Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Dynamics and Control > Exam II > Flashcards

Exam II Flashcards

1
Q

What does SISO stand for and what type of classification is it?

A

single input, single output; control

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What does MIMO stand for and what type of classification is it?

A

multiple input, multiple output; control

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What type of controller has remedial control?

A

feedback

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What type of controller has predictive control?

A

Feedforward

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Because it requires some time, control is considered what kind of process?

A

dynamic

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What kind of control logic helps control non measurable outputs?

A

Inferential

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is an example of inferential control?

A

you can measure the variable B to control variable A knowing that A=f(B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

An open looped system is not being what?

A

controlled

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What hardware is used for a FB control loop?

A

Process
Sensor or measuring device
Transmission line (pneumatic or electrical)
Controller
Final control element (or ACTUATOR, ie, valve)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What piece of hardware is neglected in dynamics?

A

Transmission line

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

In what general way do FB controllers differ?

A

they differ in the way they correlate epsilon(t) (error) with c(t) (actuating signal)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are the three control laws?

A

Proportional action

Proportional-Integral action

Proportional-Integral-Derivative action

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is the control action equation for Proportional control?

A

c(t)=Kc*epsilon(t)+cs

constitutive equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

For proportional control, what does Kc equal?

A

Proportional gain

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

For proportional control, what does cs equal?

A

Bias signal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

For proportional control, if epsilon(t)=0, what does cs represent?

A

actuating signal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is sometimes used in place of the proportional gain and what is the equation for it?

A

proportional band

PB=100/Kc

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

For proportional control, the higher the Kc the higher this is to the error signal.

A

sensitivity of the controller

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

For proportional control, what is the constitutive equation in the deviation form?

A

C(s) = Kc * E(s)

Y G F

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

The P controller can reduce this but it cannot cancel it unless Kc is very very high

A

the error

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is the constitutive equation for PI control?

A

c(t) = Kc * epsilon(t) + (Kc/tau I) * integral of (epsilon(t) dt) + cs

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

In integral control, c(t) is proportional to this of the error.

A

time integral

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What memory does the integral controller have?

A

past values of error

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

For PI what does tau I represent?

A

integral time constant

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

What is an adjustable parameter that falls between 0.1 and 50 minutes?

A

tau I

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

PI can eliminate even small what?

A

errors

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

The PI action lasts as long as there is a what?

A

non-zero error (can make the action very slow)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Because the integral action can make the action very slow it is never what?

A

used alone

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

What is the transfer function of a P controller?

A

Gc(s) = Kc

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

What is the transfer function of a PI controller?

A

Gc(s) = Kc {1 + [1 / (tauI * s)]}

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

The transfer function of a PI controller is not what, and is a function of what?

A

constant; s

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

What is the constitutive equation for a PID controller?

A

c(t) = Kc * epsilon(t) + (Kc/tau I) * integral of (epsilon(t) dt) + (Kc * tau D * (depsilon/dt)) + cs

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

In the derivative control, c(t) is proportional to what?

A

the derivative of the error

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

For derivative action, as the error increases what happens?

A

The D action compensates it without waiting for it to become to high

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Derivative control is what kind of control?

A

anticipatory

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

What does tau D represent?

A

derivative time constant

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

In derivative control, if the error changes suddenly, what could happen?

A

the actuating signal can be very strong and the system would become too sensitive (or it would yield a large control action, although it is not needed).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

What is the transfer function for a PID controller?

A

Gc(s) = Kc ( 1 + (1 /( tau I * s)) + tau D * s

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

What do you multiply the transfer function of a PID controller by to get it into standard form?

A

s

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

What does the final control action do? (Actuators)

A

receives c(t) and adjusts the manipulated variable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

The final control element is usually a what?

A

a valve

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

What can valves control?

A

flow rate, temperature, level, composition, …..

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
43
Q

What is the equation of a linear actuator?

A

f(x) = x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
44
Q

What is the equation of a square root actuator?

A

f(x) = sqrt (x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
45
Q

What is the equation of an equal percentage actuator?

A

f(x) = alpha ^ (x-1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
46
Q

What is the equation of a hyperbolic actuator?

A

f(x) = 1 / (alpha - (alpha - 1)x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
47
Q

What is the equation for volumetric flow?

A 
Q = Cv * f(x) * sqrt( delta p / rho)
where Cv is the flux constant
delta p is the pressure density
rho is the density
x is the degree of opening (position of the stem)
0 <= x <= 1
f(x) = the valve characteristic curve 
0 <= f(x) <= 1
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
48
Q

What kind of valve is commonly used and controlled by compressed air?

A

pneumatic

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
49
Q

If air supply is lost, a pneumatic valve will do either this or that?

A 
remain open (fail open)
or 
will close (fail closed)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
50
Q

A valve being fail open or fail closed depends on what?

