Question 1

Name three applications for feedback control systems.

Accepted Answer

Guided missiles
Fighter plane stability
Satellite tracking antenna

Question 2

Name three reasons for using feedback control systems and two for not.

Accepted Answer

Pro: remote control, power gain, and parameter conversion
Con: complex and expensive

Question 3

If the error signal is not the difference in input and output, by what general name can we describe the error signal?

Accepted Answer

Actuating signal

Question 4

Name two advantages for having multiple computers in the loop.

Accepted Answer

1) Multiple subsystems can time share the controller.
2) Simple software changes can be made to adjust the controller

Question 5

Name three major design criteria for control systems.

Accepted Answer

Stability, transient response, and steady-state error

Question 6

Name the two parts of the system's response.

Accepted Answer

Steady-state and transient

Question 7

Physically, what happens to a system that is unstable?

Accepted Answer

It follows a growing transient response until the steady state response can't be seen.  The system will eventually destroy itself, reach equilibrium, or hit limiters.

Question 8

Instability is attributed to what part of the total response?

Accepted Answer

The transient response

Question 9

Describe a typical control system analysis task.

Accepted Answer

Evaluate a system's transient response and steady-state error to determine if they meet the desired specifics.

Question 10

Describe a typical control system design task.

Accepted Answer

If the steady-state error and transient response do not meet the requirements for the system, the system's parameters would need to be changed and/or components would need to be added.

Question 11

Adjustments to the forward path gain can cause changes in the transient response. True or False?

Accepted Answer

True

Question 12

Name three approaches to mathematical modeling of control systems.

Accepted Answer

Transfer function
State-space
Differential equation

Question 13

What mathematical model permits easy interconnection of physical systems?

Accepted Answer

Transfer function

Question 14

To what classification of systems can the transfer function be best applied?

Accepted Answer

Linear Time-invariant

Question 15

What assumption is made concerning initial conditions when dealing with transfer functions?

Accepted Answer

Initial conditions are set to 0

Question 16

Why do transfer functions of mechanical networks look identical to transfer functions for electrical networks?

Accepted Answer

There are direct analogies between electrical variables/components and mechanical variables/components.

Question 17

The motor's transfer function relates armature displacement to armature voltage. How can a transfer function that relates load displacement and armature voltage be determined?

Accepted Answer

Multiply the transfer function by the gear ratio relating position of armature to position of load.

Question 18

Summarize the steps taken to linearize a nonlinear system.

Accepted Answer

1. Recognize the nonlinear component.
2. Write a nonlinear differential equation.
3. Select equilibrium solution.
4. Linearize the nonlinear differential equation.
5. Laplace transform the new equation.
6. Find the transfer function.

Question 19

Give two reasons for modeling a system in state space.

Accepted Answer

1. Systems do not have to be modeled with linear, constant coefficients.
2. Can be digitally simulated.

Question 20

State an advantage of the transfer function approach over the state space approach.

Accepted Answer

You get a better sense of what is going on with the system with qualitative insight.

Question 21

An eighth-order system would be represented in state space with how many state equations?

Accepted Answer

8

Question 22

If the state equations are a system of first-order differential equations whose solution yields the state variables, then the output equation performs what function?

Accepted Answer

If forms linear combinations of state variables and the input to form the desired output.

Question 23

What is meant by linear independence?

Accepted Answer

None of the variables can be written as a linear sum of any of the other variables.

Question 24

What factors influence the choice of state variables in any system?

Accepted Answer

1. Linear independence
2. The number of state variables must agree with the order of the differential equation that describes the system.
3. Difficulty in obtaining the state equations.

Question 25

What is a convenient choice of state variables for electrical networks?

Accepted Answer

The variables being differentiated in each linearly independent energy storage element (such as the inductor current and capacitor voltage).

Question 26

What is meant by the phase-variable form of the state equation?

Accepted Answer

The state variables are successive derivatives.

Question 27

Name the performance specification for first order systems.

Accepted Answer

Time constant

Question 28

What does the performance specification for first-order systems tell us?

Accepted Answer

The time for the step response to reach 67% of the final value.

