design of a simulink-based control workstation for mobile
TRANSCRIPT
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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 5, 2016
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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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
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Overview
4Fig. 1 – High Level Block Diagram
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Vehicle
5Fig. 2 – Theoretical Vehicle Design
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Transient Motor Testing
•Settling Time Error = 96.7%
•Overshoot Error = 228.1%
•Steady-State Error = 56.6%
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Simulink Vs Experimental Error
8Fig. 3 – Simulink Vs Experimental Step Waveform
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RPM Motor Testing
9Fig. 4 – Simulink Vs Experimental Final Values
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Cogging Torque Experimental Waveform
10Fig. 5 – Cogging Torque from Experimental
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Cogging Torque Specification
•Cogging Torque Percent Error = 14.5%
11Fig. 6– Cogging Torque Span
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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High Level Block Diagram
13Fig. 7– High Level Block Diagram
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Simulink System
14
Fig. 8– Simulink System Block Diagram
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Simulink System
15
Fig. 9– Simulink System Block Diagram
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Functions and Specifications
•Function: Model Accuracy
•Specification: Within ±20% for average error
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H-Bridge: Average Error of 10.046%
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Fig. 10– H-Bridge Average Error
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Rotary Encoder: Average Error of 3.47%
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Fig. 11– Rotary Encoder Average Error
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PWM: Average Error of 0.24%
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Fig. 12– PWM Average Error
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Experimental Platform
21Fig. 13– High Level Block Diagram
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Experimental Platform
22
Fig. 14– Experimental Platform Block Diagram
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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
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Current Source Torque Disturbance Matching
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Fig. 15– The Experimental Platform Disturbance Input should match that of the Simulink Model
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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
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Generator Specification: Settling Time
26Fig. 16– Experimental Platform Open Loop Settling Time Error as compared to Simulink
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Generator Specification: Overshoot
27Fig. 17– Experimental Platform Open Loop Overshoot Error as compared to Simulink
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Generator Specification: Steady-State
28Fig. 18– Experimental Platform Open Loop Steady State Error as compared to Simulink
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Generator : Average Absolute Error
29Fig. 19– Experimental Platform Absolute Error as compared to Simulink
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Generator Load: Open Loop Response
30Fig. 21–Open Loop Response with Vin = 16v and Current Load = 0 A
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Generator Load: Open Loop Response
31Fig. 22–Open Loop Response with Vin = 16v and Current Load = 1.5 A
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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
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Velocity Comparison
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Fig. 23– Velocity Output Comparison
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Position Comparison
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Fig. 24– Vehicle Position Comparison
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Zoomed Position Comparison
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Fig. 25– Vehicle Position Comparison
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Vehicle Plant Bode Diagram
37Fig. 26– Vehicle Plant Bode Diagram
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Controller and Plant Bode Diagram
38Fig. 27– Continuous Vehicle and Controller Bode with Controller Gain = 500
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Discrete PI Controller Step Response
39Fig. 28– Simulink Controller Response to Worst Case Conditions,
Settling Time = 1 second
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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%
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Disturbance Rejection Specification
•Simulink Test Measurements:•Max Instantaneous Error of 35.75% at 20 RPM•Spec has been met for the Simulink Model
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Disturbance Rejection Specification
42Fig. 29– Simulink Disturbance Response Curves with Disturbance Change at 2 seconds
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Disturbance Rejection Specification
43
•Experimental Platform Test Measurements:•Max Instantaneous Error of about 38% at 20 RPM•Spec has been met for the Experimental Platform
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Disturbance Rejection Specification
44Fig. 30– Simulink Disturbance Response Curves with Disturbance Change at 3 seconds
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Disturbance Rejection Specification
45Fig. 31– Average Instantaneous Error of Disturbance Tests in Experimental Platform
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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
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Step Tracking Specification
Simulink Test Measurements:•Max Error is about 14% at 400 RPM•Spec has been met for the Simulink Model
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Step Tracking Specification
48Fig. 32– Average Error of Step Responses in Simulink
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Step Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 22% at 40 RPM•Spec has not been met for the Experimental Platform
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Step Tracking Specification
50Fig. 33– Average Error of Step Responses in Experimental Platform
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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