A

safety requirements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
51
Q

What is the force balance?

A

F = m (d^2 * x / dt^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
52
Q

mechanical action on the valve - elastic force - viscous resistance is equal to what?

A

mass times acceleration

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
53
Q

mechanical action is defined how?

A

pressure * area

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
54
Q

elastic force is defined how?

A

k * x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
55
Q

viscous force is defined how?

A

viscosity coefficient * (dx/dt)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
56
Q

What is the transfer function of a valve?

A

(A/k) / ( (m/k) s^2 + (viscosity coefficient / k) s + 1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
57
Q

Valves behave as a what order system?

A

second order

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
58
Q

If the mass of the stem is small the mass term can be eliminated making the system what order?

A

first order

G(s) = (A/k) / ((viscosity coefficient/k) s + 1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
59
Q

What can be pneumatic or electrical?

A

Transmission lines

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
60
Q

Unless the transmission line is very long, the dynamic behavior of a pneumatic transmission line can be what?

A

neglected

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
61
Q

Electrical signals are very what?

A

fast

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
62
Q

Globally, a FB- controlled process has how many inputs and how many outputs?

A

2; 1

set point + distrubance); (y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
63
Q

For the dynamic behavior of FB controlled processes, what has inputs and outputs?

A

each component (process, sensor, controller, actuator)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
64
Q

What does each component have?

A

its own transfer function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
65
Q

What is the transfer function of the process?

A

Y(s) = Gp(s) * M(s) + Gd(s)*D(s)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
66
Q

What is the transfer function of the sensor?

A

Ym(S) = Gm(s) * Y(s)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
67
Q

What is the transfer function of the controller?

A

C(s) = Gc(s) * E(s)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
68
Q

What is the transfer function of the actuator?

A

M(s) = Gf(s) * C(s)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
69
Q

What is the final value of Y(s) for a closed loop?

A

Y(s) = ((Gp(s) * Gf(s) * Gc(s))/(Gp(s) * Gf(s) * Gc(s) * Gm(s) + 1)) * Ysp(s)
+
(Gd(s) / (Gp(s) * Gf(s) * Gc(s) * Gm(s) + 1)) * D(s)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
70
Q

The closed-loop function gives the closed-loop what?

A

response of the process

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
71
Q

In closed loop transfer functions, what is the same?

A

the denominators

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
72
Q

What is the denominator?

A

the product of the transfer functions in the loop + 1 (everything but Gd(s))

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
73
Q

In Servo control problems what is changed and what is omitted?

A

set point is changed but there is no distrubance

74
Q

In Regulator control problems what does not change?

A

the set point but a disturbance acts on the system

75
Q

Servo problems drive the process along a what?

A

trajectory

76
Q

Regulator problems suppress what?

A

the effect of disturbances

77
Q

What equation gives the poles for a FB controlled process?

A

Gp(s) * Gf(s) * Gc(s) * Gm(s) + 1 = 0

78
Q

How is the dynamic behavior described if the poles are real and negative?

A

over-damped

79
Q

How is the dynamic behavior described if the poles are complex?

A

oscillatory

80
Q

How is the dynamic behavior described if the poles have a positive real part?

A

control makes the process unstable

81
Q

To determine the effect of a controller what two terms are typically set equal to 1?

A

Gm and Gf

82
Q

For P control, what does Gc equal?

A

Kc

83
Q

For P control what does Y(s) equal?

A

Y(s) = ((Gp(s) * Kc) / (Gp(s) * Kc + 1)) Ysp(s) + (Gd(s) / (Gp(s) * Kc + 1)) D(s)

84
Q

What does Gp equal for first order systems?

A

Gp = Kp / (taup * s + 1)

85
Q

What does Gd equal for first order systems?

A

Gd = Kd / (taup * s + 1)

86
Q

Does a P controller change the order of a system?

A

no

87
Q

For a first order system under P control the time constant is (reduced/increased)?

A

reduced

88
Q

For a first order system under P control the response is (faster/slower)?

A

faster

89
Q

For a first order system under P control the static gains have been (decreased/increased)?

A

decreased

90
Q

What does a P controller add?

A

offset

91
Q

What does offset equal?

A

setpoint - actual final response

92
Q

for P control if you take the limit has time approaches infinity of y(t) what does it equal?

A

Kd’ which is not zero (here is the offset)

93
Q

What is the closed loop response of a P-FB controlled second order system?

A

Y(s) = (Kp’ / (tau’^2 * s^2 + 2 * zeta’ * tau’ * s + 1)) Ysp (s)

94
Q

What does tau ‘ equal for a second order P-FB controlled system?

A

tau / sqrt(Kc * Kp + 1)

95
Q

What does zeta’ equal for a second order P-FB controlled system?

A

zeta / sqrt (Kc * Kp + 1)

96
Q

What does K’p equal for a second order P-FB controlled system?

