mass with f(t) and x(t)
all pointing downwards
For the system shown in the given figure the transfer function X(s)/F(s) is *Translational system with hanging spring attached to mass with f(t) and x(t) all pointing downwards
Means the summing point is an adder
Means the summing point is an adder
An op-amp has
An op-amp has
Consider the loop transfer function K(s+6)/(s+3)(s+5) In the root locus dia
gram the centroid will be located at
Consider the loop transfer function K(s+6)/(s+3)(s+5) In the root locus dia gram the centroid will be located at
Complete the following sentence.
Control of an industrial process by automatic rather than manual means is
often called ____________
Complete the following sentence. Control of an industrial process by automatic rather than manual means is often called ____________
It must be additive and homogenous
It must be additive and homogenous
The transmission path from the controlled output c back to the summing
point
The transmission path from the controlled output c back to the summing point
Which of the following is not valid in case of signal flow graph
Which of the following is not valid in case of signal flow graph
For the characteristic equation of a closed loop system s^4 + 2s^3 + 6s^2 +
8s + 8 = 0
For the characteristic equation of a closed loop system s^4 + 2s^3 + 6s^2 + 8s + 8 = 0
Feedback control systems are
Feedback control systems are
One which is first degree in the dependent variables and their derivatives
One which is first degree in the dependent variables and their derivatives
Control engineering is applicable to which fields of engineering?
Control engineering is applicable to which fields of engineering?
For the block diagram shown in the figure, the closed loop transfer function
is
Block diagram with blocks 1/(s+1), 2s, and 2 from top to bottom in a straight
line in that order
For the block diagram shown in the figure, the closed loop transfer function is Block diagram with blocks 1/(s+1), 2s, and 2 from top to bottom in a straight line in that order
Elements of the forward path, between the actuating (error signal e and the
control variable u).
Elements of the forward path, between the actuating (error signal e and the control variable u).
Other differential equation not in the linear form
Other differential equation not in the linear form
Consider a feedback system with open loop transfer function
G(s) = 50/(s^2 + 12s + 20)
The break frequencies on the Bode plot are
Consider a feedback system with open loop transfer function G(s) = 50/(s^2 + 12s + 20) The break frequencies on the Bode plot are
Which of the following is the correct combination about the four statements
stated below:
- Transfer function can be obtained from the signal flow graph of the system
- Transfer function typically characterizes linear time variant system
- Block diagram of the system can be obtained from its transfer function
given the ratio of output to input in frequency domain of the system
- Transfer function gives the ratio of output to input in frequency domain of
the system
Which of the following is the correct combination about the four statements stated below:
- Transfer function can be obtained from the signal flow graph of the system
- Transfer function typically characterizes linear time variant system
- Block diagram of the system can be obtained from its transfer function given the ratio of output to input in frequency domain of the system
- Transfer function gives the ratio of output to input in frequency domain of the system
The roots of the characteristic equation of a closed loop system are
The roots of the characteristic equation of a closed loop system are
Early applications of feedback control include which of the following?
Early applications of feedback control include which of the following?
The difference between the reference input and the controlled output is the
The difference between the reference input and the controlled output is the
Flashcards
Closed-loop control system properties
Closed-loop control system properties
Closed-loop control systems have low sensitivity to changes in plant parameters, desirable responses to commands, and good regulation against disturbances.
Asymptotic plot slopes
Asymptotic plot slopes
The slope of the asymptotic plot at very low frequencies (ω<<1) is 0 dB/dec, and at high frequencies (ω>>10) is -40 dB/dec.
Root locus branches to infinity
Root locus branches to infinity
When the number of poles equals the number of zeroes, the number of root locus branches that tend towards infinity is zero.
Open-loop vs. Closed-loop
Open-loop vs. Closed-loop
Compared to a closed-loop system, an open-loop system is more stable but less accurate.
