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Dynamics and Control > Exam I > Flashcards

Exam I Flashcards

1
Q

Why is process control important?

A 
Guarantee Safety
Meet product specifications
Control emissions 
Meet operational constraints 
Optimize process economics
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2
Q

What should process controls do?

A

Suppress the influence of external disturbances
Ensure process stability
Optimize the process performance

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3
Q

When is a process defined as linear?

A

If a positive or negative input change produces a proportional change in the output, although the sign of the output change can be different.

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4
Q

How are inputs defined in controls?

A

The effect of the surroundings on the system.

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5
Q

How are outputs defined in controls?

A

The effect of the process on the surroundings.

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6
Q

What are two types of inputs?

A

Manipulated and disturbances

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7
Q

What are two types of disturbances?

A

Measured and unmeasured

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8
Q

What variable that is part of a process does control act on?

A

Manipulated variable

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9
Q

What is the principle of feed back control?

A

Feedback control is corrective

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10
Q

What is the principle of Feedforward control?

A

Feed forward control is predictive

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11
Q

If feed can be controlled by a valve it is a ________.

If feed can not be controlled it is a ________.

A

Manipulated variable; output

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12
Q

Outputs are measurable if we have appropriate what?

A

Instrumentation.

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13
Q

If the error signal equals zero, what control action is required?

A

None

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14
Q

If the error signal is greater than zero than the measured variable is _______ than expected.

A

Lower

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15
Q

If the error signal is less than zero the measured variable is _____ than expected.

A

Higher.

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16
Q

Step 1 the control does what?

A

Measures variable

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17
Q

Step two the controller does what?

A

Compare the variable (v) with the set variable (vs)

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18
Q

What describes a system, a process apparatus, a device, a chemical plant, etc, with one ore more equations?

A

mathematical model

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19
Q

We use mathematical models to predict what?

A

For a given change in the input, what is the corresponding change in the output

what is the dynamic behavior of a system, before it reaches steady state

what is the new steady state

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20
Q

What are models based on?

A

The principles of conservation (mass, energy, momentum) + constitutive equations

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21
Q

With lumped parameter models process variables are not a function of what?

A

spatial coordinates

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22
Q

What are some examples in which you would use a lumped parameter model

A

CSTR reactor, where composition and temperature distributions are uniform

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23
Q

Generally lumped parameter models are what?

A

macroscopic

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24
Q

With distributed parameter models process variables are a function of what?

A

spatial coordinates (and time)

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25
Q

What are some examples in which you would use a distributed parameter model?

A

PFR reactor, where properties change along the coordinate z.

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26
Q

Generally distributed parameter models can be what?

A

microscopic

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27
Q

You need to make sure that the number of equations matches the number of what?

A

unknowns

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28
Q

What is an example of an EOS

A

Pv=nRT

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29
Q

What is an example of a transport equation?

A

Q=UA(Tinf - T)

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30
Q

What is an example of a reaction rate?

A

R=(koe^(E/RT)Ca

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31
Q

A mathematical model is a system of what?

A

equations

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32
Q

If you have one independent variables what kind of equations do you use?

A

ODE

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33
Q

If you have two or more independent variables what kind of equations do you use?

A

PDE

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34
Q

Models can be linear or what?

A

nonlinear

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35
Q

Differential equations describe what?

A

the time evolution of a given system

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36
Q

A mathematical model has to be what?

A

flexible

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37
Q

A mathematical model should be able to describe what?

A

the dynamic state of a process, as well as its steady state

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38
Q

At steady state, time derivatives are what?

A

0

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39
Q

At steady state, derivatives with respect to the spatial coordinates may not be what?

A

0

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40
Q

ODEs contain derivatives with respect to what?

A

one independent variable

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41
Q

What is the control law with respect to heat flow?

A

Q=Qs - alpha e

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42
Q

As alpha increases it never goes to what?

A

zero (this logic does not work! have to run experiments!)

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43
Q

f’(xo) represents what in a Taylor series?

A

the slope of the line

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44
Q

before time 0 we should assume that xo equals what?

A

xs

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45
Q

What is the physical meaning of the deviation variable?

A

the departure of that variable from steady state

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46
Q

The Laplace transform is what kind of operator?

A

linear

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47
Q

The Laplace exists if what?

A

the integral above takes a finite value

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48
Q

What is a Laplace transform?

A

a transformation of the function f from the time domain to the s-domain, where s is a generic complex variable

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49
Q

Laplace transforms help develop what?

A

input/output models

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50
Q

Laplace transforms help predict what?

A

how a process reacts to external disturbances

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51
Q

What is the mathematical representation of a step input?

A

F(s)= a/s

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52
Q

In a unit impulse, what does F(s) equal?