A

(Kc * Kp) / (Kc * Kp + 1)

97
Q

What does tau ‘ equal for a first order P-FB controlled system?

A

taup / (Kc * Kp + 1)

98
Q

What does K’p equal for a first order P-FB controlled system?

A

(Kc * Kp) / (Kc * Kp + 1)

99
Q

What does K’d equal for a first order P-FB controlled system?

A

Kd / (Kc * Kp +1)

100
Q

the closed loop response of a 2nd order system under P control remains what?

A

second order

101
Q

The static gain (increases/decrease) for a 2nd order system under P control?

A

decreases

102
Q

The natural period of oscillation (tau) (increases/decreases for a 2nd order system under P control?

A

decreases

103
Q

The damping factor (increases/decrease) for a 2nd order system under P control?

A

decreases (which can be undesirable)

104
Q

We can find the final response using what?

A

final value theorem

105
Q

What is the final value theorem?

A

y (t = infinity) = limit as s approaches 0 of sY = K’p = (Kc * Kp) / (KcKp + 1)

106
Q

for a unit step change what is the offset?

A

(new set point which is the unit step change) - (actual response of the response) = 1 - ((Kc * Kp) / (Kc * Kp + 1)) = 1 / (Kc * Kp + 1)

107
Q

What does the offset go to if Kc goes to infinity?

A

zero

108
Q

zeta ‘ is (>) zeta?

A

less than

109
Q

an overdamped process can become what when it is P controlled?

A

underdamped

110
Q

generally tau’ and zeta’ do what with increasing Kc under P control?

A

decrease

111
Q

If the proportional gain increases what happens to the system?

A

the system becomes faster, the offset decreases, but it may start to oscillate

112
Q

The effect of I control on the system does what to the order of the system?

A

increases it by one

113
Q

For a servo problem with I control where the system is first order, what does Y(s) equal?

A

Y(s) = (1 / (tau^2 * s^2 + 2 * zeta * tau * s + 1)) Ysp(s)

114
Q

For a servo problem with I control where the system is first order, what does tau equal?

A

tau = sqrt((taup * tauI) / (Kp * Kc))

115
Q

For a servo problem with I control where the system is first order, what does zeta equal?

A

zeta = (1/2) * sqrt (tauI / (taup * Kp * Kc))

116
Q

The closed loop response of a 1st order system under I control (increases/decreases) its order?

A

increases

117
Q

1st order system under I control increases the order which makes the response more what?

A

sluggish

118
Q

a 1st order system under I control eliminates what?

A

offset

119
Q

We can find the the final response of a 1st order system under I control using the final value theorem. For a unit step change, what does y(t=infinity) =?

A

= limit as s approaches zero of s * Y = 1

120
Q

A rule of thumb is that if the gain of a controlled process is 1 there is no what?

A

offset

121
Q

The form of a closed loop response for I controlled systems depends on what three variables?

A

zeta, tauI, and Kc

122
Q

As tauI decreases for an I controlled system the response becomes (faster/slower) and the behavior can be (nonoscillating/oscillating)

A

faster; oscillating

123
Q

Increasing the integral action (increasing Kc and decreasing tauI) makes the closed-loop response more what?

A

sensitive

124
Q

As the integral action increases the overshoot of the closed loop response does what?

A

increases

125
Q

What is one of the most common controllers?

A

PI

126
Q

What kind of problem do we used to test the effect a control will have?

A

servo

127
Q

The effect of PI control (increases/decreases) the order of the system?

A

increases

128
Q

For a first order PI controlled system what happens to the offset?

A

eliminated

129
Q

For a first order PI controlled system the integral action does what to the closed-loop response?

A

slows down due to increasing the order

130
Q

For a first order PI controlled system as Kc increases and tauI decreases, the response becomes what?

A

faster but more oscillatory?

131
Q

Why do we use a PI controller?

A

To eliminate the offset

132
Q

Does D control stabilize the system?

A

yes

133
Q

Does the order stay the same when affected by D control?

A

yes

134
Q

The time constant increases with the addition of D control which causes what?

A

a slower closed-loop response

135
Q

The D action does not have any effect on what?

A

the set point

136
Q

If there is a step change in the set point of a D controlled system, the system reacts at t = 0 and then does what?

A

returns to the original steady state

137
Q

With D control, when a regulator problem is considered, what does y(t) do?

A

goes to the same final value of the system if there was no control but slowly

138
Q

What effect does D control have on the oscillations of a second order system?

A

stabilizes against oscillations (reduces oscillations)

139
Q

what does D control do to the damping factor?

A

increases it

140
Q

What effects does a PID control have on the response of a controlled system?

A 
order increases (integral action)
instability due to increasing Kc is stabilized
offset is eliminated (due to integral action)
141
Q

If a process parameter can vary into a range, which controller can you use?

