design of a simulink-based control workstation for mobile...
TRANSCRIPT
Design of a Simulink-Based Control
Workstation for Mobile Wheeled Vehicles with
Variable-Velocity Differential Motor Drives
Kevin Block, Timothy De Pasion, Benjamin Roos, Alexander SchmidtGary Dempsey
Bradley University Electrical and Computer Engineering Department
April 26, 2016
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System•Graphical User Interface•Conclusion
2
Overview
What: Design and Implement Control Workstation with a Model-Based PID Controller that has Feed-Forward Compensation
How: Combination Simulink and Experimental Platform
Why: Future Control Algorithm Research, Development, and Testing at Bradley University
3
Objectives
•Model the experimental platform in Simulink
•Match the generator load to the theoretical vehicle
•Design a controller to meet specifications
•Create a GUI that interfaces with the systems
5
Constraints
•The Experimental Platform must:
•24 Volt Pittman Motor GM9236S015-R1•8-bit microcontroller•Reliable•Operate in 0° to 45° Celsius•Stable•Safe
6
Constraints
•The Simulink System must:
•Use the standard library•Controlled by a GUI
•The Control System must:
•Have limited inputs to prevent saturation
7
Division of Labor
8
TABLE I. DIVISION OF LABOR
Task Name Team Member Name
Controller Development All Team Members
Current Source Circuitry Benjamin Roos
Generator Load Matching Benjamin Roos
MATLAB GUI Alexander, Timothy
Simulink Modeing Timothy De Pasion
Platform Integration Kevin Block
Simulink Motor Modeling Alexander Schmidt
Presentation Outline
•Background and Overview•Simulink System
•Motor Modeling•Simulink Modeling•Vehicle Modeling•Final Simulink Integration
•Experimental Platform•Control System•Graphical User Interface•Conclusion
12
Presentation Outline
•Background and Overview•Simulink System
•Motor Modeling•Simulink Modeling•Vehicle Modeling•Final Simulink Integration
•Experimental Platform•Control System•Graphical User Interface•Conclusion
13
Motor Function and Specification
•Function: The Simulink motor model shall accurately model the physical motors
•Specification: Model to within ±20%
15
Motor Model
16
Fig. 6 – Motor Model
Electrical Transfer Function
Mechanical Transfer Function
Input+
-
+Kt
-
Kv
Torque Load
Output
Motor Parameter Identification
19
TABLE II. MOTOR PARAMETERS
Constant Experimental Data Sheet Units
Viscous Friction 4.11E-06 3.54E-06 Nm/Rad/Sec
Coulomb Friction 0.0032 0.0056 Nm
Kv 0.0431 0.0458 V/Rad/Sec
Kt 0.0431 0.0458 Nm/A
Transient Motor Testing
•Settling Time Error = 96.7%
•Overshoot Error = 228.1%
•Steady-State Error = 56.6%
•Specification has not been met
20
Cogging Torque Function and Specification
•Function: Cogging torque shall be accurately modeled
•Specification: Model to within ±50%
24
Cogging Torque
•Interference of the permanent magnets with the rotor windings
•Primarily an issue at low velocities
25Fig. 12 – DC Motor Magnet and Windings Interactionhttp://www.microchip.com/design-centers/motor-control-and-drive/motor-types/brushed-dc
Adjusting For Current Variations
•How do we handle Cogging Torque?
