1. Abstract—In this lab, students characterized the performance
of PID and bang-bang control schemes in a motor/flywheel system.
Using LabVIEW, students added onto the LabVIEW file used in
the first lab to accommodate for closed loop PID and bang-bang
control. Using the data collected in LabVIEW, the performance of
both PID and bang-bang control were analyzed. In the next part
of the lab, students were askedto “feel” the PID gains by adjusting
the gains in LabVIEW and feeling the resistance from the
flywheel. Lastly, students were askedto tune theirmotor/flywheel
system to reduce error in the system using the manual tuning
method and the Ziegler-Nichols tuning method.
Index Terms—bang-bang, closed-loop, PID, Ziegler-Nichols
tuning method
I. INTRODUCTION
HIS lab tasked students with characterizing the
performance of both closed-loop PID control and closed-
loop bang-bang control. PID stands for proportional-integral-
derivative and is the most commonly used closed-loop control
system. Bang-bang is a simpler control method that also uses
closed-loop feedback to minimize feedback error in the system.
Students experimented with both control systemschemes using
the motor/flywheel systemand LabVIEW. The motor/flywheel
system is comprised of the motor/flywheel (the part of the
motor that spins), a motor controller (that controls the motors
position), a power amp (that powers the motor), a rotation
sensor(that outputs a voltage value that represents the motor’s
position), a tachometer (that outputs a voltage value that
represents the motor’s angular velocity) and a DAQ (the
interface between the system and the computer with
LabVIEW).
After the DAQ is wired to system, a square wave bang-bang
controller is used to control the system using three different
command efforts (C). After this is done, a square wave PID
controller is used with increasing proportional gain values to
control the system.This is done until the systemgoes unstable.
Next, students determined the “feel” of the PID gains by
adjusting the gains and qualitatively determining the resistance
of the flywheel when opposing motion is applied to the
flywheel.
Lastly, students were asked to tune their systemto minimize
error using a manual tuning method and the Ziegler-Nichols
tuning method.
II. PROCEDURE
PID/bang-bang control
A. PID control
The formula used for a PID controller is as follows:
𝑢(𝑡) = 𝑘 𝑝 𝑒(𝑡) + 𝑘 𝑑 𝑒̇( 𝑡) + 𝑘𝑖 ∫ 𝑒(𝑡)𝑑𝑡
𝑡
𝑡−𝑇
(1)
Where 𝑢(𝑡) is the command signal, 𝑘 𝑝 is the proportional gain,
𝑘 𝑑 is the derivative gain, 𝑘𝑖 is the integral gain and 𝑒(𝑡) is the
error defined as:
𝑒(𝑡) = 𝜃𝑑𝑒𝑠𝑖𝑟𝑒𝑑 (𝑡) − 𝜃𝑎𝑐𝑡𝑢𝑎𝑙 (𝑡) (2)
Where 𝜃𝑑𝑒𝑠𝑖𝑟𝑒𝑑 (𝑡) is the desired motor rotation and 𝜃𝑎𝑐𝑡𝑢𝑎𝑙 (𝑡)
is the actual motor rotation.
B. Bang-bang control
Bang-bang control is a simpler control method that adds
command effort when the error term is positive and subtracts
command effort when the error term is negative.The bang-bang
control law is as follows:
𝑢(𝑡) = {
+𝑐, 𝑒(𝑡) > 0
−𝑐, 𝑒(𝑡) < 0
(3)
Application ofeach control systemto the motor/flywheel system
In order to implement each control method into the
motor/flywheel system, the DAQ must first be wired to each of
the systemcomponents. With LabVIEW, students select which
control method is used by implementing a case structure that
contains both controlschemes.Afterthe desired controlmethod
is selected, the frequency is set to 0.25 Hz and the amplitude is
set to 90 degrees.The first method used is the bang-bang control
method. In order to control the systemwith this method, three
different command effort values (0.05, 0.25 and 1.0) are used
and data is recorded for each.
The next method used is the PID control method using only
a proportional gain term. This is done in a similar fashion to the
bang-bang controllerexcept that instead ofthe systemreceiving
a specific command effort as an input, the system receives a
Lab 2: PID and Bang Bang Control Comparison
Ballingham, Ryland
Section 7042 10/6/16
T

2. <Section 7042_Lab2> Double Click to Edit 2
2
proportional gain value. The proportional gain value is set three
different values (0.0001, 0.0005 and 0.001) and data is recorded
for each of the values. After this is done, the proportional gain
is increased until the system becomes unstable and the
associated gain is recorded.