A

P-FB can be used alone

142
Q

If the process must assume a well defined value which controller can you use?

A

PI or PID FB (offset is eliminated)

143
Q

If the system is complex which controller should you use? (higher order)

A

PID stabilizes oscillations (does not increase the order relative to the PI-controlled system)

144
Q

What controller would be used for liquid level control at the bottom of a distillation column?

A

P control alone

145
Q

What controller would be used to control flow rate that must take on a prescribed value and the control action should take place in a reasonable time (immediate action not needed)

A

PI

146
Q

What controller would be used if it needs to act quickly?

A

PID

147
Q

What units typically have a PID?

A

oven, reactors

temperature and composition control

148
Q

What are the three tunable controller parameters?

A

Kc, tau I, and tau D

149
Q

What is the Lyapunov stability criterion?

A

A linear system is defined stable if, for any given bounded input, it produces a bounded output

150
Q

Bounded input/output remain confined between what?

A

an upper and lower limit

151
Q

Poles that exhibit positive real parts give rise to what terms which produce what?

A

ci * e^(pi*t); unstable behaviors

152
Q

A FB controlled system is stable if all the roots of Gp(s) * Gf(s) * Gc(s) * Gm(s) + 1 = 0 have what?

A

a negative real part

153
Q

If any of the coefficients of the denominator set equal to zero are negative there is at least one what?

A

root with a positive real part

154
Q

If all of the coefficients of the denominator set equal to zero are positive we can use what to determine stability?

A

the Routh array

155
Q

How do you tune the controller parameters?

A

using either local/simple or integral performance criteria

156
Q

What are simple/local performance criteria?

A

criteria that use only a few points of the response

157
Q

What are integral performance criteria?

A

criteria that use the entire closed-loop response

158
Q

What do we minimize to design a robust control system?

A

overshoot
rise time
decay ratio

159
Q

Warning! the satisfaction of a single condition does not guarantee what?

A

that the closed loop response is the desired one

160
Q

We can pick parameters that minimize which errors?

A

Integral of the square error (ISE)
Integral of the absolute value of the error (IAE)
Integral of the time-weighted absolute error (ITAE)

161
Q

Which integral performance criteria should you use to suppress large errors?

A

ISE because the errors are squared and thus contribute more to the value of the integral

162
Q

Which integral performance criteria should you use to suppress small errors?

A

IAE because the square of small numbers is an even smaller quantity

163
Q

Which integral performance criteria should you use to suppress errors that persist over time?

A

ITAE because the presence of t in the integral amplifies the effect of even small errors

164
Q

Who devised a semi-empirical method which relies on both simple/local performance and integral performance criteria?

A

Cohen and Coon

165
Q

When a step change of amplitude A in the actuating signal c(t) takes place, the system’s response, ym (also called the reaction curve) is sigmoidal and can be approximated by the response of what?

A

A first order system with dead time

166
Q

In the Cohen-Coon method, what three parameters do you work with?

A

K, td, tau

167
Q

In the Cohen-Coon method, what does K equal?

A

B/A where A is the amplitude of the step

168
Q

In the Cohen-Coon method, what does tau equal?

A

B/sigma where sigma is the slope of the tangent line of the sigmoidal curve section best fit by a line

169
Q

What best values of the controller parameters did Cohen and Coon use?

A

One quarter decay ratio
minimum offset
minimum ISE

170
Q

What parameters are present for P control using the Cohen Coon method?

A

Kc = (tau/(Ktd))(1 + (td/(3tau)))

171
Q

What parameters are present for PI control using the Cohen Coon method?

A

Kc =(tau/(Ktd))(0.9 + (td/(12tau)))

tau I = td ((30 + 3(td/tau))/(9 + 20(td/tau))

172
Q

What parameters are present for PID control using the Cohen Coon method?

A

Kc = (tau/(Ktd))((4/3) + (td/(4tau)))
tau I = td ((32 + 6(td/tau))/(13 + 8(td/tau))
tau D = td (4/ (11 + 2*(td/tau)))

173
Q

What does cascade control do?

A

takes multiple measurements before acting on the manipulated variable
example (temperature control for a CSTR)

174
Q

Cascade control is only good if the disturbance effects the measured control how?

A

directly

175
Q

When K = B/A what is B? what is A?

A 
B = the asymptotic response of the system found by plotting y(t)
A = the amplitude of the disturbance
176
Q

Using experimental data, what should you treat the Cohen-Coon model as?

A

a first order system with dead time

177
Q

Fitting procedures are only what?

A

approximated

178
Q

Using a few points is more rigorous and precise than what?

A

fitting

179
Q

When you have to valves in parallel what are they called?

A

1 is called master and the other the slave

180
Q

Be aware that welding points are what?

A

critical points

Dynamics and Control (2 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions