The significance of the CLCE roots was seen in the Routh table which predicted closed loop
instability
marginal stability
all of these
stability
The significance of the CL poles is through their relationships to time domain parameters:
all of these
rise time
percent overshoot
time constant
settle time
The special form of the CLCE for making a root locus by hand is
1+k*n(s)/d(s)=0
The root locus procedure allows us to
design a controller that will yield a CL system with the desired performance
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where n(s)=0 are plotted on the root locus plot as
O's
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where d(s)=0 are plotted on the root locus plot as
X's
The root locus lies on the real axis to the left of an _____ number of X's and O's that lie on the real axis.
odd
The number of root locus segments is the number of
X's
Root locus segments begin at the ___, and begin means where k=0.
X's
As k increases the root locus segments go from the ____ to the _____, if there are the same number of O's as X's.
X's, O's
When there are more X's than O's, some of the root locus segments go to infinity along straight line segments called asymptotes.
True
The number of asymptotes is the number of ____ minus the number of _____.
X's, O's
When RL segments leave the real axis, they go in smooth arcs (usually circular) to the asymptotes or back to the real axis.
True
Sometimes that are more O's than X's.
false
If there is one asymptote, it will go to infinity
down the negative-real axis
If there are two asymptotes, they will go
up and down, parallel to the imaginary axis.
Asymptotes are symmetrical about the ___ axis.
real
All asymptotes for one system will intersect at the same point on the real axis, called the asymptote centroid.
Truee
The asmyptote centroid (sigma) = [ ( sum of the X's ) - ( sum of the O's ) ] / [ (number of X's) - (number of O's) ]
True
Break-away and break-in points are calculated from n*d'=d*n'
True
ANGLE OF DEPARTURE OR ARRIVAL: The sum of all the angles from the ___ MINUS the sum of all the angles from the ___ is equal to an odd multiple of 180 degrees.
O's, X's
The differentiator transfer function -0.4s/(0.02s+1) is due to capacitor and resistors around the differentiator opamp.
True
Gain3 is 3.75 due to
both of these
feedback capacitor around the integrator opamp
input resistor to the integrator opamp
A description of each figure is also important.
True
Figure numbers with titles are important for each figure.
True
Individual labels for each trace are necessary if printed on a black and white printer.
True
Several things have to be set in the MATLAB script for simulink to run.
False
The simulation step size of 0.02 seconds is specified in ___ and used in ___.
Simulink, simulink
The servomotor system (actual servomotor) is used in this lab.
false
The motor/amplifier transfer function and output pot transfer function are determined from
earlier labs
The ADDITIONAL derivative and integral gains are determined from
none of these
the previous lab
MATLAB
Simulink
If the PID output never exceeds plus or minus 1.25 volts, then the response will be linear
True
Which component makes the model nonlinear?
saturation
The output shaft transfer function is simulated as a
constant
The motor/amplifier is simulated as a ____-order transfer function.
1st
Differentiator part of the PID is selected or not by a
switch in simulink
Integrator part of the PID is selected or not by a
switch in simulink
The integrator and differentiator are implemented by
s-domain transfer function
Square wave and triangle wave signals are generated in ____ and used in ____.
Simulink, simulink
This lab simulates step and ramp responses of the servomotor system using PID, PD, and P controllers.
True
The integrator part of a PID controller can be implemented using an opamp with a
capacitor in the feedback path.
The derivative part of a PID controller can be implemented using an opamp with a
capacitor between the input signal and the opamp input.
The proportinal part of a PID controller can be implemented using an opamp with a
non-inverting or inverting configuration.
The integrator and differentiator time-domain effects ____independent.
are not
Increasing integral gain of a PID controller _______ overshoot.
increases
Increasing integral gain of a PID controller ______ steady state error.
decreases
Increasing derivative gain of a PID controller ______ overshoot.
possibly decreases
Increasing proportional gain of a PID controller ______ settle time.
increases
Increasing proportional gain of a PID controller _____ overshoot.
increases
Increasing proportional gain of a PID controller _____ steady-state error.
decreases
The pole in the transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) is/are
at the origin
The zeros in the transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) are
two real or a complex conjugate pair
The transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) has ___ zero(s) and ____ pole(s).
2,1
The transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) is a ____ controller, if Kp, and Kd are non-zero, and Ki is zero.
PD
The transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) is a ____ controller, if Kp, and Ki are non-zero, and Kd is zero.
PI
The transfer function (G(s) = Kd*(s^2 + (Kp/Kd)*s + (Ki/Kd)) / s) is a ____ controller, if Kp, Ki, and Kd are non-zero.
PID
The transfer function (G(s) = Kp + Kd*s) is a ____ controller
PD
The transfer function (G(s) = Kp + Ki/s) is a ____ controller.
PI
The transfer function (G(s) = Kp + Ki/s + Kd*s) is a ____ controller.
PID
The PID controller has three control operations in
parallel
The SS error for a unit parabola input is ____ for a type-2 system.
