Indiana University – Purdue University Fort Wayne

Opus: Research & Creativity at IPFW

School of Engineering, Technology and Computer
Engineering Senior Design Projects
Science Design Projects

Fall 12-16-2013

Actively-Controlled Stabilization Platform for

Automobile Applications
Mohammad Sami Al Chllk

Jacob Kryder

Graehm Sack

John Scheurich

Follow this and additional works at: http://opus.ipfw.edu/etcs_seniorproj_engineering

Part of the Engineering Commons

Opus Citation
Mohammad Sami Al Chllk, Jacob Kryder, Graehm Sack, and John Scheurich (2013). Actively-Controlled Stabilization Platform for
Automobile Applications.
http://opus.ipfw.edu/etcs_seniorproj_engineering/54

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 Indiana University – Purdue University Fort Wayne
Department of Engineering

ECE 405 – ECE 406

Senior Design Project

Report #2

Project Title: Actively-Controlled Stabilization Platform for Automobile

Applications

Team Members: Mohammad Sami Al Chllk

Jacob Kryder
Graehm Sack
John Scheurich

Advisor: Dr. Hossein Oloomi

Date: December 16, 2013

Table of Contents

Index of Figures ............................................................................................................................ 2

Index of Tables ............................................................................................................................. 3
Acknowledgements ....................................................................................................................... 4
Abstract/Summary ........................................................................................................................ 5
Section I – Conceptual Design ...................................................................................................... 6
Section II – Prototype Fabrication ............................................................................................... 16
Section III – Prototype Testing .................................................................................................... 23
Section IV – Evaluation and Recommendations ......................................................................... 46
Section V - Conclusions .............................................................................................................. 48
References.................................................................................................................................. 50
Appendix 1 – Project Schedule ................................................................................................... 51
Appendix 2 – Testing Procedures ............................................................................................... 60
Appendix 3 – Microcontroller Programming Code ...................................................................... 62
Appendix 4 – MATLAB Scripts .................................................................................................... 67

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Index of Figures

Figure 1: Conceptual diagram of a gimbal table.................................................................................. 10

Figure 2: Simplified circuit diagram of a DC motor attached to the platform. ................................. 11
Figure 3: Simulink block diagram of the open loop motor system .................................................... 12
Figure 4: Modeling of the multi-feedback loop system ...................................................................... 13
Figure 5: Angular position calculation of the platform after the initialization sequence. .............. 13
Figure 6: Finished prototype ................................................................................................................... 14
Figure 7: Modified Motor bracket for the X-axis .................................................................................. 17
Figure 8: Bracket used for mounting the Y-axis motor ....................................................................... 18
Figure 9: The Y-axis motor mount ......................................................................................................... 19
Figure 10: Circuit Diagram ..................................................................................................................... 20
Figure 11: Angular position using the angle gauge. ........................................................................... 25
Figure 12: Determination of the accelerometer gain and bias in the x axis. .................................. 27
Figure 13: Determination of gyroscope gain and bias ....................................................................... 28
Figure 14: Step response in the Y-axis CCW acceleration ............................................................... 29
Figure 15: Gain calculated from accelerometer in the Y-axis CCW direction................................. 29
Figure 16: Step response in the Y-axis CW acceleration .................................................................. 30
Figure 17: Accelerometer gain in the Y-axis CW direction ................................................................ 30
Figure 18: Acceleration in the X-axis CCW direction.......................................................................... 31
Figure 19: Step response in the X-axis CW direction ......................................................................... 31
Figure 20: Gain calculation of the Accelerometer in the X-axis CW direction ................................ 32
Figure 21: Complementary filter response tracking ............................................................................ 33
Figure 22: Model of the Plant (Motor) ................................................................................................... 34
Figure 23: Full System with Controller .................................................................................................. 35
Figure 24: Impulse Response of X Axis................................................................................................ 36
Figure 25: Error on X Axis Produced by an Impulse .......................................................................... 37
Figure 26: Impulse Response of Y Axis................................................................................................ 38
Figure 27: Error on X Axis Produced by an Impulse .......................................................................... 39
Figure 28: Step Response of X Axis ..................................................................................................... 40
Figure 29: Error on X Axis Produced by a Step .................................................................................. 41
Figure 30: Step Response of Y Axis ..................................................................................................... 42
Figure 31: Error on Y Axis Produced by a Step .................................................................................. 43
Figure 32: Optimized Simulink Model of the Full System .................................................................. 44
Figure 33: Optimized Simulation of Impulse Response ..................................................................... 44
Figure 34: Optimized Simulation Step Response ............................................................................... 45

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Index of Tables

Table 1: Component Testing .................................................................................................................. 24

Table 2: Performance Requirements .................................................................................................... 25
Table 3: Range of Motion....................................................................................................................... 26
Table 4: Measurements Taken to Determine Gain of the Motor Driver ........................................... 34
Table 5: Constants Used for Simulation ............................................................................................... 34
Table 6: Controller Gain Constants ....................................................................................................... 35

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 Acknowledgements

We would like to thank Kerry Scheurich for fabrication feasibility analysis and support. His
technical knowledge and skill in aluminum fabrication and machining, along with his donated
time, were critical to the success of the development of the prototype fabrication.

We would also like to thank Gary Traxler for use of his machine shop which allowed us to
fabricate the prototype in a timely and cost-effective manner.

We would also like to thank Dr. Hossein Oloomi for his technical support and assistance without
which this project would not have been possible.

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 Abstract/Summary

During the operation of a vehicle, pitching and rolling cause surfaces in the interior of the vehicle
to deviate from level. This can cause driver inattention when an object within the vehicle, such
as a beverage, needs to be stabilized and level. Automatic control systems are used to provide
a desired output from a system during changing operating conditions without human
intervention. A common application of control systems is stabilization of a system throughout a
variety of changing environmental conditions.

By employing an automatic control system, a platform can be kept level during movement of the
vehicle. This can reduce driver inattention during demanding driving conditions. This stabilized
platform must be powered by the auto's electrical system, be lightweight and have a small
footprint so as to allow integration into the interior of an automobile.

This report covers the design process beginning with the implementation of the detailed
conceptual design selected in Report #1. In particular, this report covers the fabrication process
and software development, calibration and testing as well as evaluation and recommendations
for improvement.

5
 Section I

Conceptual Design

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To address the need for an actively-controlled stabilized platform within a vehicle occupant
compartment, a detailed design process determined the best conceptual design is a gimbal
table utilizing PMDC motors for actuation and relying on sensor feedback from an
accelerometer and a MEMS gyroscope. A detailed analysis of the conceptual design process
can be found in Report #1. This document addresses the implementation and refinement of the
prototype. This section contains a summary of the amended problem statement, requirements
and specifications, an overview of the subsystems, and the mathematical model.

Requirements and Specifications

To ensure a stabilization system with sufficient performance under the conditions that exist in
the intended application, the following requirements and specifications are set forth.

• System Response
o The control system shall maintain a level surface with a maximum of 10%
overshoot when subjected to a step input.
o The control system used must be able to perform corrections of 30˚ within 0.25
seconds.
o The steady state tracking error of the control system shall be no more than 5%.

• Range of Motion
The stabilized platform will have a minimum 60˚ range of motion on each rotational axis.

• Power Consumption
The maximum current draw of the system must be less than 15 amperes.

• Device Physical Characteristics

o To ensure the device does not encroach on occupant space, the footprint shall
be no more than 500 in3.
o The mass of the device shall be no more than 5 lbs.

• Load Capacity
To accommodate different types and sizes of objects, the platform shall handle an object
weight up to 2.0 pounds. This accommodates either a digital camera such as the Nikon
- D5100 weighing 1.2 lbs. or a 24 oz. beverage weighing approximately 1.7 lbs.

After carefully considering the proposed specifications for our stabilization system, the different
subsystems necessary for a stabilization system to operate were identified and investigated to
determine the most suitable options. These systems were identified as follows: power supply,
frame and platform, sensor, control system and drive system. The power supply must be able to
deliver power to the required subsystems either directly from the vehicle’s electrical system or
from a rechargeable battery source. The frame and platform contains the entirety of the device
and provides the surface which must be stabilized. The sensors determine the state of the
system and each sends a signal that describes that state. The control system interprets the
signals sent by the sensors and initiates an appropriate response, which also induces a

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feedback signal based on both sensors’ response. The drive system receives a signal from the
controller and responds accordingly by bringing the platform back to a stable position (i.e. level).
Neglecting any of these subsystems renders the device incapable of fulfilling its need.

Control Subsystem:
The control system is the computational center of the device. It must be able to detect when the
device is operating properly and correct that operation when it is not. The control system
receives a sensory signal and based on that signal prompts a response from the drive system.
That response is then re-sensed and fed back through the control system which creates a
feedback loop. This endless loop is what allows the stabilization device to constantly maintain a
level surface. As in most electrical systems there is a defining choice to make as to how a
system will send and receive signals, analogously or digitally.

