design of a simulink-based control workstation for mobile...

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

November 24, 2015

Presentation Outline

•Background•Kevin Block•Timothy De Pasion•Benjamin Roos•Alexander Schmidt•Conclusion

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

Objectives

•Cogging Torque Modeled

•Current Source Developed and Modeled

•Kinematic Model Finished

•Dynamic Model Started

•Input Commands Communicated

•Disturbance Commands Communicated

•I2C Communication Established with DAC

Specifications Related to Current Progress

•Motor : Model to within ±20%

•Rotary Encoder: Model to within ±20%

•Pulse-width modulation: Model to within ±20%

•H-Bridge: Model to within ±20%

•Cogging Torque: Model to within ±50%

•DC Generator Loads: Model to within ±50%

Division of Labor

Task Name Team Member Name

Cogging Torque Alexander Schmidt

Motor Models Alexander Schmidt

Current Source Benjamin Roos

Generator Model Benjamin Roos

Serial Communication Kevin Block

I2C Communication Kevin Block

Kinematic and Dynamic Models Timothy De Pasion

Component Models Timothy De Pasion

TABLE I. DIVISION OF LABOR

Overview

7Fig. 1 – High Level Block Diagram

Experimental Platform

MCUMotor

Platform

Generator Set/Current

Source

Rotary Encoder

User Input

Motor PWM

Encoder Feedback

Motor/Gen Coupling

H-Bridge Interface2 2 2

Rotational Motion

I2C Debug

Rotational Motion

RS-232

Motor PWM

Debug Signal

Generator PWM

Fig. 2 – Experimental Platform Block Diagram

Simulink System

Fig. 3 – Simulink System Block Diagram

•Background•Kevin Block•Overview•Input and Disturbance Commands•I2C Communication•Future Work

•Timothy De Pasion•Benjamin Roos•Alexander Schmidt•Conclusion

Overview

12Fig. 4 – Kevin’s Gantt Chart

7 11 14 18 21 25 28 1 4 8 11 15 18

Input Command

Disturbance Command

I2C and new D/As

October NovemberTask Name

Input and Disturbance Commands: Limitations and Requirements

•Interrupt Time: 1 ms•Data: 60 bits•Baud Rate: 38.4 kbps

Controller: 800 μs 200 μs

Interrupt Period: 1 ms

Fig. 5 – Interrupt Timing Diagram

Input and Disturbance Commands: Synchronization

Legend:Command – CMDAcknowledge – ACK

Atmega128 MATLAB

CMD1ACK1

CMD2ACK2

CMD3ACK3

Etc…

Fig. 6 – ATmega128/MATLAB Acknowledgements

Input and Disturbance Commands: Baud Rate

•With Acknowledgments

•# of Bits: 100

•Baud Rate: 38.4 kbps

•Transfer Time: 2.6 ms

•Max Time: 13 ms

•No Acknowledgments

•# of Bits: 60

•Baud Rate: 38.4 kbps

•Transfer Time: 1.56 ms

•Max Time: 7.8 ms

I2C Communication

Fig. 7 – New Experimental Platform Block Diagram

•Requirements Prior:•5 Timer/Counters•4 PWM Channels

• Requirements After:• 4 Timer/Counters• 2 PWM Channels

I2C Communication

19Fig. 8 – I2C Communication Output

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

I2C Communication

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

Future Work

15-25 29 2-13 16-20 23 27-30 3 6-10 13 17 20-27 31 3-14 17-28

Experimental Platform Integration

Simulink Integration

Controller Development

Controller Model

Controller Code

Simulink GUI Control

Experimental Platform Testing

Simulink System Testing

November FebruaryJanuaryDecemberTask Name

Fig. 9 – Kevin’s Future Gantt Chart

•Kevin Block•Timothy De Pasion•Overview•H-Bridge Model/PWM Model•Kinematic Model•Dynamic Model•Future Work

•Benjamin Roos•Alexander Schmidt•Conclusion

Overview

14 18 21 25 28 1 4 8 11 15 18 22 25

H-Bridge Model

PWM Model

PWM Frequency Optimized

Kinematic Model

Dynamic Model

October November

Task Name

Plan Actual % CompleteActual

(beyond plan)

% Complete

(beyond plan)

Fig. 10 – Tim’s Gantt Chart

Simulink System: H-Bridge and PWM

26Fig. 11 – Simulink System Block Diagram

Results

•H-Bridge Model•0.038% error for the duty cycle test•10.04% error for the voltage output test•Meets the ±20% Specification