Determining “feel” of PID gains
The “feel” of the gains is a qualitative assessment ofhow the
system responds when an opposing motion is applied to the
flywheel. In order to perform this task, the magnitude is set to
zero as well as the derivative and integral gains. The
proportional gain is then set to 0.0001 and then the flywheel is
manually rotated by the students and system response is felt.
The proportional gain is then increased by factors of 10, 100
and 1,000 and the system response is felt. This is done in a
similar fashion for the derivative gain. The derivative/integral
gains are done in a similar fashion. For the derivative gain, the
numerical derivative and tachometer input are used to compute
the error and the feel of each is assessed. For the integral gain,
the points to integrate overis assessedat 30 and then at 200 and
then compared.
Tuning the PID controller
A. Manual tuning method
The goal of manual tuning is to reduce rise time, overshoot
and steady-state error. This is done by increasing the
proportional gain until the output starts to oscillate. This gain
value is then divided in half to obtain the quarter amp decay.
Next, the integral gain is increased until the offset is corrected.
Lastly, the derivative gain is increased to reduce overshoot and
excessive response [1].
B. Ziegler-Nichols tuning method
The steps to perform the Ziegler-Nichols tuning method is
described in [2]. Essentially, students manually turn the
flywheel and release it until the systemgoes unstable and then
they slowly decrease the proportional gain value until the
systemhas a stable, oscillatory response.This gain value is 𝐾𝑢.
The associated period of one cycle of this oscillation is 𝑃𝑢. The
following equations showhowthe gains can be calculated from
these parameters.
𝐾𝑝 = 0.60𝐾𝑢 (4)
𝐾𝑖 =
2𝐾𝑝
𝑃𝑢
(5)
𝐾𝑑 =
𝐾𝑝 𝑃𝑢
8
(6)
III. RESULTS
TABLE I
MEAN/STANDARD DEVIATION OF ERROR/COMMAND SIGNALS
Control
scheme
Mean,
error
Standard
deviation,error
Command,
error
Command,
standard.
deviation
Bang-bang
(C=0.05)
3.45 86.83 0.05 0
Bang-bang
(C=0.25)
-1.88 85.89 0.25 0
Bang-bang
(C=1.0)
4.94 73.65 1 0
PID
(Kp=0.0001)
11.84 89.24 0.009 5.11E-05
PID
(Kp=0.0005)
-1.14 56.83 0.018 0.022
PID
(Kp=0.001)
-2.47 59.39 0.033 0.050
Manual
tuning
0.137 52.41 0.0003 0.111
Ziegler-
Nichols
tuning
6.06 59.14 0.004 0.234
TABLE II
ROOT-MEAN SQUARE VALUES
Control
Scheme
Error, rms Command, rms
Bang-bang
(C=0.05)
86.90 0.05
Bang-bang
(C=0.25)
85.91 0.25
Bang-bang
(C=1)
73.82 1.0
PID
(Kp=0.0001)
90.02 0.009
PID
(Kp=0.0005)
56.84 0.028
PID
(Kp=0.001)
59.44 0.059
Manual-
tuning
52.41 0.111
Ziegler-
Nichols
tuning
59.46 0.145
TABLE III
RISE-TIME/OVERSHOOT VALUES
Control
Scheme
Rise-time (s) Overshoot (deg)
Bang-bang
(C=0.05)
0.281 156.78
Bang-bang
(C=0.25)
0.279 162.76
Bang-bang
(C=1)
0.262 167.89
PID
(Kp=0.0001)
N/A N/A
PID
(Kp=0.0005)
0.406 -11.26
PID
(Kp=0.001)
0.537 11.07
Manual-
tuning
0.348 5.09
Ziegler-
Nichols
tuning
0.378 8.11

3. <Section 7042_Lab2> Double Click to Edit 3
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TABLE IV
TUNING VALUES
Tuningmethod 𝐾𝑝 𝐾𝑑 𝐾𝑖
Manual tuning 0.002 0.0002 0
Ziegler-
Nichols
0.00235 0.0125 0.000110
Fig. 1. Motor rotation/command signal vs. time for C=0.05
Fig. 2. Motor rotation/command signal vs. time for C=0.25
Fig. 3. Motor rotation/command signal vs. time for C=1.0
Fig. 4. Motor rotation/command signal vs. time for Kp=0.0001 (No visual
system response)
Fig. 5. Motor rotation/command signal vs. time for Kp=0.0005
Fig. 6. Motor rotation/command signal vs. time for Kp=0.001

4. <Section 7042_Lab2> Double Click to Edit 4
4
Fig. 7. Motor rotation/command signal vs. time manual tuning
IV. DISCUSSION
A. Root Mean Square of mean/standard deviation for
error/command signals
Table I shows all the values for mean and standard
deviations of the error and command signals. From table II, it
can be seen that with increasing command effort for the bang-
bang controller, the root mean square of the error signal
decreases. For the PID controller, with increasing
proportional gain, the root mean square of the error signal
decreases up until a proportional gain value of 0.005 and then
it increased. The formulas used to find these values can be
found in the appendix section
B. Bang-bang vs. PID comparison
The bang-bang and PID controllers performed much
differently. From figs 1-3, it is clear that the bang-bang
controller is much more erratic in behavior as it always has
large oscillations around the desired command signal. Because
of this, bang-bang controllers can’t compensate for steady-state
error in an efficient fashion. For bang-bang controllers,
overshoot is always going to be a problem since the controller
is either on or off. There is no condition for a bang-bang
controller in which the error is zero.