A digital control system for this application requires the sensory input and driving output to be
converted to a digital signal. Some drive systems operate specifically on a pulse width
modulation (PWM) scheme, which is a digital communication scheme. The digital approach
allows for simple changes to be made throughout the design process through the programming
of the digital control device source code.

The digital system was selected primarily as it is a relatively cheap option where reasonably-
sized microcontrollers range from $20-$70. Additionally, with a digital system there is a wealth
of open source code which can be adapted, modified, and re-created to generate a working
digital control device. This provides additional savings in cost and manpower resources.

In order for the digital control system to work properly with any analog components it must be
interfaced accordingly. This requires additional signal processing. These additional steps
introduce an increased delay in the system response. This delay may cause detrimental device
behavior and must be accounted for when digital control schemes are being considered. In
particular, the data transmission rates and processing times are critical to the appropriate
response signal being sent from the controller. Code optimization is a key to limiting the
negative implications of the processing delay.

Drive Subsystem:
For the platform to be stable and also maintain a level surface, a method of controlled rotation
must be developed. The drive system of the platform receives signal commands from the
control system to rotate the surface along the two axes in order to maintain level orientation.
Many different methods of providing rotational motion were considered and the DC gear motor
was chosen.

DC gear motors are widely available with operational voltages between 3 V and 24 V.
Depending on the power and speed required, a motor that will produce satisfactory performance
is commercially available and a stock item. The PWM frequency used as a control signal is
configurable and based on duty cycle opposed to pulse width in time. This allows for a greater
resolution of control signal and a faster response. Many commercially available motor drivers

8
have a current sense feedback that expands the number of possible configurations of the
control system.

The impact of choosing DC gear motors is that the physical size of gear motors is typically
larger than servo motors. This results in an increased footprint of the system which may
adversely affect the performance of the system particularly in this application. Motor control
hardware must also be purchased for the application which results in added cost to the design
and added complexity in the source code.

Sensor Subsystem:
A major component of our device is the sensing system. In order for the control system to
determine the necessary corrections, there needs to be a constant stream of data indicating the
relative position and predictors of future position such as velocity and acceleration. The sensors
selected are the digital gyroscope and accelerometer.

Gyroscopes are effective in providing the necessary sensory feedback in the form of angular
velocity. The cost is relatively low and the resolution available is adequate for this project.
However, there are some drawbacks. Drift occurs over time as the integration error compounds
when determining the platform’s position. The sensor cannot determine the global level and
also changes in the levelness of the platform.

For this reason, an accelerometer is also used to provide feedback to the control system.
Accelerometers provide a low-cost solution to the sensory system requirements and
demonstrate flexibility in being either analog or digital models. Accelerometers can determine
the global level of the platform at start-up. Some design considerations for using
accelerometers are the resolution sensitivity particularly when gravity readings are important
and the adverse effect of high level of noise created when the vehicle is in motion.

MEMS Gyroscope

The gyroscope measures the angular velocity about a given axis. Micro-electro-mechanical
systems (MEMS) gyroscopes use the Coriolis Effect to measure the angular rate by utilizing a
tuning fork configuration. Two masses oscillate and move constantly in opposite directions.
When angular velocity is applied, the Coriolis force on each mass also acts in opposite
directions, which result in a change of capacitance. This differential value in capacitance is
proportional to the angular velocity and is then converted into output voltage for analog
gyroscopes or LSBs for digital gyroscopes. When linear acceleration is applied to two masses,
they move in the same direction. Therefore, there will be no capacitance difference detected.
The gyroscope will output zero-rate level of voltage or LSBs, which shows that the MEMS
gyroscopes are not sensitive to linear acceleration such as tilt, shock, or vibration. Supply
voltage can be between 3-5 V with the output is a low voltage signal either analog or digital.
Resolution is available from 2° to 25000°.

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Accelerometer

Tilt or inclination sensors utilize an accelerometer to determine position through gravitational

forces. Accelerometers are used to sense both static (e.g. gravity) and dynamic (e.g. sudden
starts/stops) acceleration. One of the more widely used applications for accelerometers is tilt-
sensing. Because they are affected by the acceleration of gravity, an accelerometer can be
used to determine its orientation with respect to the Earth's surface. A smaller full-scale range
means a more sensitive output; therefore more precise reading is output from an accelerometer
with a low full-scale range. A range of 1-2 g is appropriate for this application.

Accelerometers with an analog output will produce a voltage that is directly proportional to the
sensed acceleration. At 0 g, the analog output will usually reside at about the middle of the
supplied voltage (e.g. 1.65 V for a 3.3 V sensor).

Frame and Platform Subsystem:

The platform design is a gimbal table. Figure 1 below illustrates the interaction between
components. The platform is attached by pins to the first frame, which itself is attached to a
fixed second frame with pins. The first frame will allow the movement along the pitch axis, while
the other will allow the movement along the roll axis.

Second Frame

First Frame

Gimbal
Platform

Figure 1: Conceptual diagram of a gimbal table

This design minimizes the complication in the delivery of motor torque compared to other frame
systems. This design also yields a slightly smaller footprint with easily fabricated parts. An
additional design consideration is that the motors must not only provide the movement, but also
be able to maintain the position of the platform and handle the stress created by the weight of
the placed object on the platform. Motor interface with the frame requires more consideration
with respect to space constraints and mechanical connection issues.

Control System Modeling

For permanent magnet direct current (PMDC) motors, control is done by adjusting the armature
current. Motor speed is not controlled as the armature current is used to adjust the motor
shaft’s position.

The simplified circuit representation of the PMDC motor and actuator system is shown in Figure
2 below where:

va(t) = armature voltage (V)

ia(t) = armature current (A)

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Ra = armature resistance (Ω)
La = armature inductance (H)
vb(t) = back emf (V)
Tm = torque generated by the motor (N-m)
ωm= angular velocity of the motor shaft (rad/s)
θm= position of the motor shaft (rad)
Jm = moment of inertia of the rotor
Bm = viscous friction coefficient of the motor
T’m = net torque generated by the motor (N-m)
T”m = torque of the motor after gear reduction (N-m)
Tl = torque generated on the load (N-m)
ω l= angular velocity of the load(rad/s)
θ l= position of the load (rad)
Jl = moment of inertia of the load
Bl = viscous friction coefficient of the load
g1 = number of teeth of drive gear
g2 = number of teeth of driven gear

Figure 2: Simplified circuit diagram of a DC motor attached to the platform.

From Figure 2 above, the plant transfer function can be derived:

𝜃𝑙 (𝑠) 𝑛𝐾𝑡
=
𝑉𝑎 (𝑠) 𝑠[𝐿𝑎 𝐽𝑒𝑞 𝑠 + �𝐿𝑎 𝐵𝑒𝑞 + 𝑅𝑎 𝐽𝑒𝑞 �𝑠 + 𝑅𝑎 𝐵𝑒𝑞 + 𝐾𝑡 𝐾𝑏 ]
2

(1)

From this equation, the motor block diagram can be generated as shown below in Figure 3. A
reference voltage signal correlating to the angular velocity of the platform is input into the motor
system and summed with the back emf (vb) to generate the armature voltage to the motor. The
resulting torque produced by the motor (Tm) is summed with the input torque of the load (Tload) to
create the total torque (Te) on the system. Using the transfer function found in Equation 1, this
torque signal is then converted into the angular velocity of the motor shaft. Integrating and
multiplying by the gear ratio (n) results in the output signal correlating to the platform position.

11
Figure 3: Simulink block diagram of the open loop motor system

Understanding the input and output variables of the plant consisting of the motor, gearing and
platform, a block diagram of the entire system can be generated. The system consists of the
plant, controller, sensors and an amplifier as shown in Figure 4 below. A reference signal for
the initial angular position is input into the system and summed with the measured angular
position of the platform to generate an error signal. The error signal is conditioned by the
proportional-integral (PI) controller and then amplified. This voltage is then input to the motor
creating the desired torque to level the system. The angular velocity of the shaft is output from
the motor and amplified by the gear ratio to simulate the reading from the gyroscope sensor.
The shaft position is determined by the accelerometer and combined with the gyroscope
reading to generate the feedback signal. This value representing position of the platform is the
fed back into the summer to produce the error signal.

With the closed loop control system established, a transfer function can be created to reflect the
response of the controller. By considering an open circuit between the controller amplifier gain
(Ka) and the feedback signal of the gyroscope (Kg), the equation for this transfer function can be
created as shown below:

𝑛𝐾𝐾𝑎 𝐾𝑔
𝑇(𝑠) =
𝐿𝑎 𝐽𝑒𝑞 𝑠3 + �𝐿𝑎 𝐵𝑒𝑞 + 𝑅𝑎 𝐽𝑒𝑞 �𝑠 2 + �𝑅𝑎 𝐵𝑒𝑞 + 𝐾𝑏 𝐾𝑡 + 𝑛𝐾𝐾𝑔 𝐾𝑡 �𝑠 + 𝑛𝐾𝐾𝑎 𝐾𝑔

(2)

where K = system gain constant

Ka = accelerometer gain constant
Kg = gyro conversion constant

Based on hardware selection, the following variables are defined:

Kg = 0.000133 bits-s/ rad

Kt = 3.34 oz-in/ A
La = 1 mH
Ra = 1.17 Ω
Kb = 2.47 V/ krpm
Km = 3.09 oz-in/ W1/2

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Bm = 0.05 oz-in/ krpm
Jm = 0.00082 oz-in-s2
n = 30.9:1

The closed loop system can be modeled in Simulink as shown in Figure 4 below.