1/Ka where Ka=s^2*G(s)|(s=0)
The SS error for a unit parabola input is ____ for a type-1 system.
infinity
The SS error for a unit parabola input is ____ for a type-0 system.
infinity
The SS error for a unit ramp input is ____ for a type-2 system
0
The SS error for a unit ramp input is ____ for a type-1 system.
1/Kv where Kv=s*G(s)|(s=0)
The SS error for a unit ramp input is ____ for a type-0 system.
infinity
The SS error for a unit step input is ____ for a type-2 system.
0
The SS error for a unit step input is ____ for a type-1 system.
0
The SS error for a unit step input is ____ for a type-0 system.
1/(1+Kp) where Kp=G(s)|(s=0)
In determining SS errors, does it matter what N(s) in the forward transfer function G(s)?
yes, if there are free factors of s
Which of the following is the forward transfer functions of a unity feedback closed loop system, which is known as a type-2 system:
G(s) = N(s) / ( s^2(s+1)(s+2)
Which of the following is the forward transfer functions of a unity feedback closed loop system, which is known as a type-1 system:
G(s) = N(s) / ( s(s+1)(s+2)(s+3)(s+4) )
Which of the following is the forward transfer functions of a unity feedback closed loop system, which is known as a type-0 system:
G(s) = N(s) / ( (s+1)(s^2+4s+13) )
Which of the following is a unit parabola function?
R(s)=1/s^3
Which of the following is a unit ramp function?
R(s)=1/s^2
Which of the following is a unit step function?
R(s)=1/s
Which of the following is a unit parabola function?
r(t)=t^2/2
Which of the following is a unit ramp function?
r(t)=t
Which of the following is a unit step function?
r(t)=1
The angle of departure or arrival is calculated by adding all the angles from the X's minus the sum of all the angles from the O's which is equal to an ___ multiple of 180 deg.
odd
The angle of departure or arrival is calculated relative to a point on the RL that is ______the complex X or O.
as close as possible to
Angles of departure and angles of arrival are always measured relative to the ____ axis direction
positive real
The angle that a RL segment arrives at a complex O is called
angle of arrival
The angle that a RL segment leaves a complex X is called
angle of departure
When two X's are a complex conjugate pair, the two RL segments
still leave the X's
When there are more X's than O's, some of the root locus segments go to infinity along straight line segments called asymptotes.
True
As k increases the root locus segments go from the ____ to the _____, if there are the same number of O's as X's.
X's, O's
Root locus segments begin at the ___, and begin means where k=0.
X's
The number of root locus segments is the number of
X's
The root locus lies on the real axis to the left of an _____ number of X's and O's that lie on the real axis.
odd
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where d(s)=0 are plotted on the root locus plot as
X's
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where n(s)=0 are plotted on the root locus plot as
O's
The root locus procedure allows us to
design a controller that will yield a CL system with the desired performance
The special form of the CLCE for making a root locus by hand is:
1+k*n(s)/d(s)=0
The significance of the CL poles is through their relationships to time domain parameters:
all of these
rise time
percent overshoot
time constant
settle time
The significance of the CLCE roots was seen in the Routh table which predicted closed loop
all of these
instability
marginal stability
stability
A root locus is a plot of
both of these
poles of the CLTF
roots of the CLCE
Break-away and break-in points are calculated from n*d'=d*n'
True
The asmyptote centroid (sigma) = [ ( sum of the X's ) - ( sum of the O's ) ] / [ (number of X's) - (number of O's) ]
True
All asymptotes for one system will intersect at the same point on the real axis, called the asymptote centroid.
True
Asymptotes are symmetrical about the ___ axis.
real
If there are two asymptotes, they will go up and down, parallel to the imaginary axis.
True
If there is one asymptote, it will go to infinity down the negative-real axis.
True
Sometimes that are more O's than X's.
False
When RL segments leave the real axis, they go in smooth arcs (usually circular) to the asymptotes or back to the real axis.
True
The number of asymptotes is the number of X's minus the number of O's.
True
When there are more X's than O's, some of the root locus segments go to infinity along straight line segments called asymptotes.
True
As k increases the root locus segments go from the X's to the O's, if there are the same number of O's as X's.
True
Root locus segments begin at the O's, and begin means where k=0.
false, RL segments begin at the X's
The number of root locus segments is the number of X's.
True
The root locus lies on the real axis to the left of an ODD number of X's and O's that lie on the real axis.
True
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where d(s)=0 are plotted on the root locus plot as X's.
True
The CLCE is 1+k*n(s)/d(s)=0, and the values of s where n(s)=0 are plotted on the root locus plot as X's.
false, roots of n(s) are plotted with O's
The root locus procedure allows us to design a controller that will yield a CL system with the desired performance.
True
The special form of the CLCE for making a root locus by hand is 1+k*n(s)/d(s)=0.