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Closed-loop transfer function poles
Closed-loop transfer function poles
The open-loop transfer function G(s) = 1/(s+2)^2 will have poles at -2 ± j1 in the closed-loop transfer function.
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Stability Condition
Stability Condition
The characteristic equation for a closed loop system is s^4 + as^3 + bs^2 + cs + K = 0. For the system to be stable, K < (abc - c^2) / a^2
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Vanishing Row
Vanishing Row
When there is a vanishing row in the Routh array for a characteristic equation, there is a possibility of a pair of roots lying on the jw axis.
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Error signal
Error signal
The input to the controller is the error signal, which is the difference between the reference input and the feedback signal.
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Multivariable control system
Multivariable control system
A system with more than one input variable or more than one output variable is known as a multivariable control system.
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Nyquist Contour Radius
Nyquist Contour Radius
For Nyquist Contour, the size of radius is infinity
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Forward Path
Forward Path
The transmission path from the summing point to the controlled output is the Forward Path.
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Op-amp Impedance
Op-amp Impedance
An op-amp has a high input impedance and a low output impedance.
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Block Diagram Reduction
Block Diagram Reduction
A system represented by a block diagram with a summing point (circle) between G1(s) and G2(s), and H(s) directly below G2(s) becomes G1G2/(1 + G1G2 + G2H).
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Feedback Path
Feedback Path
The transmission Path from the controlled output back to the summing point is the feedback path.
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Poles on imaginary axis
Poles on imaginary axis
For the characteristic equation of a closed loop system s^4 + 2s^3 + 6s^2 + 8s + 8 = 0, a pair of poles lies on the imaginary axis
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- Closed-loop control system properties include:
- Low sensitivity to plant parameter changes
- Desirable responses to commands
- Good regulation against disturbances
- The slopes of the asymptotic plot at very low (ω<<1) and high (ω>>10) frequencies when the slope at low frequency is 0 dB/dec and at high frequency is -40 dB/dec.
- For a feedback system with blocks 8/(s+2), 1/s, and 0.125s, then using an equivalent unity feedback system, the forward path transfer function is 4 / s(s + 1).
- When the number of poles equals the number of zeroes, zero branches of the root locus tend towards infinity.
- A signal flow graph with a yin/yang half symbol has three forward paths, four loops, and no non-touching loops
- Given an open-loop transfer function of G(s) = 1/(s+2)^2 for a unity feedback control system, the closed-loop transfer function will have poles at -2 +-j1.
- An open-loop system is more stable but less accurate as compared to a closed-loop system.
- In a signal flow graph presented in the image, the value of the C/R ratio is 40/81.
- For a closed-loop system with the characteristic equation s^4 + as^3 + bs^2 + cs + K = 0 to be stable, K < (abc - c^2) / a^2.
- For a feedback system with the characteristic equation s^5 + 2s^4 + 8s^3 + 16s^2 + 16s + 16 = 0, the system is unstable.
- Poles in the RHP: 0.1838 + 2.4588i, 0.1838 - 2.4588i.
- Other Poles: -1.6438, -0.3619 + 1.2125i, -0.3619 - 1.2125i
- For a Nyquist contour, the size of radius is infinity.
- A vanishing row in the Routh array possibly indicates a pair of roots lying on the jw axis for a characteristic equation.
- The input to the controller is the error signal.
- For a system with blocks G2(s), G1(s), and H(s) connected top to bottom in a straight line, the overall transfer function is (G1 + G2) / (1 + G1H).
- A system with more than one input or output variable is known as a multivariable control system.
- For a single-input, single-output system with state variable representation:
- x' = | 0 1 || 1 | | -5 -10 |x + | 0 |u
- y = | 0 10 | x
- The transfer function of the system T(s) = Y(s) / U(s) is -50/(s^2 + 10s + 5).
- The characteristic equation of a system is s^5 + s^4 + 2s^3 + 2s^2 + s + 1 = 0 which results in four roots lying on the imaginary axis.