•Adjusting with Nonlinear Gain
27Fig. 14 – Flowchart for Cogging Torque
Cogging Torque Specification
•Cogging Torque Percent Error = 14.5%•Specification has been met
30Fig. 19 – Cogging Torque Span
Motor Thermals: 4 Sources of Heat
•Resistance in the brushes
•Coulomb Friction
•Viscous Friction
•Dynamic Loads
31
Presentation Outline
•Background and Overview•Simulink System
•Motor Modeling•Simulink Modeling•Vehicle Modeling•Final Simulink Integration
•Experimental Platform•Control System•Graphical User Interface•Conclusion
33
Functions and Specifications
•Function: Model Accuracy
•Specification: Within ±20% for average error
37
H-Bridge Model
•Test the physical H-Bridge voltage output versus the Simulink model voltage output
•Results: •10.04% error for the voltage output test
•Spec has been met
39
Rotary Encoder Model
•Testing Method: Compare the output of the actual and Simulink rotary encoders with voltage inputs from 0.5 to 24 volts in 0.5 volt steps
•Results: •Average error of 3.47% over the whole range
•Spec has been met
42
PWM Model Testing
•Test the Simulink model duty cycle versus the microcontroller duty cycle
•Result: •0.24% error over the range of 4 to 100% duty cycle with 4% steps
•Spec has been met
45
Presentation Outline
•Background and Overview•Simulink System
•Motor Modeling•Simulink Modeling•Vehicle Modeling•Simulink Final Integration
•Experimental Platform•Control System•Graphical User Interface•Conclusion
47
Vehicle Modeling
Kinematic Models•Position and Orientation
48
Dynamic Models•Inertia and External Forces
https://chess.eecs.berkeley.edu/eecs149/documentation/differentialDrive.pdfhttp://www.intechopen.com/books/motion-control/a-novel-traction-control-for-electric-vehicle-without-chassis-velocity
Fig. 30 – Kinematic Model
Fig. 31 – Dynamic Model
Dynamic Model: Disturbance Torques
•Aerodynamic Drag•Aerodynamic Lift•Gravitational•Rolling Resistance•Acceleration
51
Vehicle Dynamic Model
•Torque inputs into the Simulink motor model
53
Fig. 35 – Dynamic Model Connection to Motor Model
Presentation Outline
•Background and Overview•Simulink System
•Motor Modeling•Simulink Modeling•Vehicle Modeling•Simulink Final Integration
•Experimental Platform•Control System•Graphical User Interface•Conclusion
59
Simulink System
•Contains over 80 subsystems
•8 sublevels deep for some parts
•Average and Designed system models•Average models are simple linear gains•Designed models follow their physical counterparts
62
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System•Graphical User Interface•Conclusion
63
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform
•Microcontroller Software•Serial Communication•Current Source and Torque Matching
•Control System•Graphical User Interface•Conclusion
64
MCU Specifications and Resources
•Function: Graphical User Interface (GUI) Communication
•Specification: Successfully send and receive commands
•Spec has been met
66
MCU Specifications and Resources
• All Four Timer/Counter Units• USART Communication• Two I2C Devices• Flash: 11,166 bytes (8.5%)• SRAM: 2,032 bytes (49.6%)
67
MCU Software
69
• Interrupt Duration: 600 μs to 900 μs
Controller: 800 μs Communication:200 μs
Interrupt Period: 1 ms
Fig. 45 – Interrupt Diagram
MCU Software: Interrupt Software
70Fig. 46 – Interrupt Software Flowchart
• Command Conditioning • Model Based PID Controller• Feed-Forward Controller• Anti-Windup Software• Dynamic Model
•Taylor Series
• Torque Matching Software• I2C Communication
MCU Software: Interrupt Software
72
I2C Hardware Execution Time: 300 μsI2C Software Execution Time: 20 μs
Fig. 48 – Oscilloscope Image Grab of I2C Clock Line
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform
•Microcontroller Software•Serial Communication•Current Source and Torque Matching
•Control System•Graphical User Interface•Conclusion
73
MCU Software: Serial Communication
75
•MATLAB Instrument Control Toolbox•Communication Time: 45 ms to 60 ms•120 bits data•Baud Rate: 38.4 kbps
Controller: 800 μs Communication:200 μs
Interrupt Period: 1 ms
Fig. 50– Interrupt Diagram
MCU Software: Serial Communication
76
Legend:Command – CMDAcknowledge – ACK
Atmega128 MATLAB
CMD1ACK1
CMD2ACK2
CMD3ACK3
Etc…
Time
Fig. 51 – ATmega128/MATLAB Acknowledgements
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform
•Microcontroller Software•Serial Communication•Current Source and Torque Matching
•Control System•Graphical User Interface•Conclusion
77
High Level Block Diagram – Experimental Platform
78
Fig. 52 – The experimental platform should mimic the Simulink vehicle model
Current Source Torque Disturbance Matching
79
Fig. 53 – The Experimental Platform Disturbance Input should match that of the Simulink Model
Compensated Circuit Schematic
81Fig. 55 – Compensated Lead Network Current Source Circuit Schematic
Generator Model
Compensated Circuit Schematic
82Fig. 56 – Compensated Lead Network Current Source Circuit Schematic
Lead Compensator
Compensated Circuit Schematic
83Fig. 57 – Compensated Lead Network Current Source Circuit Schematic
AC Ground
Current Circuit Controller
•Lead-compensator to cancel pole at crossover•Pole placed near DC to ground AC signals
84Fig. 58 – Compensated Nonlinear Frequency Response of Open Loop Circuit System
Plant Inertia Differences Between Systems
•Simulink Vehicle and Motor Inertia:𝐽 = 5.28 ∙ 10−3 𝑘𝑔 𝑚2
•Experimental Platform Motor and Generator Inertia:𝐽 = 6.12 ∙ 10−6 𝑘𝑔 𝑚2
•Goal: Match Acceleration Based on𝑇𝑆𝐼𝑀𝐽𝑆𝐼𝑀
=𝑇𝐸𝑋𝑃𝐽𝐸𝑋𝑃
= 𝑎
𝑇 = 𝑁𝑒𝑡 𝑇𝑜𝑟𝑞𝑢𝑒𝐽 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎
𝑎 = 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
86
Net Torque Reduction System
87
Derivative Lowpass FilterAveraging
FilterMotor Speed
Simulink Torque Load
Generator Friction Torque
Experimental Platform Torque Load
++
-
Fig. 60 – The Experimental Platform Torque Correction System Block Diagram
Generator Load: Open Loop Response
88Fig. 61 – Open Loop Response with Vin = 16v Step and Current Load = 0 A
Generator Load: Open Loop Response
89Fig. 62 – Open Loop Response with Vin = 16v Step and Current Load = 1.5 A
Generator Load Specification
•The DC generator loads shall be designed to mimic the prototype vehicle.
•Performance Specification:•Model within ±50% of the Simulink Model
•Settling Time Error•Overshoot Error•Steady-State Error•Average Absolute Error
90
Generator Load Specification
Experimental Platform Test Measurements:•Average Settling Time Error = 70.4%•Average Overshoot Error = Undefined•Average Steady-State Error = 24.6%•Average Absolute Error = 34.3%
•Spec has not been met for the Experimental Platform
•Performance still sufficient for this project’s purpose
91
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System•Graphical User Interface•Conclusion
92
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System
•Development•Verification
•Graphical User Interface•Conclusion
93
Controller and Plant Bode Diagram
95Fig. 64 – Continuous Vehicle and Controller Bode with added Integrator, Zero = -19.5 rad/s and Controller Gain = 500
Discrete PI Controller Step Response
96
Fig. 65 – Complete Controller Response to Worst Case Conditions,Settling Time = 1 second
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System
•Development•Verification
•Graphical User Interface•Conclusion
97
Controller Functional Requirements
98
Functional Requirement for the
Drive Control SystemSpecification Simulink
Experimental
Platform
Minimize the effect of external
torque disturbances Shaft RPM change ≤ 40%Spec has
been met
Spec has been
met
Reduce vehicle tracking errors for
step commands
Average difference between input
and output ≤ 20% over 4 seconds
Spec has
been metNot Met
Reduce vehicle tracking errors for
ramp commands
Average difference between input
and output ≤ 20% over 4 secondsNot Met
Spec has been
met
Reduce vehicle tracking errors for
parabolic commands
Average difference between input
and output ≤ 40% over 4 seconds
Spec has
been met
Spec has been
met
Reduce the effect of motor mismatch Shaft RPM change ≤ 15%Spec has
been metN/A
TABLE III. DRIVE CONTROL SYSTEM SPECIFICATIONS
Step Tracking Specification
•The drive control system shall reduce vehicle tracking errors for step commands.
•Performance Specification: •Average difference between input and output of less than or equal to 20% over 4 seconds
99
Step Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 22% at 20 RPM•Spec has not been met for the Experimental Platform
100
Ramp Tracking Specification
•The drive control system shall reduce vehicle tracking errors for ramp commands.