A

1

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53
Q

a unit impulse can be defined mathematically as what?

A

d(step)/dt

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54
Q

a ramp can be defined mathematically as what?

A

the integral (step) dt

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55
Q

What kind of step is defined by F(s) = (a/s)(1-e^(-deltats))

A

rectangular

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56
Q

What kind of pulse is define as F(s) = (aw/(s^2+ w^2))

A

sinusoidal pulse

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57
Q

For systems that are not perfectly mixed describe the translated functions

A

if f is advanced f(t+to) —-> Laplace e^(sto)F(s)
if f is normal f(t)—–> Laplace F(s)
if f is delayed f(t-to)—–> Laplace e^(-sto)F(s)

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58
Q

what is td?

A

the time delay or dead time

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59
Q

With Laplace what disappears?

A

derivatives and integrals

60
Q

We can compute f(t) at t = infinity if we know what?

A

its Laplace transform at t=0 (final value theorem)

61
Q

We can compute f(t) at t=0 if we know its Laplace at t equals what?

A

infinity (Initial value theorem)

62
Q

What is the patch to solving differential equations using the Laplace transform?

A

linearize differential equations in the time domain
algebraic equations in the s domain
solution (expressed in the time domain)

63
Q

the zeroes of the numerator are called what?

A

zeros

64
Q

the zeroes of the denominator are called what?

A

poles

65
Q

Which Heaviside Theorem do you use if your poles are real and distinct?

A

1

66
Q

For denominators of a polynomial 3 how many terms would you expect?

A

3

67
Q

What theorem do you use if your poles are real but repeated with a multiplicity of q?

A

Heaviside 2

68
Q

What theorem would you use if your poles are complex?

A

Heaviside 3

69
Q

What are the generalized equations used in Heaviside Theorem 3?

A 
F(s) = N(s)/D(s) = N(s)/(Q(s)[((s-a)^2)+b^2]
f(t) = (e^(at)/b)(Psi(i) cos (bt)+ Psi(r) sin (bt))

where b is the positive imaginary part of the pole.

70
Q

When the system is initially at steady-state at t=0 what are y and its derivatives equal to?

A

zero

71
Q

G(s) is equal to what mathematically?

A

Y(s)/F(s)

72
Q

What is the physical meaning of the transfer function?

A

The laplace transform of the output in the deviation form / The Laplace transform of the input in deviation form

73
Q

Systems with multiple inputs and 1 output are the sum of what?

A

The transfer functions

74
Q

Gi is the transfer function that does what?

A

relates the output of the process to each of the inputs

75
Q

The order of the denominator has to be what of the numerator?

A

greater or equal

76
Q

Distinct real poles give rise to what?

A

exponential factors that decay over time if p < 0 or grow grow exponentially if p > 0.

77
Q

If one pole is positive the system is what?

A

unstable

78
Q

based on the 2nd Heaviside Theorem, the polynomial term goes to what with time?

A

infinity

79
Q

The exponential terms in the 2nd heaviside theorem depend on what?

A

the pole being positive, negative, or zero

80
Q

If the pole is positive in the exponential term the term goes to what?

A

infinity

81
Q

if the pole equals zero in the exponential term the term goes to what?

A

1

82
Q

If the pole is negative in the exponential term the term goes to what?

A

zero

83
Q

For the third Heaviside Theorem, the behavior of the function is what and what does it depend on?

A

oscillating, the real part

84
Q

If the real part of a complex pole is greater than zero what happens?

A

you have exponentially growing sinusoidal behavior

85
Q

If the real part of a complex pole is less than zero what happens?

A

you have damped sinusoidal behavior( amplitude of oscillation decreases continuously)

86
Q

If the real part of a complex pole is equal to zero what happens?

A

Harmonic oscillation (constant amplitude)

87
Q

Poles located on the right side of the imaginary axis give rise to terms that do what?

A

grow to infinity with time

88
Q

if terms grow to infinity with time, the system is defined as what?

A

unstable

89
Q

Poles located on the left side of the imaginary axis give rise to terms that do what?

A

terms that decay to zero with time

90
Q

terms that decay to zero give rise to systems that are defined how?

A

stable

91
Q

If any of the coefficients are negative, there is at least one positive pole, the system is defined as what?

A

unstable

92
Q

If all coefficients are positive then you can test the system using what?

A

Routh Array

93
Q

The Routh array contains n+1 row, where n is the order of what?

A

the transfer function G(s)

94
Q

If any number in the first column of the Routh array are negative the system is what?

A

unstable

95
Q

The input/output relationship for any of the TF in the sequence is what?

A

G1 * G2 * G3 *….

96
Q

So the overall TF of a sequence is what?