Question 29

In a system with input and output, what poles generate the steady-state response?

Accepted Answer

Input pole

Question 30

In a system with input and output, what poles generate the transient response?

Accepted Answer

System poles

Question 31

The imaginary part of the pole generates what part of a response?

Accepted Answer

Radian frequency of a sinusoidal response.

Question 32

The real part of a pole generates what part of a response?

Accepted Answer

Time constant of an exponential response.

Question 33

What is the difference between the natural frequency and the damped frequency of oscillation?

Accepted Answer

Damped frequencies have poles on the real axis or between the real and imaginary
Natural frequency has poles only on the imaginary and is the frequency with all damping removed.

Question 34

If a pole is moved along the radial line extending from the origin, what will the responses have in common?

Accepted Answer

If it is along the imaginary line, damped frequency will remain the same.
If it is along the real line, they will exist under the same exponential decay envelope.

Question 35

List five specifications for a second-order under damped system.

Accepted Answer

1. Natural Frequency
2. Damping ratio
3. Rise time
4. Peak time
5. % Overshoot
6. Settling time

Question 36

For a second-order under damped system, how many specifications completely determine the response?

Accepted Answer

2

Question 37

Name two conditions under which the response generated by a pole can be neglected.

Accepted Answer

1. The pole's real part is significantly larger than dominant poles
2. The pole is near a zero

Question 38

Does the solution of the state equation yield the output response of the system?

Accepted Answer

No, the output equation must be used to find the output response.

Question 39

Name a major advantage of using time domain techniques for the solution of the response.

Accepted Answer

Computer simulation is possible

Question 40

Name a major advantage of using frequency domain techniques for the solution of the response.

Accepted Answer

Pole-zero concepts give an intuitive feel for the problem.

Question 41

What three pieces of information must be given in order to solve for the output response of the system using state space techniques.

Accepted Answer

1. State equations
2. Output equations
3. Initial value of the state vector

Question 42

How can the poles of a system be found from the state equations?

Accepted Answer

Det(sI-A) = 0

Question 43

Name the four components of a block diagram for a linear time-invariant system.

Accepted Answer

Signals, systems, summing junctions, and pick-off points.

Question 44

Name three different forms of interconnecting subsystems and for each of the forms, state how the equivalent transfer function is found.

Accepted Answer

Cascade form: Ge(s)=G3(s)G2(s)G1(s)
Parallel form: Ge(s)=+-G3(s)+-G2(s)+-G1(s)
Feedback form: Ge(s)=G(s)/[1+-G(s)H(s)]

Question 45

For a simple, second-order feedback control system of the type shown, describe the effect that variations of forward path gain, K, have on the transient response.

Accepted Answer

As K varies, the poles move through the three ranges of operation of a second-order system: over damped, critically damped, and under damped.  Under damped system's settling time remains constant.