Figure 4: Modeling of the multi-feedback loop system

Sensor Data Processing

During the initial start, the system begins by reading the accelerometer and the microcontroller
integrates the reading to get the initial angle of the platform as shown in Figure 5 below. This
angle becomes the reference angle for the system. At this point the controller begins the steady
state process by reading the gyroscope and calculating any change in the angle of the platform.
Then the microcontroller reads the accelerometer and calculates the angle of the platform. Next,
the filtering algorithm calculates the estimated error and passes that value to the control
equations to generate the appropriate PWM duty cycle. Based on this PWM signal, the
necessary corrections to the X (roll) and the Y (pitch) axes are relayed to the motor. The
microcontroller repeats these steps until the system is powered off.

Figure 5: Angular position of the platform is calculated in a continuous loop process for each
axis after the initialization sequence.

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Mechanical Design
Material selection consists of aluminum sheet stock for the platform and a combination of
aluminum bar stock and aluminum angles for the frame system. The aluminum sheet was
selected to ensure adequate rigidity and durability of the platform throughout the device’s life
cycle.
Inner platform
rotates about
Y-axis

Sensors
mounted
underneath Y-axis motor

Microcontroller

Figure 6: Finished prototype

As shown in Figure 6 above, the two sensors are mounted to the underside of the platform as
close to the platform centroid as feasible. The gyroboard is stacked on top of the
accelerometer. The controller is mounted directly to the aluminum angle base.

For the remainder of this report, all data relative to the outer frame is referenced as the x
axis and the inner platform is considered to be the y axis.

14
15
 Section II

Prototype Fabrication

16
Hardware and Frame Components:
The mechanical components of the prototype platform were fabricated according to the drawing
packet contained the previous report. Minor issues such as missing dimensions and incomplete
hardware data were resolved verbally with the fabricator. The entire fabrication process took 42
man-hours and incurred a cost of $12 in shop supplies. There was no cost for labor, since the
fabricator donated his time to this project.

Several modifications were made to the detailed design previously put forth. These
modifications were limited to the mounting methods of the motors, to allow for adjustment of in
the location of the motors. The first change that was made was the motor that actuated
produced movement on the Y-axis. Instead of the motor being mounted to the external part of
the platform which would cause it to extend beyond the frame of the platform, it was moved to a
position directly under the platform. This was necessary for a control algorithm that is symmetric
about both axes. The face mount in the original detailed design was decided to be infeasible
due to the difficulty in screw-hole location in the fabricated bracket. While it was possible to
fabricate a bracket as such, this method does not allow for adjustment in the location of the
motor. The method chosen for mounting of the motors was to use a U-bolt that would clamp the
motor to a flat surface of a bracket. This allows for adjustment longitudinally and rotationally.
First, 18 gauge steel was bent up in an L-shape as seen in Figure 7. This shape of bracket was
used for the motor that controls the movement of the X-axis.

Figure 7: Modified Motor bracket for the X-axis

A similar bracket was bent up from the same material but in a U-shape for mounting of the Y-
axis motor. Figure 8 is an illustration of the bracket fabricated for the Y-axis motor.

17
Figure 8: Bracket used for mounting the Y-axis motor.

In initial tests of the platform, these motor brackets proved to have too much flex in them and
would result in too much extraneous movement of the platform. It was then decided the
brackets would have to be made of a stiffer material. These same brackets were fabricated out
of 3/16” mild steel. These brackets proved to be stiff enough so that all flex in the motor
mounting system was removed.

The next problem faced in fabrication was the mounting of the Y-axis motor. By mounting it to
the bottom of the platform, the weight of the motor and bracket produced a torque around the X-
axis. The resulted in an unbalanced load on the X-axis motor. This presented significant
difficulties in obtaining any sort of a stable system. It was then determined that a mounting
system would have to be created which the weight of the motor and bracket would have to be
supported by the frame and not be bared by any part of the platform itself. Figure 9 shows the
new Y-axis motor mount that is supported by the frame legs and rotates along the X-axis. These
were the only modifications to the structure of the platform.

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Figure 9: The Y-axis motor mount shown in black

Circuit Design
The components of the control system are the microcontroller, a motor driver to power the two
PMDC motors and the two sensors, a gyroscope and an accelerometer. As shown in Figure 10
below, the sytem power is provided to the motor driver which in turn powers the controller. The
sensors draw power from the microcontroller. Both sensors output directly to the microcontroller
via the Analog In pins located by the processor chip. The microcontroller in turn transmits a
PWM signal to the motor driver using the Digital pins located on the opposite side. The motor
driver converts the input signal frequency to one used by the motors and relays the
corresponding PWM signal to each motor. Connections between the sensors and controller are
soldered while stackable headers and terminal blocks are used to connect the motor driver with
the microprocessor.

19
Figure 10: Circuit Diagram shows the wiring connections from the microcontroller to the motor
driver and sensors.

The accelerometer is mounted directly to the underside of the platform as close to center as
possible. The gyroscope is stacked on it by using standoffs to mount the accelerometer and
screws to secure the gyroscope.

Software Development:
The software development was broken into several different functions as outlined below.
Additionally, different methods and algorithms were derived to improve the performance of the
system throughout the testing period.

• LCD display:

The first taken approach with the programing process was to connect an LCD to the MCU to
display the sensors outputs, which will help with the trouble shooting process. However, this
method turned out to be unnecessary after discovering that the Arduino Programing Software
(1.0.5) has a serial monitor that allows the programmer to display on it in real-time, which has
been a huge bonus for the project, since that there was too much information to be displayed
which the LCD couldn’t accommodate on its two displaying lines. Wiring the LCD and
connecting it to the MCU and then programing the MCU for the LCD was a waste of time.

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• Motor Driver:

Although the motor driver, which is also referred to as motor shield, can be used with any type
of motors and interfaced with any microcontroller, it has made for Arduino applications which
means that it comes with a lot of documentations that ease the process of integrating it with the
project. The manufacture has a pre written code and heard file that can be easily integrated with
the code and reduce the learning curve.

The use of this particular motor driver introduced some problems that will be discussed in the
fallowing section; however, the motor driver had more advantages over other commercial
alternatives that excluded the idea of having substituted. A major advantage of using this motor
was its ability to handle high currents up to 30 Amps compared to the 2-10 Amps commercial
alternatives.

Most of the problems, one way or the other, was associated with motor driver.

o Taking up all the pins:

The motor driver, or so called motor shield, supposed to shield the motor driver logical layer
from the top layer in a way that preserve all the pins or at least most of them. However, it didn’t
and furthermore it occupied the unused pins which aren’t being directly connected to driver for
command. For example p.13 is one of the pins that is supposed to be free, however one of the
motor led direction indicators was connected to it.

This was very inconvenient since it prevented us to connect anything else, like an LCD to
display sensor data, a button to rest or to calibrate, or a knob which would have been greatly
advantages into calibrating the PI controller constants rather than manually changing the values
in the code and recompiling and uploading the code to the MCU.

o Directional Un-linarites:

The motor driver provided a different motor speed on each axis and each direction for the same
output value. This might be associated to the motors themselves rather than being caused by
the motor driver. This problem was addressed by detecting this un-linarites and fixing it in the
code by outputting the corrected value.

o Voltage Regulator:

The motor driver on chip voltage regulator introduced a different DC offset on the accelerometer
angular readings for three different power source cases(USB powered, power supply powered,
both USB and PS powered, and in the car powered). This means different code for different
power source since that it is a different DC offset and different accelerometer calibration.

21
• Accelerometer:

Programing the code for the analog accelerometer wasn’t much of a challenge, especially after
mounting it to the bottom of the platform and displaying its output data, which gave away the
relationship between the analog output voltage and the angular displacement.

• Gyroscope Calibration:

Luckily The Arduino wire library supports I2C protocols which is the protocol that is used to get
the data from the digital gyroscope’s buffer. The gyroscope can operate on different buffer
transfer modes. For this project stream mode, which is the default mode, is used since it
provides the most resent angular velocity rate. The data is provided as a signed 16 bit digital
number for each of the axis. The digital number needed to be processed and converted into
meaningful information, angular displacement in this case.

On the other hand, calibrating the gyroscope and eliminating the drift consumed a good amount
of time. The datasheet oddly didn’t include the procedure of converting the digital number into
angular displacement, or how to eliminate the drifting problem.

• Complimentary Filter:

Implementing the complimentary filter was straight forward process, however, varying its
parameter to test the behavior for different values was time consuming with manually changing
the values in the code and recompiling and uploading the code to the MCU.