A

The product of the TFs in the sequence

97
Q

The order of the denominator of a transfer function is the same as what?

A

the order of the differential equation from which it was derived

98
Q

What is Kp defined as?

A

steady-state gain

99
Q

What is tau p defined as?

A

time constant

100
Q

at steady state, what does Kp equal?

A

delta y/ delta f = change in the output/ change in the input at steady state

101
Q

What systems behave like first order systems?

A

tanks, mixers, isothermal CSTR with a 1 st order reaction

102
Q

What is the Laplace definition of an impulse of magnitude A?

A

A

103
Q

What is the Laplace definition of a step size of A?

A

A/s

104
Q

The smaller the tau p the system reaches a new steady state _______.

A

faster

105
Q

The larger the Kp the larger the what?

A

the final steady-state value of the output

106
Q

experimentally impose what kind of change because it is much easier to realize?

A

step

107
Q

The slope of the experimental dynamic data is what?

A

-t/tau p

108
Q

a ramp disturbance with a slope of a has an input transfer function defined how?

A

F(s) = a / (s^2)

109
Q

Are ramp systems self regulating?

A

No!

110
Q

What is an example of a system that exhibits a ramp disturbance?

A

membrane system

111
Q

tau decreases with increasing what?

A

h (heat transfer)

112
Q

what is one way you can increase h?

A

Use better material with higher heat transfer

113
Q

What is another way to decrease the time constant involved in heat transfer?

A

increase the area of thermocouple

114
Q

In heat transfer how is tau defined?

A

the capability to store energy times the resistance to transfer energy

115
Q

For volume level how is tau defined?

A

A/alpha where A is the capability to store liquid and 1/alpha is the resistance to flow

116
Q

In second order systems how many terms define the system?

A

3

117
Q

What are the terms that define a second order system?

A

tau, episilon, and K

118
Q

In a second order system what is the definition of tau

A

natural period of oscillation tau = 1/w w is the frequency of the oscillations

119
Q

In a second order system what is the definition of epsilon?

A

the damping factor, determines the shape of the dynamic response (oscillating, non oscillating)

120
Q

In a second order system what is the definition of Kp?

A

steady-state gain (how sensitive a system is to a stimulus)

121
Q

What processes can be described as 2nd order systems?

A

a series of two first order systems,

inherently second order systems that exhibit resistance to motion

controlled processes

122
Q

if epsilon is greater than one how can the poles be described and what is the system defined as?

A

2 distinct real poles, both negative; overdamped

123
Q

if epsilon is equal to one than how can the poles be described and what is the system defined as?

A

2 repeated poles, both negative; critically damped

124
Q

if epsilon is less than one how can the poles be described and what is the system defined as?

A

2 complex conjugate poles with negative real part; underdamped

125
Q

Critically damped systems respond faster than what?

A

overdamped systems

126
Q

the higher the order of the transform function the system is more what?

A

sluggish

127
Q

As epsilon increases the system becomes more what?

A

sluggish

128
Q

2 complex conjugate poles implies that the system will exhibit what with underdamped systems?

A

oscillations

129
Q

the negative real parts of an underdamped system relates how it what?

A

decays with time (oscillations)

130
Q

The underdamped response is initially what?

A

faster than the overdamped or critically damped responses.

131
Q

What is overshoot?

A

The phenomenon where an underdamped system exceeds by several times the steady state value.

132
Q

Overshooting can create what?

A

dangerous situations

133
Q

What is rise time?

A

The initial time to achieve steady state

134
Q

what is the decay ratio?

A

the amplitude of the second departure divided by the amplitude of the first

135
Q

What is the period of oscillation?

A

the time needed to complete 1 oscillation

136
Q

When designing a good controller, tau and epsilon need to be selected carefully, so that what?

A

overshoot is small, the rise time is short, and the decay ratio is small.

137
Q

A series of N first order systems gives rise to what order of system?

A

N-order

138
Q

As N increases, the system becomes more what?

A

sluggish

139
Q

If the system is controlled, the controller should help do what?

A

improve the speed of the system’s response

140
Q

Dead time shows up when you consider what kind of systems?

A

PFR, shell-and-tube heat exchangers, and plug flow systems

141
Q

A system exhibits inverse response if its transfer function has what?

A

any zero with positive real part (zeroes = roots of numerator)

142
Q

The zeroes of the numerator determine what?

A

whether an inverse response takes place

143
Q

the zeroes of the denominator deterime what?

A

the shape of the response and the stability

144
Q

What systems exhibit an inverse response?

A

reboilers

145
Q

Two first order, noninteracting systems in a series give rise to what kind of second order system?

A

Overdamped

Dynamics and Control (2 decks)

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