•Performance Specification: Average difference between input and output of less than or equal to 20% over 4 seconds
102
Ramp Tracking Specification
Simulink Test Measurements:•Max Error is about 35% at 400 RPM/s•Spec has not been met for Simulink
103
Parabolic Tracking Specification
106Fig. 69 – Parabola Response Curve with a Parabola Input = 400 RPM/s^2
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System•Graphical User Interface•Conclusion
107
GUI Demonstration
Run-through of the GUI for a Simulink Simulation:https://www.youtube.com/watch?v=vuGQLxFuk8A
109
Video of GUI Demonstration
GUI Demonstration
Run-through of the GUI for the Experimental Platform:https://www.youtube.com/watch?v=zawAYN9LUPA
Experimental Platform Demonstration:https://www.youtube.com/watch?v=ao5LDD65wgI
110
Video of GUI Demonstration
Video of Experimental Platform Demonstration
Presentation Outline
•Background and Overview•Simulink System•Experimental Platform•Control System•Graphical User Interface•Conclusion
111
Nonfunctional Requirements
• The workstation should be reliable•Met with a Metric of 4/5
• Velocity commands shall be easy to issue to both the experimental platform and the Simulink model•Met with a Metric of 5/5
• Modifying the load shall be easy on both the experimental platform and the Simulink model•Met with a Metric of 5/5
112
Constraints
•The Experimental Platform must: ✓
•24 Volt Pittman Motor GM9236S015-R1 ✓
•8-bit microcontroller ✓
•Reliable ✓
•Operate in 0° to 45° Celsius ✓
•Stable ✓
•Safe ✓
113
Constraints
•The Simulink System must: ✓
•Use the standard library ✓
•Controlled by a GUI ✓
•The Control System must: ✓
•Have limited inputs to prevent saturation ✓
114
Objectives
•Model the experimental platform in Simulink ✓
•Match the generator load to the theoretical vehicle ✓
•Design a controller to meet specifications ✓
•Create a GUI that interfaces with the systems ✓
115
Design of a Simulink-Based Control
Workstation for Mobile Wheeled Vehicles with
Variable-Velocity Differential Motor Drives
Kevin Block, Timothy De Pasion, Benjamin Roos, Alexander SchmidtGary Dempsey
Bradley University Electrical and Computer Engineering Department
April 26, 2016
Op-Amp: LMC6482
Maximum Ratings:
Supply Voltage: 15.5 V
Sourcing Output Current: 8 mA
Junction Temperature: -40 – 85 C
Storage Temperature: -65 – 150 C
118
Source: National Semiconductor, “LMC6482 CMOS Dual Rail-to-Rail Input and Output Operation Amplifier,” LMC6482 Datasheet, Sept. 2003.
Transistor: TIP120
Maximum Ratings:
Collector-Emitter Voltage: 60 V
Collector-Base Voltage: 60V
Collector Current (Continuous): 5 A
Total Power Dissipation: 65 W
Junction Temperature: 150 C
Storage Temperature: -65 – 150 C
119
Source: Motorola, Inc., “Plastic Medium-Power Complementary Silicon Transistors,” TIP120 Datasheet, 1995.
Transistor Heat Sink Calculation
Max Power Dissipation = 20 W
Junction-to-case Thermal Resistance 𝑅𝐽𝐶 = 1.92℃/𝑊
𝑅𝑇𝑜𝑡𝑎𝑙 =150℃ − 45℃
20𝑊= 5.23℃/𝑊
𝑅ℎ𝑒𝑎𝑡 𝑠𝑖𝑛𝑘 = 5.23 ℃/𝑊 − 1.92 ℃/𝑊 = 3.31 ℃/𝑊
𝑅𝑐ℎ𝑜𝑠𝑒𝑛 = 2.6 ℃/𝑊
120
Source: Motorola, Inc., “Plastic Medium-Power Complementary Silicon Transistors,” TIP120 Datasheet, 1995.