• Control Algorithm:

o Proportional:

At first a pure proportional was used to control the platform by simply having the output to the
motors multiplied by the output of the complimentary filter (the error) as OutputX(Proportional *
Error);

This method didn’t lead to solid results since that it would have to much gain for high error
values which causes a big overshoot, and a very small gain for small error values which isn’t
enough to move the motors.

o Conditional:

The use of if..else conditional statements improved the performance with the use of different
proportion values for different intervals, which eliminated some of the previous discussed
disadvantages.

o Proportional Integral:

The PI controller proved to be a great solution for the problem. It had a fast response and better
study state error correction capabilities when it is compared to the previous ones. However, it
had a undesired behavior caused by the motor’s gear backlashing. It slowly oscillates around
the 0 degrees and can’t come to a complete stop.

22
 Section III

Prototype Testing

23
Testing Criteria and Procedures
In-depth testing is performed to ensure that the prototype successfully addresses the problem
statement. Testing of the design is organized into two categories, component verification and
project performance requirements. For each test the expected result must be determined.
Therefore, test variables and validation criteria must be determined.

For component verification, the following tests must be performed as indicated in Table 1 below.
Each major component is listed with the necessary tests, the corresponding output
measurement and unit of measure. Function testing of the electrical devices ensures the
components are free of defects. Additionally the two sensors are tested for calibration with the
system after mounting. The prototype power supply is tested to verify it is within the design
parameter of 9 to 16 V.

Table 1: Component Testing

Item Description Response Unit of

variable Measure
Platform Determine rotation Angle Degree
about pitch and roll
axes
Microcontroller Function test of input Digital logic and
and output pins PWM signal
output
Accelerometer Function test and Angular position Degree
calibration
Gyroscope Function test and Angular velocity Degrees
calibration per second
(dps)
DC Motor (2) Confirm motor design Torque constant,
parameters per armature
manufacturer’s resistance,
specifications armature
inductance
Motor Driver Function test of input Digital logic and
and output pins PWM signal
output
Battery Verify power supply Voltage Volts (v)
range

Based on suitable components, the assembled prototype must meet the performance guidelines
stated in the design phase of this project. Table 2 below lists the system requirements, the
measured output variable, corresponding unit of measure and the acceptable value range
necessary to validate the design solution. The system response overshoot and steady state
tracking error requirements are not measured variables but calculated based on the measured
response of the sensors.

24
 Table 2: Performance Requirements

Requirement Response Unit of Measure Acceptable value range

variable
System response Calculated Unit-less 10% maximum
overshoot from angle
measurements
Correction time Time Seconds 250 ms or less for a 30°
error correction
Steady state tracking Calculated Unit-less 5% maximum
error from angle
measurements
Range of motion Angle Degrees 30° deviation from
reference angle
Power consumption Current Amperes 15 amperes maximum
draw
Footprint size Volume Cubic inches 500 cubic inches
maximum
Unit weight Weight Pounds 5 lbs. maximum
Load capacity Weight Pounds 2 lbs. minimum

Physical Specifications

The range of motion was measured using a Wixey Model WR300 Digital Angle Gauge as shown
in Figure 11 below. A torpedo bubble level was used to determine the global level with the
gauge being calibrated from this position. Moving the platform through the full range of
operation for each axis yielded the relative range of motion.

Figure 11: Determining the platform angular position using the angle gauge.

25
 Table 3: Range of Motion

Axis of Measurement Clockwise Angle Counterclockwise Angle

X - axis 30.1 31.2
Y- axis 31.3 31.3

Power consumption was calculated by measuring the maximum current drawn by the motor
driver and the maximum voltage supplied to the motor driver. The maximum current was 3.5
Amps when the platform was given a step response. The non-vehicular power supply used in
testing was rated for 12 V but actually provided 13.5 V under testing conditions. This indicates
that the maximum power consumption will not exceed 45.25 W.

The overall size of the device is 8.25” x 8.25” x 8” high measured with a standard tape measure
with a 1/16” resolution. This equates to a volume of 544.5 cubic inches.

The device was weighed on a Salter Brecknell Model 311 scale rated to 11 pounds with a
resolution of 0.1 ounces. A total of three measurements were taken with the results being
consistent within 0.1 ounces. The device was determined to weigh 6 pounds, 6.5 ounces.

Sensor Calibration

Upon mounting, the accelerometer was calibrated using a Wixey Model WR300 Digital Angle
Gauge as shown in Figure 11 above. This level provides an accuracy of 0.1° when measured
at 0°. The test procedure is outlined in Appendix 2 – Testing Procedures. The results of the X
axis calibration are shown in Figure 12 below.

26
 X Axis Acceleration
2.6
X: 63
Y: 2.38
2.4

2.2
Voltage (V)

X: 105 X: 186
Y: 1.75
1.8 Y: 1.73

X: 12
1.6 Y: 1.72

1.4
X: 124
Y: 1.22

0 50 100 150 200 250

Time (ms)

Figure 12: Determination of the accelerometer gain and bias in the x axis.

This indicates that the accelerometer reference voltage for the x-axis is 1.72 V. There is a linear
increase as the platform is rotated to 30° and then stabilized for half a second. There is then a
linear decrement as the platform returns to the global level and another linear decrement as the
platform is rotated to its clockwise limit before returning to the global level. Linearizing the
platform change in position indicates that the gain constant averages out to be 75.

Testing of the Y axis indicated the global level to be 1.63 V likely due to the chip’s center being
closer to the platform center than in the X axis. With the voltage varying from 0 to 3.3 V, a
precisely aligned accelerometer would read 1.65 V at global level. The gain constant for the Y
axis is the same as the X axis.

The calibrated accelerometer angular data is then used to calibrate the gyroscope. Since the
gyroscope returns digital values relative to the angular velocity of the platform, the data must be
integrated over the time period to determine the change in angular position. The procedure for
calibrating the gyroscope can be found in Appendix 2 – Testing Procedures and is based on a
technique devised by Mark Looney of Analog Systems. [1]

27
 X Axis Angular Rate
5000

4000

Angular Velocity (millidegrees/sec) 3000

2000

1000
X: 1.93e+004
Y: -144
0
X: 1662
-1000 Y: -159

-2000

-3000

-4000

-5000
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (ms) 4
x 10

Figure 13: Angular velocity of the platform as it moves from global level to maximum
counterclockwise displacement, remains stationary for approximately 1 second, moves back to
level and then to the maximum clockwise displacement before returning to global level.

As shown in Figure 13 above, the gyroscope has an initial bias of approximately 159 mdeg/s.
This is considered drift as it will indicate the platform is moving over time when integrated.
Subtracting the average drift allows for the integration during movement to be done using
Reimann sums. Comparison of the integrated angle with the accelerometer data indicates the
gain of the gyroscope is approximately 0.18 along both axes.

Initial Step Input Readings

To generate initial step input readings without damaging the motors or the linkage, the
microcontroller was programmed to provide a step response in the form of a constant PWM
signal of 47 to the motor. The platform was oriented at maximum angle before applying power
to the motor driver. The measured response for each axis in both directions is detailed below in
Figure 14 through Figure 20.

28
 Y Axis Acceleration CCW at PWM = 47
2.5

X: 1.248
Y: 2.21

Voltage(V) 2

1.5

X: 0.835
Y: 1.16
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)

Figure 14: With the platform initially at -33°, movement begins at 0.8 seconds and reaches
maximum extension at 1.2 seconds with an ending position of +44°.

Y Axis Acceleration CCW at PWM = 47

2.5

y = 2.8*x - 1.2

2
Voltage(V)

1.5
data 1
linear

1
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25
Time (s)
residuals
0.2
Linear: norm of residuals = 0.193

0.1

-0.1

-0.2
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

Figure 15: The movement appears to be linear for the time period of 0.8 to 1.2 seconds with a
gain of 2.8 V/s.

29
 Y Axis Acceleration CW at PWM = 47
2.5

X: 0.572
Y: 2.09

2
Voltage (V)

1.5

X: 0.822
Y: 1.21

1
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Time (s)

Figure 16: The platform traverses from 42° to -33° and appears linear from 0.6 to 0.8 seconds.

Y Axis Acceleration CW at PWM = 47

2.5
data 1
y = - 3.4*x + 4 linear
2
Voltage (V)

1.5

0.5
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Time (s)
residuals
0.1
Linear: norm of residuals = 0.10017

0.05

-0.05

-0.1
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

Figure 17: The linearization of the axial acceleration results in a gain of -3.4 V/s

30
 X Axis Acceleration CCW at PWM = 47
2.6

2.4

2.2
Voltage (V)

1.8

1.6

1.4

0 1 2 3 4 5 6
Time (s)

Figure 18: Acceleration in the x-axis from -37° to +49° indicates a non-linear response likely
due to the asymmetrical motor position.

X Axis Acceleration CW at PWM = 47

2.5

X: 1.406
Y: 2.36

2
Voltage (V)

1.5

X: 1.765
Y: 1.17
1
1 1.5 2 2.5
Time (s)

Figure 19: Platform moves from 52° to -36° with one outlier data sample occurring at 1.7
seconds.

31
 X Axis Acceleration CW at PWM = 47
2.5

y = - 4.2*x + 8.3
2

Voltage (V)
1.5

0.5
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85
Time (s)
residuals
0.1
Linear: norm of residuals = 0.10233

0.05

-0.05

-0.1
1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85

Figure 20: Linearizing the response from 1.4 to 1.8 seconds indicates a gain of -4.2 V/s.

Based on this data with Figure 18 in particular, the decision was made to relocate the X-axis
motor to a more central location. This necessitated the need to revise the plant moment of
inertia but allowed for a more symmetrical response to counterclockwise and clockwise error
corrections made by the microcontroller.

Complementary Filter Design

The complementary filter design requires that the data from both sensors is incorporated using
specific design ratio. Adjusting this ratio affects the sensitivity of platform to lateral movement
against the settling time. The contribution of the accelerometer readings provide a quicker
response to a step response but create significant noise to the system when there is axial
movement. A ratio of 93:7 has been selected to meet the performance goals of this project.

32
 Sensor Calibration
40
Accelerometer
Gyroscope
30
Complementary

20
Angular Position (Deg)

10

-10

-20

-30

-40
0 2 4 6 8 10 12 14 16 18
Time (s)

Figure 21: Comparison of the Complementary filter (red) with the two sensors shows the filter
works as designed through the full range of operation. The Gyroscope (green) tends to provide
a slightly less accurate reading.

Calculating Experimental Values

After completing the construction of the prototype it is necessary to recalculate values to better
model the system. The accelerometer, gyroscope, and motor driver gain are primarily the
components in question. The remaining values are based on the datasheet provided by the
motor manufacturer and digital values calculated and contained within the microcontroller. Both
the accelerometer and the gyroscope convert an angle into a voltage. The method used to
determine the gain for each of these components is the same. These gains are found by taking
output voltage measurements at two different angles and calculating the slope. After taking
measurements we determined that at 44° and 33° the accelerometer produced output voltages
of 2.2V and 1.17V respectively and the gyroscope produced output voltages of -1.37V and
0.01V. The calculations are as follows in Equations 3 and 4:
2.20—1.17 𝑉𝑜𝑙𝑡𝑠
𝐾𝑎𝑐 = = 0.01338 ( )
44−33 𝐷𝑒𝑔𝑟𝑒𝑒
(3)

−1.37−0.01 𝑉𝑜𝑙𝑡𝑠
𝐾𝑔 = = −0.178( )
44−33 𝐷𝑒𝑔𝑟𝑒𝑒
(4)

To determine the gain of the motor driver a similar process was used. The output of the motor
driver is based on the duty cycle output of the micro controller. Table 4 shows the values
recorded at different duty cycles and the corresponding output voltage when the driver is fed by
a 13.5 Volt 3.2 Amp power supply.

33
Table 4: Measurements Taken to Determine Gain of the Motor Driver

Duty Cycle (%) 13 25 50 75 87.5 100

Output Voltage (V) 1.365 2.625 5.25 7.875 9.1875 10.5

After evaluating these values the gain was found to be 0.105. Now after having found the values
for these components a software model can be developed and tested. This model will now
accurately represent the prototype.

Developing the Simulink Model

Before the model is created in Simulink it is important to know all of the values necessary for its
operation. Table 5 shows all of the experimental values from the calculations and the given
values from the datasheet for the motor.

Table 5: Constants Used for Simulation

Inertia (ounce*inches)
Armature Resistance

Armature Inductance
(ounce*inches/ amp)

Accelerometer Gain
Back EMV Voltage
Torque Constant

Gyroscope Gain
Amplifier Gain
Description

Gear Ratio

Friction

(Volts)
(Ω)

(H)

Variable Td n Ra La Jeq Beq Kb Ka Kac Kg

Value 3.34 30.9 1.17 0.001 0.0008 2E-09 0.0025 0.105 0.0134 0.178

The next step in developing the model is being able to model individual components. The plant
in this particular control system consists of the motor and platform frame. It is known that the
motor is given some input voltage and this will result in some angular velocity Ω, which will
induce an angular displacement Ɵ. The system defined by the motor is shown in Figure 22.

Figure 22: Model of the Plant (Motor)

Then the output Ɵ is sensed by the accelerometer and gyroscope. The voltage values sent by
these sensors are passed to the controller of the system. This controller includes the process

34
used by the microcontroller and the motor driver. The decided design for the controller is a PID
topology. This means proportionality, integration, and derivative control algorithms will be used.
There will be proportionality constants for both the accelerometer and the gyroscope. The
accelerometer signal will be controlled with the integration part of the control algorithm and the
gyroscope will be controlled with the derivative. The derivation for these values is done using
the PID control block in Simulink. This software plug-in is placed in the system where the control
is desired. It then scans the system and develops gains for the proportional, integral, and
derivative constants. The full system with the controller is shown in Figure 23. The tuned system
parameters are then shown in Table 6.

Figure 23: Full System with Controller

Table 6: Controller Gain Constants

𝐾𝑃 𝐾𝐼 𝐾𝐷
-0.0289665190436555 -0.258654492473789 0.000422783661267403

With the system built simulations were run to determine the impulse and step responses of the
system. Before making any changes to the system, to ensure the software model is
representative of the prototype, physical measurements were recorded and plotted in MATLAB.
The following plots show the impulse and step responses of the system as well as the error of
the system and integration error measurements. Note that in several figures the accelerometer,
gyroscope, and complimentary filter are plotted. The complimentary filter is the value which the
microcontroller uses for its computations and that is what will be analyzed. Also, note that the
plots for positive and negative axes for all of the following figures were produced by separate
trials. They are shown together to depict similarities.

35
 Impulse Response of Positive X Axis
10

Offset Angle (degrees)

Accelerometer
Gycroscope
5 X: 1210
X: 1030 Complimentery Filter
Y: 1.15
Y: 0.49

-5
0 500 1000 1500 2000 2500 3000 3500
Time (ms)
Impulse Response of Negative X Axis
5
Offset Angle (degrees)

X: 1210
Y: -0.1
0

X: 1399 Accelerometer
-5 Y: -1.37
Gycroscope
Complimentery Filter
-10
0 500 1000 1500 2000 2500 3000 3500
Time (ms)

Figure 24: Impulse Response of X Axis

Figure 24 depicts the impulse response for both the positive and negative x axis. At time 1030
ms the impulse is introduced to the positive x axis. It is at time 1210 ms that the system returns
to steady state, where the offset of the angle is less than 5% of the maximum offset of 30°,
which is 1.5°. Also, the settling time is given by this time interval, which is 180 ms and is within
the settling time parameter. At time 1210 ms the impulse is introduced to the negative x axis. It
is at time 1399 ms that the system returns to steady state. The settling time for this response is
189 ms. On the positive axis graph note some of the problems that were dealt with in the design
process. In this plot it is observed that the accelerometer signal contains high noise
components. Also, the gyroscope contains a drift offset. Although in this example the filter
output remains within the steady state range there is a significant amount of error introduced by
these characteristics of the components.

36
 Error for Positive X Axis from Impulse
200
Total Error
100 Integrator Error
Error (%)

-100

-200
0 500 1000 1500 2000 2500 3000 3500
Time (ms)
Error for Negative X Axis from Impulse
20
Total Error
Integrator Error
10
Error (%)

-10
0 500 1000 1500 2000 2500 3000 3500
Time (ms)

Figure 25: Error on X Axis Produced by an Impulse

Figure 25 depicts the error observed by the controller. The error is produced by an impulse
introduced to the positive x axis at 1030 and negative x axis at 1210. The errors recorded
represent both in the total proportional, derivative, and integral portions of the error and
specifically the integrator error as it is the most prevalent.

37
 Impulse Response of Positive Y Axis
10

Offset Angle (degrees) 5

X: 1206
X: 854 Y: 1.39
Y: -0.03
0
Accelerometer
-5 Gyroscope
Complimentery Filter
-10
0 500 1000 1500 2000 2500 3000
Time (ms)
Impulse Response of Negative Y Axis
10
Offset Angle (degrees)

5 X: 534
Y: 0.29
0
Accelerometer
X: 854
-5 Y: -1.38 Gyroscope
Complimentery Filter
-10
0 500 1000 1500 2000 2500 3000
Time (ms)

Figure 26: Impulse Response of Y Axis

Figure 26 depicts the impulse response for both the positive and negative y axis. At time 854 ms
the impulse is introduced to the positive y axis. It is at time 1206 ms that the system returns to
steady state. Also, the settling time is given by this time interval, which is 352 ms. At time 534
ms the impulse is introduced to the negative y axis. It is at time 854 ms that the system returns
to steady state. The settling time for this response is 320 ms.

38
 Error for Positive Y Axis from Impulse
1

0
Error (%)

Total Error
-1
Integrator Error

-2
0 500 1000 1500 2000 2500 3000
Time (ms)
Error for Negative Y Axis from Impulse
1
Total Error
0.5 Integrator Error
Error (%)

-0.5

-1
0 500 1000 1500 2000 2500 3000
Time (ms)

Figure 27: Error on X Axis Produced by an Impulse

Figure 27 depicts the error observed by the controller. The error is produced by an impulse
introduced to the positive y axis at 854 and negative y axis at 534.