The PID controller has much a smoother operation than the
bang-bang controller as seen in figs 4-7. The PID controller is
better at compensating for rise-time, stability and steady-state
error as it has proportional gain term that is used to manipulate
rise-time, a derivative gain term for adjusting the stability of the
system and an integral gain term that focuses on reducing
steady-state error.
C. Control effort magnitude effect
When the control effort magnitude is increased for the
bang-bang controller, the rise-time decreases and the percent
overshoot increases. With large effort values,the systemgoes
unstable.
D. Effect of proportional gain value on system performance
The larger the proportional gain value, the faster the rise-
time and the more likely that overshoot will occur. If the gain
value is increased to a value too large, the system will go
unstable. This systemwent unstable at 𝐾𝑝 = 0.015.
E. “Feel” of PID gains
The higher the 𝐾𝑝 value, the more the flywheel resist manual
movements in a linear fashion (the more force used to turn to
the flywheel, the more it resists the motion). This is because the
proportional gain is proportional to position. The higher 𝐾𝑑
value, the more the flywheel fights against manual hand
movements in an incremental fashion (The faster the flywheel
is rotated, the more it resists the motion). This is because the
derivative gain is proportional to the velocity of the flywheel.
For 𝐾𝑖, there was no visual response until 𝐾𝑖 was increased to
1. From there 𝐾𝑖 was gradually decreased until the flywheel
could be manually turned without risk of injury. The system
response seemed very slow. It doesn’t resist manual hand turns
initially, but after some time the flywheel resistance gradually
increases with time. This because the error term is being
integrated over a long time interval thus the errors of position
are becoming greater and greater.
F. Tuning method Comparison
The manual tuning method had betterresults and was easier
to implement. The manual tuning method was less intricate
and allowed for the system to be tuned in a more visual
manner. The Ziegler-Nichols method was much more time
consuming as well. Table IV shows the results forboth tuning
methods.
V. CONCLUSION
A. Bang-bang vs. PID
PID is a better way to control the motor flywheel systemdue
to its less erratic behavior. Bang-bang control seems to be much
too crude to have effective closed-loop control for the
motor/flywheel system. Since PID control has gains that can be
adjusted, it is much easier to fine tune a system properly to
increase rise time, yet decrease overshoot and steady-state
errors.
B. Manual tuning vs. Ziegler-Nichols tuning
In the lab, manual tuning yielded better results than Ziegler-
Nichols tuning. This is likely because there is less error
propagation using manual tuning as it is a less arbitrary tuning
method and it is more simple to implement.
C. Ways to improve lab
Unfortunately, while performing the lab the motor that was
being used kept overheating.This was frustrating as the there
was a large amount of down time waiting for the motor to cool
off. If the lab had a better way of keeping the motors cool it
would be highly beneficial to lab efficiency.
APPENDIX
.
𝐸𝑟𝑟𝑜𝑟𝑅𝑀 𝑆 = √ 𝑀𝑒𝑎𝑛 𝐸𝑟𝑟𝑜𝑟2 + 𝑆𝑇𝐷 𝐸𝑟𝑟𝑜𝑟2 (7)
𝐶𝑜𝑚𝑚𝑎𝑛𝑑 𝑅𝑀𝑆
= √ 𝑀𝑒𝑎𝑛 𝐶𝑜𝑚𝑚𝑎𝑛𝑑 2 + 𝑆𝑇𝐷 𝐶𝑜𝑚𝑚𝑎𝑛𝑑2
(8)
REFERENCES
[1] Wikipedia, “PID Controller”, 2016 [Online].
Available: https://en.wikipedia.org/wiki/PID_controller. Accessed: Oct
7th
, 2016
[2] LabAssignment 2, S. Banks, 2016