Physical Current Source Testing
121
Fig. 73 – Gain Reduction Compensated Physical Current Source Circuit 1V Step Response
Compensated Linear Frequency Response
122
Fig. 74 – Compensated Open Loop Linear Frequency Response of Current Source Circuit
Nonlinear Current Source Gain
123
Fig. 75 – Nonlinear Current Source Gain Adjustment for Better PSPICE Matching
126
𝐺𝐵𝐽𝑇−𝑔𝑒𝑛𝑠𝑒𝑡 𝑠 =1
(1
2𝜋∗104𝑠+1)2(
1
2𝜋∗3∗105)2
Current Source Circuit Plant:Transistor and Generator
127
𝐺𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑜𝑟 𝑠 = 0.233(
1
2𝜋∗3.18∗104𝑠+1)
(1
2𝜋∗15.9𝑠+1)(
1
2𝜋∗1.38∗105𝑠+1)(
1
2𝜋∗106𝑠+1)
Current Source Compensator
Vehicle Plant in Laplace Domain
128
𝐺𝑃𝐻 𝑠 =0.0001606
1.389 ∙ 10−6𝑠2 + 0.001315𝑠 + 0.001877
𝑤𝑖𝑡ℎ 𝑝𝑜𝑙𝑒𝑠 𝑎𝑡 𝑠 = −1.43, −945.4 𝑟𝑎𝑑/𝑠
Model-based PID controller
𝐺𝑃𝐼𝐷 𝑠 =𝐾𝑃𝑠+𝐾𝐼+𝐾𝐷𝑠
2
𝑠=19.5𝑘
𝑠
19.5+1
𝑠
𝑘 = 500𝐾𝑃 = 500𝐾𝐼 = 9750𝐾𝐷 = 0
130
Eq. 130-1 – Continuous Feedback Controller with individual PID component gains
Discrete Feedback Controller
131
𝐺𝑐 𝑧 = 𝑘1.01𝑧 − 0.9902
𝑧 − 1
𝑤ℎ𝑒𝑟𝑒 𝑘 = 500
Eq. 131-1 – Discrete Feedback Controller Converted with the Tustin Method and Pre-warped at 63.8 rad/s
Plant and Controller Root Locus
133Fig. 77 – Vehicle and Controller Root Locus with Zero at s = -19.5 rad/s
Generator Specification: Settling Time
135Fig. 79 – Experimental Platform Open Loop Settling Time Error as compared to Simulink
Generator Specification: Overshoot
136Fig. 80 – Experimental Platform Open Loop Overshoot Error as compared to Simulink
Generator Specification: Steady-State
137Fig. 81 – Experimental Platform Open Loop Steady State Error as compared to Simulink
Generator : Average Absolute Error
138Fig. 82 – Experimental Platform Absolute Error as compared to Simulink
Disturbance Rejection Specification
•The drive control system shall minimize the effect of external torque disturbances.
•Performance Specification:•Shaft RPM change of less than or equal to 40%
139
Disturbance Rejection Specification
•Simulink Test Measurements:•Max Instantaneous Error of 35.75% at 20 RPM•Spec has been met for the Simulink Model
140
Disturbance Rejection Specification
141Fig. 83 – Simulink Disturbance Response Curves with Disturbance Change at 2 seconds
Disturbance Rejection Specification
142Fig. 84 – Maximum Instantaneous Error of Disturbance Tests in Simulink
Disturbance Rejection Specification
143
•Experimental Platform Test Measurements:•Max Instantaneous Error of about 38% at 20 RPM•Spec has been met for the Experimental Platform
Disturbance Rejection Specification
144Fig. 85 – Simulink Disturbance Response Curves with Disturbance Change at 3 seconds
Disturbance Rejection Specification
145Fig. 86 – Maximum Instantaneous Error of Disturbance Tests in Experimental Platform
Step Tracking Specification
Simulink Test Measurements:•Max Error is about 14% at 400 RPM•Spec has been met for the Simulink Model
146
Ramp Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 19% at 20 RPM/s•Spec has been met for the Experimental Platform
148
Ramp Tracking Specification
150Fig. 89– Experimental Platform Ramp Response Curve with a Ramp Input = 400 RPM/s
Parabolic Tracking Specification
•The drive control system shall reduce vehicle tracking errors for parabolic commands.