True
The significance of the CL poles is through their relationships to time domain parameters:
all of these
rise time
percent overshoot
time constant
settle time
The significance of the CLCE roots was seen in the Routh table which predicted closed loop
all of these
instability
marginal stability
stability
CLTF=Closed Loop Transfer function. CLCE=Closed Loop Characteristic Equation. A root locus is a plot of
both of these p
oles of the CLTF
roots of the CLCE
The Routh-table procuedure was very useful in 1905, and even with today's calculators, it continues to be very useful.
True
A Routh table with a whole row of zeros (initially) will have ____ CLTF poles.
jw-axis
The number of unstable CLTF poles is the number of ______ in the first column of the Routh table.
sign changes
When the Routh table is completed, the number of CLTF poles ____ can be determined.
all of these
in the LHP
on the jw axis
in the RHP
Alternative-Routh table procedures are
required when a zero shows up in the first column
The right-hand column of each determinant is always the elements of the columns
above and to the right
The left-hand column of each determinant is always the ______ column of the previous two rows.
first
Every calculated entry in the Routh table is the negative determinant of entries in the previous two rows divided by the entry in the first column
of the row directly above the calculated row.
Are there any calculated entries in the first two rows of the Routh table
no, because they come directly from D(s)
Every entry in the Routh table starting with the third row is calculated from the
previous two rows
The second row of the Routh table contains all the other coefficients of D(s) that are not in the first row.
true, and in decreasing powers of s like the first row
The top row of the Routh table contains every other coefficient of D(s), where CLTF=N(s)/D(s).
True
The top row of the Routh table (first column) contains the coefficient of the highest power of s
True
The CLTF=N(s)/D(s). The coefficients of D(s), ordered from highst to lowest, are placed in the top ______ of the Routh table.
two rows
The number of columns in the Routh table is _____ number of terms in the denominator of the CLTF.
half the
The Routh table has row _____ starting at the top with highest power (s^n) and continuing all the way down to the lowest (s^0)
labels
In 1905, Routh-Hurwitz showed how to determine the number of closed loop poles in the left-half plane, right-half plane, and on the jw axis.
True
The question of closed loop stability is easily determined by the location of the closed loop poles.
True
Marginally stable closed loop poles are located in the complex plane
on the jw axis
Unstable closed loop poles are located in the complex plane
in the right-half
Stable closed loop poles are located in the complex plane
in the left-half
The significance of the closed loop poles is that they can be used to predict time-domain performance (settle time, rise time, percent overshoot) for stable systems.
true, and are called stable poles
The CLTF = N(s)/D(s), and the equation D(s)=0 can be formed. The values of s that satisfy D(s)=0 are the
all of these and D(s)=0 is known as the closed loop characteristic equation
The closed loop transfer function (CLTF) can be represented as N(s)/D(s), where the roots of D(s) are the _____ of the CLTF.
poles
The closed loop transfer function (CLTF) is a(n) _____-domain concept.
s
f.9070 Square or triangle signal to main summing junction
YZ
fig 9070
If you want a PI controller, set the
derivative-gain pot to zero only
fig 9070
If you want a PD controller, set the
integral-gain pot to zero and short the integrator caps
fig 9070
f,g,h, and i connect any signal on the control panel to the simulated oscilloscope channels in the Espial program
True
fig 9070
Output of PID controllers to Power Amp
Le
fig 9070
Main summing junction to PID controllers
ac
fig 9070
Proportional controller to summing junction
IJ
fig 9070
Integrator controller to summing junction
FH
fig 9070
Differentiator controller to summing junction
SU
fig 9070
Main-summing juction to 360-deg output pot
kb
fig 9070
Triangle-wave signal
WX
fig 9070
Square-wave signal
VX
fig 9070
Integrator caps in series. Do not connct to
E
fig 9070
Differentiator caps in series. Do not connect to
O
fig 9070
Integrator caps in parallel
CG
fig 9070
Differentiator caps in parallel
NP
fig 9070
Opamp-summing junction feedback for 360deg-output pot & input signal (square or triangle)
ad
fig 9070
Opamp-summing junction feedback for PID-controllers
KL
fig 9070
Integrator-opamp feedback
FG
fig 9070
Differentiator-opamp feedback
ST
fig 9060
If non-inverting transfer functions are required, then a simple solution for all the configurations in Fig9060 is
cascade with an inverting opamp
fig 9060
All the transfer functions in Fig9060 have negative signs because
the single-opamp is an inverting configuration
fig 9060
Can lag and lead active-circuits be constructed using series Rs and Cs instead of parallel Rs and Cs?
yes
fig 9060
A passive-circuit realization has
only passive components (R and C), and no opamps
fig 9060
Gc(s) is the transfer function in Fig9060 of the active-circuit realization using one opamp in Fig9060B.
True
fig 9060
Ia(s) is _____ in Fig9060B.
zero
fig 9060
Z1(s) is the ______ impedance in Fig9060B.
input
fig 9060
Z2(s) is the ______ impedance in Fig9060B.