39
 Step Response of Positive X Axis
10

Offset Angle (degrees)

Accelerometer
X: 1082
5 Y: 1.46 Gyroscope
Complimentery Filter
0
X: 622
Y: 0.28
-5

-10
0 1000 2000 3000 4000 5000 6000 7000 8000
Time (ms)
Step Response of Negative X Axis
5
Offset Angle (degrees)

X: 3203
Y: -0.14
0

X: 3617 Accelerometer
-5 Y: -1.46
Gyroscope
Complimentery Filter
-10
0 1000 2000 3000 4000 5000 6000 7000 8000
Time (ms)

Figure 28: Step Response of X Axis

Figure 28 depicts the step response for both the positive and negative x axis. At time 622 ms
the step is introduced to the positive x axis. It is at time 1082 ms that the system returns to
steady state. Also, the settling time is given by this time interval, which is 460 ms. At time 3203
ms the step is introduced to the negative x axis. It is at time 3617 ms that the system returns to
steady state. The settling time for this response is 414 ms.

40
 Error for Positive X Axis from Step Response
1
Total Error
Integrator Error
0.5
Error (%)

-0.5
0 1000 2000 3000 4000 5000 6000 7000 8000
Time (ms)
Error for Negative X Axis from Step Response
20

0
Error (%)

-20 Total Error

Integrator Error
-40

-60
0 1000 2000 3000 4000 5000 6000 7000 8000
Time (ms)

Figure 29: Error on X Axis Produced by a Step

Figure 29 depicts the error observed by the controller. The error is produced by an step
introduced to the positive x axis at 622 and negative x axis at 3203.

41
 Step Response of Positive Y Axis
10

Offset Angle (degrees)

Accelerometer
Gyroscope
5 X: 1199
Y: 1.5 Complimentery Filter

0
X: 623
Y: -0.18
-5
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (ms)
Step Response of Negative Y Axis
10
Offset Angle (degrees)

5 X: 1272
Y: 0.36
0
Accelerometer
X: 1879
-5 Y: -1.45 Gyroscope
Complimentery Filter
-10
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (ms)

Figure 30: Step Response of Y Axis

Figure 30 depicts the step response for both the positive and negative y axis. At time 623 ms
the step is introduced to the positive y axis. It is at time 1199 ms that the system returns to
steady state. Also, the settling time is given by this time interval, which is 576 ms. At time 1272
ms the step is introduced to the negative y axis. It is at time 1879 ms that the system returns to
steady state. The settling time for this response is 607 ms.

42
 Error for Positive Y Axis from Step Response
1
Total Error
Integrator Error
0.5
Error (%)

-0.5
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (ms)
Error for Negative Y Axis from Step Response
2

0
Error (%)

-2

-4 Total Error
Integrator Error
-6
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Time (ms)

Figure 31: Error on Y Axis Produced by a Step

Figure 31 depicts the error observed by the controller. The error is produced by an impulse
introduced to the positive y axis at 623 and negative y axis at 1272.

Now with physical data the simulation is run. After confirming that the simulation is accurately
representing the output model the simulation can be used to optimize the control system
parameters. Note that it is assumed in the software model that the positive and negative axes,
as well as the x and y axes, do not differentiate from each other. Because of this there is one
plot for the impulse and step responses which can be applied to each axis.

Figure 32 shows the updated controlled closed loop system. Figure 33 and Figure 34 depict the
adjusted system responses that represent and will be observed in the physical prototype.

43
 Figure 32: Optimized Simulink Model of the Full System

After optimizing the simulation model the transfer functions that governed the controller have
been modified to be represented with a simple proportional gain for the accelerometer and
gyroscope. Also, the integration variable is held constant.

X: 1.087
Y: 0.6543 Angular Displacement of the System

-1

-2
Offset Angle (Degrees)

-3

-4

-5

-6

-7

-8
0 2 4 6 8 10 12 14 16 18 20
Time (x100 ms)

Figure 33: Optimized Simulation of Impulse Response

The figure shown above depicts the response of the system due to an impulse. The overshoot
here is .6543°. This overshoot meets the requirements previously set forth. The system also
meets the steady state requirements as it reaches ±5% of steady state before 200 ms. Note that
there is no steady state error with these control parameters for impulse responses.

44
 Angular Displacement of the System
0

-1

-2

-3
Offset Angle (Degrees)

-4

-5

-6

X: 9.286
Y: -6.939

-7
X: 1.09
Y: -7.62

-8
0 2 4 6 8 10 12 14 16 18 20
Time (x100 ms)

Figure 34: Optimized Simulation Step Response

The figure shown above depicts the response of the system due to a step. The overshoot here
is 0.62°. Again the overshoot is acceptable as well as the settling time settling time, which in this
case is 112.5 ms. The steady state error due to a step response is minimal (i.e. less than 10%
of the steady state tolerance of 1.5°.)

After running additional tests on the prototype the optimization is confirmed. With these updated
system gains the prototype now meets both the settling time and overshoot parameters. It is
now appropriate to proceed with testing of the prototype in its real world application.

All plots have been produced in Matlab and Simulink. Code for physical data plots is attached in
Appendix 4 – MATLAB Scripts.

45
 Section IV

Evaluation and Recommendations

46
Control Design
The step response for the X-axis has an overshoot of 0.654° which is a 9.8% overshoot. The Y-
axis response is slightly better with the angular overshoot being 0.62°. This response meets the
specifications and indicates it can further refined with additional testing.

Response settling time for an impulse input is 101.3 ms while a step input yields 112.5 ms. This
is within the 250 ms requirement.

Steady state error for a step input results in 0.0783° for an allowed 1.5°. This equates to a 5%
steady state error which is the requirement.

Physical Parameters
Weight

The weight of the platform is 6 pounds 6.5 ounces which exceeds the performance
specifications. Using a thinner platform surface of 3/16” instead of 1/4” as well as optimizing the
material used in the frame may reduce the overall weight to within the desired range without
compromising the structural integrity and robustness of the system.

Footprint

The footprint is 544.5 cubic inches which exceeds the performance specifications of 500 cubic
inches. There are limitations on the height based on the motor size and location; therefore, any
footprint reduction would impact the size of the platform. The outer frame width may be reduced
pending structural analysis which would bring the footprint within the design requirements. This
is a design consideration relative to the specific vehicle where the device would be incorporated.

Range of motion

The prototype meets the requirements for the total 60° range of motion for each axes.
Additional range is unlikely due to the location of the motors and mounting bracket
configuration.

Load capacity

The device easily handles the 2 pound load capacity. The load capacity can be increased or
the current motors may be replaced with a lower HP motor.

Power consumption

The device draws a maximum of 3.5 Amps when the power source must supply 13.5 V. This is
well below the 15 Amp requirement.

47
 Section V

Conclusions

48
This prototype addresses the design requirements for range of motion, load capacity, and power
consumption. The controller overshoot is within the requirements as is the settling time in the
specifications. The steady state error is 5% as required which does not allow adjustment of the
steady state response. The prototype failed to meet the weight and footprint requirements,
however and this should be taken into consideration before moving forward. Reducing the
amount of material in the structural subsystem is likely solution for the weight. It is
recommended that further structural analysis be conducted to produce a more efficient and
lighter-weight unit. The footprint size cannot be easily reduced and as such, market research
should be conducted to determine whether a reduction in the platform size is necessary.

Furthermore, the application of this solution requires specific conditions for operational use. The
power supply may vary from vehicle to vehicle and effects the performance due to requirements
for the motor driver. In addition, the position which the platform is mounted may also vary. This
would require a separate calibration for each vehicle. In order for this solution to be universally
applicable these issues must be considered and corrected. In conclusion the final design
operates with acceptable performance and solves the initial problem of stabilizing objects within
a motor vehicle but a marketable solution will require more time and resources to produce.