- Roots: -1.0000, 1.0000i, -1.0000i, 1.0000i, -1.0000i
- The principles of homogeneity and superposition are applied to linear time-invariant systems.
- Advantages of closed-loop negative feedback control systems over open-loop systems:
- The transient response in the closed-loop system decays more quickly than in an open-loop system.
- The effect of variation of component parameters on its performance is reduced in the closed-loop system.
- According to the Nyquist stability criterion, all zeros of q(s) should be positioned on the On left half in the s-plane.
- The sum of the gains of the feedback paths in a signal flow graph with three half-circles in series (paths a, b, c, f, e, d) is af + be + cd.
- For a closed-loop system with the characteristic equation s^3 + as^2 + bs + K = 0, the marginal value of K is ab.
- In polar plots, every point represents a Phasor with magnitude and angle.
- Important modern applications of control systems include:
- Fuel-efficient and safe automobiles
- Autonomous robots
- Automated manufacturing
- The difference between the reference input and the feedback signal is the actuating signal.
- The transmission path from the summing point to the controlled output is the Forward Path,
- For a system a tranlational system with hanging spring attached to mass with f(t) and x(t) all pointing downwards, the transfer function X(s)/F(s) is 1/(Ms^2 + K).
- An electrical network with 2 meshes with two 1-ohm resistors, an inductor, and a capacitor has the correct transfer function Vo(s)/V1(s) of s/(2s^2+2s+1).
- A summing point is an adder with Positive feedback
- An op-amp has a high input impedance and a low output impedance.
- In the root locus diagram for the loop transfer function K(s+6)/(s+3)(s+5), the centroid will be located at -2.
- A system is represented by where G1(s) and G2(s) are in a summing point with H(s) directly below G2(s), its transfer function is G1G2/(1 + G1G2 + G2H).
- Control of an industrial process by automatic rather than manual means is often called automation.
- A Linear System must be additive and homogenous
- The transmission path from the controlled output back to the summing point is the Feedback Path.
- Nodes are arranged from right to left in a sequence is not valid in case of signal flow graph.
- For the characteristic equation of a closed loop system s^4 + 2s^3 + 6s^2 + 8s + 8 = 0, a pair of poles lies on the imaginary axis.
- Poles: -0.0000 + 2.0000i, -0.0000 - 2.0000i, -1.0000 + 1.0000i, -1.0000 - 1.0000i
- Feedback control systems are Less sensitive to forward-path parameter changes than to feedback-path parameter changes.
- Linear DE is one which is first degree in the dependent variables and their derivatives.
- Control engineering is applicable to:
- Electrical and biomedical
- Chemical and environmental
- Mechanical and aerospace
- Blocks 1/(s+1), 2s, and 2 connected in a straight line order, will result in a closed loop transfer function of 1/3(s+1)
- Controller/Compensator is an element of the forward path, between the actuating (error signal e and the control variable u).
- In a feedback system function G(s) is transfered to the feed back function H(s) as G(s)/(1 + G(s)H(s) - G(s)).
- A non-linear DE (Differential Equation) is any differential equation not in the linear form.
- For a mechanical system with a dampener, mass, y2(t), spring, y1(t), and f(t) from left to right with formulas: M(d^2y2(t)/dt^2) + B(dy2(t)/dt) = k[y1(t) -y2(t)]
- A feedback system with open loop transfer function G(s) = 50/(s^2 + 12s + 20) has break frequencies on the Bode plot are w = 2 and w = 10 rad/s.
- Block diagram of the system can be obtained from its transfer function given the ratio of output to input in frequency domain of the system, and transfer function gives the ratio of output to input in frequency domain of the system are true regarding control theory.
- The roots of the characteristic equation of a closed loop system are closed loop poles.
- Early applications of feedback control include:
- Water clock of Ktesibios
- Watt's flyball governor
- Drebbel's temperature regulator
- The difference between the reference input and the controlled output is the error.
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