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Ramp Tracking Specification
Simulink Test Measurements:•Max Error is about 35% at 400 RPM/s•Spec has not been met for Simulink
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Ramp Tracking Specification
53Fig. 34– Average Error for Ramp Responses in Simulink
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Ramp Tracking Specification
54Fig. 35– Simulink Ramp Response Curve with a Ramp Input = 400 RPM/s
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Ramp Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 19% at 20 RPM/s•Spec has been met for the Experimental Platform
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Ramp Tracking Specification
56Fig. 36– Average Error for Ramp Responses in Experimental Platform
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Ramp Tracking Specification
57Fig. 37– Experimental Platform Ramp Response Curve with a Ramp Input = 400 RPM/s
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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
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Parabolic Tracking Specification
Simulink Test Measurements:•Max Error is about 20% at 400 RPM/s^2•Spec has been met for Simulink
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Parabolic Tracking Specification
60Fig. 38– Average Error for Parabolic Responses in Simulink
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Parabolic Tracking Specification
Experimental Platform Test Measurements:•Max Error is about 23% at 80 RPM/s^2•Spec has been met for Experimental Platform
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Parabolic Tracking Specification
62Fig. 39– Average Error for Parabolic Responses in Experimental Platform
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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%
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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%
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Motor Mismatch Specification
Simulink Test Measurements:•Max Error is about 4.25% at 20 RPM•Spec has been met
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Motor Mismatch Specification
66Fig. 40–Error for Motor Mismatch in the Simulink Model
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Overview
68Fig. 40– High Level Block Diagram
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Function and Specification
•Function: Graphical User Interface (GUI) Communication
•Specification: Successfully send and receive commands
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Experimental Platform Software
•Design and MCU Resources•Interrupt Software•Communication Software
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Experimental Platform Software: Design
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• Interrupt Time: 600 μs to 900 μs•Communication Time: 45 ms to 60 ms•70 bits data•Baud Rate: 38.4 kbps
Controller: 800 μs Communication:200 μs
Interrupt Period: 1 ms
Fig. 42– Interrupt Diagram
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Graphical User Interface Communication: Serial Communication
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Legend:Command – CMDAcknowledge – ACK
Atmega128 MATLAB
CMD1ACK1
CMD2ACK2
CMD3ACK3
Etc…
Time
Fig. 43– Communication Protocol Diagram
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Experimental Platform Software: MCU Resources
• All Four Timer/Counter Units• USART Communication• Two I2C Devices• Flash: 11,166 bytes (8.5%)• SRAM: 2,032 bytes (49.6%)
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Graphical User Interface Communication: Interrupt Contents
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•Rate Limiting•Command Conditioning•Anti-Windup Software•Model Based PID Controller•Feed-Forward Controller•Dynamic Model •Taylor Series Expansion
•Torque Matching Software•I2C Communication
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Graphical User Interface Communication: I2C Communication
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I2C Hardware Execution Time: 300 μsI2C Software Execution Time: 20 μs
Fig. 44– I2C Communication Plot
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Demonstration Outline
•Background and Overview•Motor Modeling and Cogging Torque•Simulink Modeling•Experimental Platform•Controller Development and Specifications•Graphical User Interface Design•Graphical User Interface Communication•Nonfunctional Requirements
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Nonfunctional Requirements
• The workstation should be reliable.
• Velocity commands shall be easy to issue to both the experimental platform and the Simulink model
• Modifying the load shall be easy on both the experimental platform and the Simulink model
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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 5, 2016
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Appendix Slides
•Benjamin Roos
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Vehicle Plant Root Locus
81Fig. 7 – Vehicle Plant Root Locus
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Plant and Controller Root Locus
82Fig.8– Vehicle and Controller Root Locus with Zero at s = -19.5 rad/s
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Vehicle Plant
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𝐺𝑃𝐻 𝑠 =0.0001606
1.389 ∙ 10−6𝑠2 + 0.001315𝑠 + 0.001877
𝑤𝑖𝑡ℎ 𝑝𝑜𝑙𝑒𝑠 𝑎𝑡 𝑠 = −1.43, −945.4 𝑟𝑎𝑑/𝑠
Eq. 101-1 – Vehicle Plant and Encoder Gain Model in the Laplace Domain
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Continuous Feedback Controller
𝐺𝑐 𝑠 = 19.5𝑘
𝑠19.5
+ 1
𝑠
𝑤ℎ𝑒𝑟𝑒 𝑘 = 500
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Eq. 102-1 – Continuous Feedback Controller in the Laplace Domain
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Discrete Feedback Controller
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𝐺𝑐 𝑧 = 𝑘1.01𝑧 − 0.9902
𝑧 − 1
𝑤ℎ𝑒𝑟𝑒 𝑘 = 500
Eq. 103-1 – Discrete Feedback Controller Converted with the Tustin Method and Pre-warped at 63.8 rad/s
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Step Tracking Specification
86Fig. 54 – Step Response Curves in Simulink
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Step Tracking Specification
87Fig. 54 – Step Response Curves in Experimental Platform
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Parabolic Tracking Specification
88Fig. 55 – Simulink Parabola Response Curve with a Parabola Input = 400 RPM/s^2
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Parabolic Tracking Specification
89Fig. 55 – Exp. Platform Parabola Response Curve with a Parabola Input = 400 RPM/s^2
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Disturbance Rejection Specification
90Fig. 11 –Open Loop Response with Vin = 16v and Current Load = 0 A and no filtering