49
 References

[1] A SIMPLE CALIBRATION FOR MEMS GYROSCOPES, Mark Looney. EDN May 13, 2010.
http://www.edn.com/design/sensors/4363439/A-simple-calibration-for-MEMS-gyroscopes

50
 Appendix 1 – Project Schedule

Project Schedule
September October November December
Action Owner Comments 2 9 16 23 30 7 14 21 28 4 11 18 25 2 9 16 23
Prototype fabrication and
implementation
Material acquisition JS
Fabrication and component
JS
mounting
Live demonstration SS Due November 19
Programming
functional code for sensors SS
functional code for actuators SS
functional code for controller SS
interfacing SS
implementation of complementary
SS
filter
Simulation and analysis
Simulink model with revised motor
JK
parameters
Analysis of working prototype JK
Testing
Identify testing parameters GS Due September 10
Develop test procedures GS
Component functionality testing JS
Sensor calibration GS
Testing of working prototype GS
Troubleshooting/optimization SS
Final Presentation Due December 12
Presentation section drafts
Presentation rehearsal
Final Report Due December 16
First Draft GS Due December 9

51
 Appendix 2 – Testing Procedures

Accelerometer Calibration Procedure

1. Initialize the Arduino microprocessor to power sensor, read sensor, output the readings
to the serial port and disable the motors.
2. Level the platform relative to the desired axis using a digital level
3. Take continuous readings from the Arduino microprocessor for approximately 2
seconds.
4. Rotate platform counterclockwise to 30°. Verify angle with digital level.
5. Take continuous readings from the Arduino microprocessor for approximately 2
seconds.
6. Rotate platform clockwise to 0°. Verify angle with digital level.
7. Take continuous readings from the Arduino microprocessor for approximately 2
seconds.
8. Rotate platform clockwise to 30°. Verify angle with digital level.
9. Take continuous readings from the Arduino microprocessor for approximately 2
seconds.
10. Rotate platform counterclockwise to 0°. Verify angle with digital level.
11. Take continuous readings from the Arduino microprocessor for approximately 2
seconds.
12. Calculate the bias-offset-correction factor by averaging the values at 0°.
13. A linear plot in MATLAB is used to determine accelerometer gain correction.
14. Repeat process for the axis of rotation.

Gyroscope Calibration Procedure

1. Initialize the Arduino microprocessor to power sensor, read sensor, output the readings
to the serial port and disable the motors.
2. Power the gyroscope on and allow it to reach thermal stability.
3. Continuously record the output throughout the remainder of the procedure.
4. Hold the gyroscope against the first stop position (30° clockwise) for 5 seconds.
5. After 5 seconds turn the gyroscope toward the second stop. Begin with a smooth motion
that takes approximately 4 seconds to move the 60° span.
6. Hold the gyroscope against the second stop position for 5 seconds.
7. Rotate the gyro back to the first stop using a similar motion.
8. Hold the gyroscope against the first stop position for 5 seconds.
9. Turn the gyroscope off.
10. Calculate the bias-offset-correction factor by averaging the first 3 seconds of data. The
bias correction will be the opposite polarity of this average.
11. Subtract the bias estimate from the time record. Then integrate output data from the 4-
second time stamp to the 10-second time stamp (before the start of movement until after

60
 the platform stops). The scale factor is calculated by dividing the known angle by the
measured angle calculated from the integration.
12. Using the bias-corrected response from Step 2, integrate output data from the 12-
second time stamp to the 19-second time stamp.
13. Average the results of steps 2 and 3 to calculate the scale-factor correction.
14. Repeat process for the other axis of rotation.

Step Response Testing

1. Initialize microcontroller with stabilization program.

2. Turn on power supply and allow platform to auto-level.
3. Place the test object on platform frame specific to the testing axis.
4. Measure the response using the output generated by the microcontroller serial port.

Power Consumption Testing Procedure

1. Initialize microcontroller with stabilization program.

2. Attach multimeter leads to the wires supplying power to the motor responsible for
actuation in the tested axis.
3. Turn on power supply and allow platform to auto-level.
4. Place the test object on platform frame specific to the testing axis.
5. Measure the response using the output generated by the microcontroller serial port.

61
 Appendix 3 – Microcontroller Programming Code

#include "DualVNH5019MotorShield.h"
// include the libraGRY code for the gyro:
#include <Wire.h>
#include <L3G.h>

DualVNH5019MotorShield md;
L3G gyro;

//SC (dps/LSB): sensitivity

//The gyro has SC = 8.75 (mdps/digit), and R0 = ±10 for FS = 250 dps
// 8.72 / 250 * 1023 = 35.68224
float R0=10;
float SC=35.68224;
float GX,GY,GZ=0;

float GXX,GYY,GZZ=0;
float GRRX=0;
float Xout,Yout=0;
// Variables for Accelerometer
float AX;
float AY;
float Time=0;
float QX=0;
float QX_OLD=0;
float QX_OLD_OLD=0;
float SPDX=0;

float QY=0;
float QY_OLD=0;
float QY_OLD_OLD=0;
float SPDY=0;
float YDIR=0;
float GX0 = 0;
float GY0 = 0;

float AngleX=0;
float AngleY=0;

float DGX=0;
float DGY=0;
// Motor Driver
//Pin map

62
float dt=0;
float a=0;
float b=0;

//PID Variable
float InputX, OutputX;
float dErrX=0;
float errSumX=0;
float lastErrX=0;
float kpX=9;
float kiX=0.025;
float kdX=0;

float InputY, OutputY;

float dErrY=0;
float errSumY=0;
float lastErrY=0;
float kpY=11;
float kiY=0.03;
float kdY=0;

void setup() {

pinMode(A0,INPUT);
pinMode(A1,INPUT);

//Serial.begin(115200);

md.init();
Wire.begin();

if (!gyro.init())
{
while (1);
}

//startup the Gyro in the default mode

gyro.enableDefault();

//take 100 sample and get the average to the gyro offset and accelerometer offset to calibrate
for(int i=0; i<100; i++)
{
gyro.read();

63
 GX = (float)gyro.g.x;
GY = (float)gyro.g.y;
GX0=GX0+GX;
GY0=GY0+GY;

}
GX0=GX0/100;
GY0=GY0/100;

AX = analogRead(A3);
QX_OLD_OLD = (-0.3571*AX + 116.63);
AX = analogRead(A3);
QX_OLD = (-0.3571*AX + 116.63);
DGX=QX_OLD;
AY = analogRead(A2);
QY_OLD_OLD = (-0.3352*AY + 116.88);
AY = analogRead(A2);
QY_OLD = (-0.3352*AY + 116.88);
DGY=QY_OLD;
AngleX= QX_OLD;
AngleY= QY_OLD;
}

//super-loop
void loop() {
//Acc
//Linear equation and subtracting the error angle (7)
AX = analogRead(A3);
QX = (-0.3571*AX + 116.63)-3;
QX=(QX+QX_OLD+QX_OLD_OLD)/3;
QX_OLD_OLD=QX_OLD;
QX_OLD=QX;

//Linear equation and subtracting the error angle (10)

AY = analogRead(A2);
QY = (-0.3352*AY + 116.88);
QY=(QY+QY_OLD+QY_OLD_OLD)/3;
QY_OLD_OLD=QY_OLD;
QY_OLD=QY;

//Gyro
gyro.read();
GX = (float)gyro.g.x;
GY = (float)gyro.g.y;

64
 //this need to be commented out
Time=Time+1;
//subtracting the zero rate from the last gyro rate reading and then converting the digital
number by multiplying by the gyro degree per digit (0.000875 for +-250 sensitivity
GXX=0.000875*(GX-GX0);
GYY=0.000875*(GY-GY0);

// reman sum; dt=0.0519 sampling period

DGX = DGX + (0.01 * dt * GXX);
DGY = DGY + (0.01 *dt * GYY);

b=millis();
dt=b-a;

// Complementary Filter
//dt=0.067; note that 0.98 + 0.02 = 1
AngleX= (0.98*(AngleX+(0.01 *dt * GXX))) + ((0.02)*(QX));
AngleY= (0.98*(AngleY+(0.01 *dt * GYY))) + ((0.02)*(QY));

//PID Controller Code

errSumX += (AngleX * dt);
dErrX = (AngleX - lastErrX) / dt;
OutputX = kpX * AngleX + kiX * errSumX + kdX * dErrX;
lastErrX = AngleX;

errSumY += (AngleY * dt);

dErrY = (AngleY - lastErrY) / dt;
OutputY = kpY * AngleY + kiY * errSumY + kdY * dErrY;
lastErrY = AngleY;

//This is important to insure that the output value never exceeds the 400 limit
if(OutputX>399)
{
OutputX=399;
lastErrX=399;
errSumX=0;
}
if(OutputX<-399)
{
OutputX=-399;
lastErrX=-399;
errSumX=0;
}

65
 if(OutputY>399)
{
OutputY=399;
lastErrY=399;
errSumY=0;
}
if(OutputY<-399)
{
OutputY=-399;
lastErrY=-399;
errSumY=0;
}

a=millis();

//Movment Code
// the md.setM1Speed(0-400) maps the to 255 by multiplying the vlaue by (255/400) which is
the mapping factor that the functions uses
// the mapped value in the range 0-255 which is % duty cycle

md.setM1Speed(OutputX);
md.setM2Speed(OutputY);
}

66
Appendix 4 – MATLAB Scripts

%Jacob Kryder
%ECE406 Senior Design Project
%Stabilization Platform

clear

%loads recorded movement data

movement_file='H:\Program Files\MATLAB\angle_data.txt'; %assigns load
variable
movement_data=load(movement_file); %assigns total data
array
time_M=movement_data(:,1); %time vector for position data
ax=movement_data(:,2); %accelerometer x axis position
data
gx=movement_data(:,3); %gyroscope x axis position data
cx=movement_data(:,4); %complimentery filter x axis
position data
ay=movement_data(:,5); %accelerometer y axis position
data
gy=movement_data(:,6); %gyroscope y axis position data
cy=movement_data(:,7); %complimentery filter y axis
position data