•Performance Specification: Average difference between input and output of less than or equal to 40% over 4 seconds
151
Parabolic Tracking Specification
Simulink Test Measurements:•Max Error is about 20% at 400 RPM/s^2•Spec has been met for Simulink
152
Parabolic Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 23% at 80 RPM/s^2•Spec has been met for Experimental Platform
154
Parabolic Tracking Specification
155Fig. 91 – Average Error for Parabolic Responses in Experimental Platform
Motor Mismatch Specification
•The drive control system shall reduce the effect of motor mismatch
•Performance Specification: Shaft RPM change less than or equal to 15%
156
Motor Mismatch Specification
Simulink Test Measurements:•Max Error is about 4.25% at 20 RPM•Spec has been met
157
In Depth View of Dynamic Model
•Aerodynamic Lift Torque
175
Fig. 108 – Aerodynamic Lift Torque Subsystem
In Depth View of the Dynamic Model
•Acceleration Torque
177
Fig. 110 – Acceleration Torque Subsystem
Static Friction Logic
184
function [y,flag_out] = fcn(u,flag_in) if u >= 0.1738 flag_out = 1; elseif u == 0 flag_out = 0; else flag_out = flag_in; end
y = u*flag_out;
Fig. 116 – Static Friction Code
Scale Method
192
Fig. 125 – Scale Method Diagram
Z. Zhu, “A Simple Method for Measuring Cogging Torque in Permanent Magnet Machines”. 2009.
Cogging Current
Voltage (V) Average Current (A) Maximum Current (A) Minimum Current (A) Corrective Gain
1 0.0738 0.132 0.028 2
2 0.0784 0.118 0.046 3
3 0.0831 0.125 0.052 2.5
4 0.0856 0.133 0.048 1.7
5 0.0858 0.141 0.046 1.6
7 0.0917 0.154 0.042 1.4
10 0.0977 0.164 0.042 1.4
12 0.1017 0.17 0.04 1.4
24 0.1206 0.208 0.043 1.4
193
TABLE IV. Cogging Current Data
Resistance in the Windings
•I2*R Losses
195
Fig. 127 – Top Level Resistance Power Loss
Fig. 128 – Bottom Level Resistance Power Loss
Viscous, Coulomb, and Dynamic Loads
•V*T Losses
196
Fig. 129 – Coulomb Friction Losses
Fig. 131 – Dynamic Load Losses
Fig. 130 – Viscous Friction Losses
H-Bridge Build
198
Fig. 133 – H-Bridge Pinout
“LMD1820 3A, 55V H-Bridge” National Semiconductor, Dec. 1999.
H-Bridge Thermals
•Total Power of H-BridgePTotal = PQ + PCOND + PSW
PQ = Quiescent Power Dissipation
PCOND = Conductive Power Dissipation
PSW = Switching Power Dissipation
199
Conductive Power Dissipation
PCOND = 2 * I2RMS * RDS (ON)
IRMS = RMS Current
RDS (ON) = On Resistance of the Power Switch
201
Switching Power Dissipation
PSW = (EON + EOFF) * F
EON = Turn On Energy
EOFF = Turn Off Energy
F = Switching Frequency
202
H-Bridge Total Power
PTotal = 0.6[W] + 2.7[W] + 0.3 [W]
•Maximum power dissipation of the H-Bridge without a heat sink is 3.0 Watts
•PTotal = 3.6 Watts
•Heat Sink is Required!
203
Taylor Series Error
205
Order Sin Error Order Cos Error
1 -11.07207345 0 -41.42135624
3 0.34706639 2 2.19654501
5 -5.13E-03 4 -0.000455979
7 4.41E-05 6 5.04E-04
9 -2.48E-07 8 -3.46E-06
TABLE V. TAYLOR SERIES EXPANSION ERROR
Input and Disturbance Commands: Baud Rate
206
UBRR: USART Baud Rate Registers
𝐵𝐴𝑈𝐷 =𝑓𝑂𝑆𝐶
16 𝑈𝐵𝑅𝑅 + 1
I2C Communication: Clock Speed
207
TWBR: TWI Bit Rate RegisterTWPS: TWI Bit Rate Prescalar
𝑓𝑆𝐶𝐿 =𝑓𝑂𝑆𝐶
16 + 2 𝑇𝑊𝐵𝑅 ∗ 4𝑇𝑊𝑃𝑆
Metric - Reliability
•Very reliable 5 points•Reliable 4 points•Average Reliability 3 points•Not reliable 2 points•Very unreliable 1 point
210
Metric – Issue a command
•Very easy to issue 5 points•Easy to issue 4 points•Average difficulty to issue 3 points•Difficult to issue 2 points•Very difficult to issue 1 point
211