Question	Answer
Name three applications for feedback control systems.	Guided missiles Fighter plane stability Satellite tracking antenna
Name three reasons for using feedback control systems and two for not.	Pro: remote control, power gain, and parameter conversion Con: complex and expensive
If the error signal is not the difference in input and output, by what general name can we describe the error signal?	Actuating signal
Name two advantages for having multiple computers in the loop.	1) Multiple subsystems can time share the controller. 2) Simple software changes can be made to adjust the controller
Name three major design criteria for control systems.	Stability, transient response, and steady-state error
Name the two parts of the system's response.	Steady-state and transient
Physically, what happens to a system that is unstable?	It follows a growing transient response until the steady state response can't be seen. The system will eventually destroy itself, reach equilibrium, or hit limiters.
Instability is attributed to what part of the total response?	The transient response
Describe a typical control system analysis task.	Evaluate a system's transient response and steady-state error to determine if they meet the desired specifics.
Describe a typical control system design task.	If the steady-state error and transient response do not meet the requirements for the system, the system's parameters would need to be changed and/or components would need to be added.
Adjustments to the forward path gain can cause changes in the transient response. True or False?	True
Name three approaches to mathematical modeling of control systems.	Transfer function State-space Differential equation
What mathematical model permits easy interconnection of physical systems?	Transfer function
To what classification of systems can the transfer function be best applied?	Linear Time-invariant
What assumption is made concerning initial conditions when dealing with transfer functions?	Initial conditions are set to 0
Why do transfer functions of mechanical networks look identical to transfer functions for electrical networks?	There are direct analogies between electrical variables/components and mechanical variables/components.
The motor's transfer function relates armature displacement to armature voltage. How can a transfer function that relates load displacement and armature voltage be determined?	Multiply the transfer function by the gear ratio relating position of armature to position of load.
Summarize the steps taken to linearize a nonlinear system.	1. Recognize the nonlinear component. 2. Write a nonlinear differential equation. 3. Select equilibrium solution. 4. Linearize the nonlinear differential equation. 5. Laplace transform the new equation. 6. Find the transfer function.
Give two reasons for modeling a system in state space.	1. Systems do not have to be modeled with linear, constant coefficients. 2. Can be digitally simulated.
State an advantage of the transfer function approach over the state space approach.	You get a better sense of what is going on with the system with qualitative insight.
An eighth-order system would be represented in state space with how many state equations?	8
If the state equations are a system of first-order differential equations whose solution yields the state variables, then the output equation performs what function?	If forms linear combinations of state variables and the input to form the desired output.
What is meant by linear independence?	None of the variables can be written as a linear sum of any of the other variables.
What factors influence the choice of state variables in any system?	1. Linear independence 2. The number of state variables must agree with the order of the differential equation that describes the system. 3. Difficulty in obtaining the state equations.
What is a convenient choice of state variables for electrical networks?	The variables being differentiated in each linearly independent energy storage element (such as the inductor current and capacitor voltage).
What is meant by the phase-variable form of the state equation?	The state variables are successive derivatives.
Name the performance specification for first order systems.	Time constant
What does the performance specification for first-order systems tell us?	The time for the step response to reach 67% of the final value.
In a system with input and output, what poles generate the steady-state response?	Input pole
In a system with input and output, what poles generate the transient response?	System poles
The imaginary part of the pole generates what part of a response?	Radian frequency of a sinusoidal response.
The real part of a pole generates what part of a response?	Time constant of an exponential response.
What is the difference between the natural frequency and the damped frequency of oscillation?	Damped frequencies have poles on the real axis or between the real and imaginary Natural frequency has poles only on the imaginary and is the frequency with all damping removed.
If a pole is moved along the radial line extending from the origin, what will the responses have in common?	If it is along the imaginary line, damped frequency will remain the same. If it is along the real line, they will exist under the same exponential decay envelope.
List five specifications for a second-order under damped system.	1. Natural Frequency 2. Damping ratio 3. Rise time 4. Peak time 5. % Overshoot 6. Settling time
For a second-order under damped system, how many specifications completely determine the response?	2
Name two conditions under which the response generated by a pole can be neglected.	1. The pole's real part is significantly larger than dominant poles 2. The pole is near a zero
Does the solution of the state equation yield the output response of the system?	No, the output equation must be used to find the output response.
Name a major advantage of using time domain techniques for the solution of the response.	Computer simulation is possible
Name a major advantage of using frequency domain techniques for the solution of the response.	Pole-zero concepts give an intuitive feel for the problem.
What three pieces of information must be given in order to solve for the output response of the system using state space techniques.	1. State equations 2. Output equations 3. Initial value of the state vector
How can the poles of a system be found from the state equations?	Det(sI-A) = 0
Name the four components of a block diagram for a linear time-invariant system.	Signals, systems, summing junctions, and pick-off points.
Name three different forms of interconnecting subsystems and for each of the forms, state how the equivalent transfer function is found.	Cascade form: Ge(s)=G3(s)G2(s)G1(s) Parallel form: Ge(s)=+-G3(s)+-G2(s)+-G1(s) Feedback form: Ge(s)=G(s)/[1+-G(s)H(s)]
For a simple, second-order feedback control system of the type shown, describe the effect that variations of forward path gain, K, have on the transient response.	As K varies, the poles move through the three ranges of operation of a second-order system: over damped, critically damped, and under damped. Under damped system's settling time remains constant.

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