%plots movement data

figure(1)
subplot(2,1,1)
plot(time_M,ax,time_M,gx,time_M,cx)
title('Movement Data for X Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gycroscope','Complimentery Filter');
subplot(2,1,2)
plot(time_M,ay,time_M,gy,time_M,cy)
title('Movement Data for Y Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gycroscope','Complimentery Filter');

%loads recorded x axis impules response data

x_impulse_response_file='H:\Program
Files\MATLAB\x_impulse_response_data.txt'; %assigns load variable
x_impulse_response_data=load(x_impulse_response_file);
%assigns total data array
time_IRX=x_impulse_response_data(:,1); %time vector for x axis impulse
response
iaxp=x_impulse_response_data(:,2); %accelerometer positive x axis
impulse response
igxp=x_impulse_response_data(:,3); %gyroscope positive x axis
impulse response
icxp=x_impulse_response_data(:,4); %complimentery filter positive x
axis impulse response

67
iaxn=x_impulse_response_data(:,5); %accelerometer negative x axis
impulse response
igxn=x_impulse_response_data(:,6); %gyroscope negative x axis
impulse response
icxn=x_impulse_response_data(:,7); %complimentery filter negative x
axis impulse response
ixpe=x_impulse_response_data(:,8); %error on positive x axis
imxpe=max(ixpe); %max error on positive x axis
ixpie=x_impulse_response_data(:,9); %integral error on positive x
axis
imxpie=max(ixpe); %max integral error on positive x
axis
ixpmd=x_impulse_response_data(:,10); %positive x axis output to motor
driver
ixne=x_impulse_response_data(:,11); %error on negative x axis
imxne=max(ixne); %max error on negative x axis
ixnie=x_impulse_response_data(:,12); %integral error on negative x
axis
imxnie=max(ixnie); %max integral error on negative x
axis
ixnmd=x_impulse_response_data(:,13); %negative x axis output to motor
driver

%for each of the following sections of code the variables are the same as
%in the the preceeding with the only changes being in the x or y axis and
%the impulse or step response.

%plots x axis impulse response

figure;
subplot(2,1,1)
plot(time_IRX,iaxp,time_IRX,igxp,time_IRX,icxp)
title('Impulse Response of Positive X Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gycroscope','Complimentery Filter');
subplot(2,1,2)
plot(time_IRX,iaxn,time_IRX,igxn,time_IRX,icxn)
title('Impulse Response of Negative X Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gycroscope','Complimentery Filter');

figure;
subplot(2,1,1)
plot(time_IRX,(ixpe/imxpe),time_IRX,(ixpie/imxpie))
title('Error for Positive X Axis from Impulse');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');
subplot(2,1,2)
plot(time_IRX,(ixne/imxne),time_IRX,(ixnie/imxnie))
title('Error for Negative X Axis from Impulse');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');

68
figure;
subplot(2,1,1)
plot(time_IRX,ixpmd)
title('Microprocessor Output to Motor Driver for Positive X Axis from Impulse
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');
subplot(2,1,2)
plot(time_IRX,ixnmd)
title('Microprocessor Output to Motor Driver for Negative X Axis from Impulse
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');

%loads recroded y axis impulse response data

y_impulse_response_file='H:\Program
Files\MATLAB\y_impulse_response_data.txt';
y_impulse_response_data=load(y_impulse_response_file);
time_IRY=y_impulse_response_data(:,1);
iayp=y_impulse_response_data(:,2);
igyp=y_impulse_response_data(:,3);
icyp=y_impulse_response_data(:,4);
iayn=y_impulse_response_data(:,5);
igyn=y_impulse_response_data(:,6);
icyn=y_impulse_response_data(:,7);
iype=y_impulse_response_data(:,8);
imype=max(iype);
iypie=y_impulse_response_data(:,9);
imypie=max(iypie);
iypmd=y_impulse_response_data(:,10);
iyne=y_impulse_response_data(:,11);
imyne=max(iyne);
iynie=y_impulse_response_data(:,12);
imynie=max(iynie);
iynmd=y_impulse_response_data(:,13);

%plots y axis impulse response

figure;
subplot(2,1,1)
plot(time_IRY,iayp,time_IRY,igyp,time_IRY,icyp)
title('Impulse Response of Positive Y Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');
subplot(2,1,2)
plot(time_IRY,iayn,time_IRY,igyn,time_IRY,icyn)
title('Impulse Response of Negative Y Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');

figure;
subplot(2,1,1)
plot(time_IRY,(iype/imype),time_IRY,(iypie/imypie))
title('Error for Positive Y Axis from Impulse');
ylabel('Error (%)');

69
xlabel('Time (ms)');
legend('Total Error','Integrator Error');
subplot(2,1,2)
plot(time_IRY,(iyne/imyne),time_IRY,(iynie/imynie))
title('Error for Negative Y Axis from Impulse');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');

figure;
subplot(2,1,1)
plot(time_IRY,iypmd)
title('Microprocessor Output to Motor Driver for Positive Y Axis from Impulse
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');
subplot(2,1,2)
plot(time_IRY,iynmd)
title('Microprocessor Output to Motor Driver for Negative Y Axis from Impulse
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');

%loads recorded x axis step response data

x_step_response_file='H:\Program Files\MATLAB\x_step_response_data.txt';
x_step_response_data=load(x_step_response_file);
time_SRX=x_step_response_data(:,1);
saxp=x_step_response_data(:,2);
sgxp=x_step_response_data(:,3);
scxp=x_step_response_data(:,4);
saxn=x_step_response_data(:,5);
sgxn=x_step_response_data(:,6);
scxn=x_step_response_data(:,7);
sxpe=x_step_response_data(:,8);
smxpe=max(sxpe);
sxpie=x_step_response_data(:,9);
smxpie=max(sxpie);
sxpmd=x_step_response_data(:,10);
sxne=x_step_response_data(:,11);
smxne=max(sxne);
sxnie=x_step_response_data(:,12);
smxnie=max(sxnie);
sxnmd=x_step_response_data(:,13);

%plots x axis step response

figure;
subplot(2,1,1)
plot(time_SRX,saxp,time_SRX,sgxp,time_SRX,scxp)
title('Step Response of Positive X Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');
subplot(2,1,2)
plot(time_SRX,saxn,time_SRX,sgxn,time_SRX,scxn)
title('Step Response of Negative X Axis');
ylabel('Offset Angle (degrees)');

70
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');

figure;
subplot(2,1,1)
plot(time_SRX,(sxpe/smxpe),time_SRX,(sxpie/smxpie))
title('Error for Positive X Axis from Step Response');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');
subplot(2,1,2)
plot(time_SRX,(sxne/smxne),time_SRX,(sxnie/smxnie))
title('Error for Negative X Axis from Step Response');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');

figure;
subplot(2,1,1)
plot(time_SRX,sxpmd)
title('Microprocessor Output to Motor Driver for Positive X Axis from Step
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');
subplot(2,1,2)
plot(time_SRX,sxnmd)
title('Microprocessor Output to Motor Driver for Negative X Axis from Step
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');

%loads recorded y axis step response data

y_step_response_file='H:\Program Files\MATLAB\y_step_response_data.txt';
y_step_response_data=load(y_step_response_file);
time_SRY=y_step_response_data(:,1);
sayp=y_step_response_data(:,2);
sgyp=y_step_response_data(:,3);
scyp=y_step_response_data(:,4);
sayn=y_step_response_data(:,5);
sgyn=y_step_response_data(:,6);
scyn=y_step_response_data(:,7);
sype=y_step_response_data(:,8);
smype=max(sype);
sypie=y_step_response_data(:,9);
smypie=max(sypie);
sypmd=y_step_response_data(:,10);
syne=y_step_response_data(:,11);
smyne=max(syne);
synie=y_step_response_data(:,12);
smynie=max(synie);
synmd=y_step_response_data(:,13);

%plots y axis step response

figure;
subplot(2,1,1)
plot(time_SRY,sayp,time_SRY,sgyp,time_SRY,scyp)

71
title('Step Response of Positive Y Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');
subplot(2,1,2)
plot(time_SRY,sayn,time_SRY,sgyn,time_SRY,scyn)
title('Step Response of Negative Y Axis');
ylabel('Offset Angle (degrees)');
xlabel('Time (ms)');
legend('Accelerometer','Gyroscope','Complimentery Filter');

figure;
subplot(2,1,1)
plot(time_SRY,(sype/smype),time_SRY,(sypie/smypie))
title('Error for Positive Y Axis from Step Response');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');
subplot(2,1,2)
plot(time_SRY,(syne/smyne),time_SRY,(synie/smynie))
title('Error for Negative Y Axis from Step Response');
ylabel('Error (%)');
xlabel('Time (ms)');
legend('Total Error','Integrator Error');

figure;
subplot(2,1,1)
plot(time_SRY,sypmd)
title('Microprocessor Output to Motor Driver for Positive Y Axis from Step
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');
subplot(2,1,2)
plot(time_SRY,synmd)
title('Microprocessor Output to Motor Driver for Negative Y Axis from Step
Response');
ylabel('Output PWM (0-400)');
xlabel('Time (ms)');

72