•PWM Model•Average of 0.24% error •This meets the ±20% specification

Simulink System: Kinematic Model

Motor Coupling

Differential Motor Model

Motor Coupling

Vehicle Dynamic Model

Rotary Encoder Model

Vehicle Kinematic

VelocityPosition XPosition Y

AccelerationOrientation

User Input

Rotational Velocity2

Pulses per Rotation

Controller

H-Bridge/PWM

Fig. 12 – Simulink System Block Diagram

Kinematic Model

•The motion of the theoretical vehicle model

•Modified the standard differential drive kinematic model

30Fig. 13 – Standard Differential Drive Center Point

Kinematic Model: Center of Gravity

31Fig. 14 – Theoretical Vehicle Center of Gravity

Kinematic Model: Simulink Model

Fig. 15 – Simulink Kinematic System

Kinematic Model: Results

33Fig. 16 – Standard Kinematic Model Versus the Modified Model

Simulink System: Dynamic Model

35Fig. 17 – Simulink System Block Diagram

Dynamic Model

•Torque inputs into the Simulink motor model

Fig. 18 – Dynamic Model Connection to Motor Model

Dynamic Model: Forces

•Aerodynamic Drag•Aerodynamic Lift•Gravitational•Rolling Resistance•Acceleration

Dynamic Model

Fig. 19 – Dynamic Vehicle Model

Dynamic Model: Results

39Fig. 20 – Torque Output of Dynamic Model

Dynamic Model: Results

40Fig. 21 – Velocity Output of Motor Model with Dynamic Model

Future Work

February

15-25 29 2-13 16-20 23 27-30 3 6-13 17 20-31 3-28

Controller Model

Terrain Testing

November December January

Task Name

Fig. 22 Tim’s Future Gantt Chart

•Background•Kevin Block•Timothy De Pasion•Benjamin Roos•Overview•Initial Generator Current Control Circuit Testing•Circuit Plant Model Estimation•Circuit Controller•Future Work

•Alexander Schmidt•Conclusion

Overview

45Fig. 23 – Ben’s Gantt Chart

4 7 11 14 18 21 25 28 1 4 8 11 15 18 22 25

Current Source Research and Experimental

Digital Filter

Dynamic Model

Experimental Platform: Current Source

Fig. 24 – Current Source Located in the Experimental Platform

Generator Current Control Design

•Current through RS is delivered to the generator

•VS = supply voltage

•VG = induced voltage

•VI = current control voltage

Fig. 25 – Basic Current Source Diagram

Initial Circuit Testing: Generator Load

Fig. 26 – Current Source Testing Schematic

Initial Circuit Testing: Generator Load

Fig. 27 – Physical Circuit Step Response

PSPICE Circuit Testing

•PSPICE generator load output matches physical observations

52Fig. 28 – PSPICE Circuit Step Response

PSPICE Plant Model Estimation•PSPICE op-amp and BJT-generator sub-circuits tested for frequency response

53Fig. 29 – Frequency Response of Open Loop Circuit System

Current Circuit Controller

•Lead-compensator to cancel pole at crossover•Pole placed near DC to ground AC signals

55Fig. 30 – Compensated Nonlinear Frequency Response of Open Loop Circuit System

Compensated Circuit Testing

Fig. 31 – Compensated Physical Circuit Step Response

Future Work

February

15 18-22 25-29 2-6 9-13 16-30 3 6-10 13-17 20-31 3-28

Digital Filter

Efficiency Model

Controller Model

JanuaryDecemberNovemberTask Name

Fig. 32 – Ben’s Future Gantt Chart

•Background•Kevin Block•Timothy De Pasion•Benjamin Roos•Alexander Schmidt

•Overview

•Motor System Identification•Cogging Torque Measurement•Cogging Torque Modeling•Cogging Torque Tuning•Future Work

•Conclusion

Overview

4 7 11 14 18 21 25 28 1 4 8 11 15 18 22

Cogging Torque Experimental and Research

Cogging Torque Model

Experimental Thermal Measurements

Thermal Simulink Model

Fig. 33 – Alex’s Gantt Chart

•Overview

•Conclusion

Motor Model

Fig. 34 – Motor Model

Motor Model

64Fig. 35 – Advanced Motor Model

Motor Variable Identification

65Fig. 36 – Experimental Motor Response

Motor Parameter Identification

66Fig. 37 – Coulomb & Viscous Friction

Motor Parameter Identification

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

•Overview

•Conclusion

Current Probe Method

69Fig. 38 – Cogging Torque Current Scope Waveform

•Overview

•Conclusion

Adjusting For Current Variations

•How do we handle Cogging Torque?

•Adjusting with Nonlinear Gain

71Fig. 39 – Flowchart for Cogging Torque

•Overview

•Conclusion

Without Nonlinear Gain

Fig. 41 – Current Output without GainFig. 40 – Voltage Input

With Nonlinear Gain

Fig. 42 – Voltage Input Fig. 43 – Current Output with Gain

Results

75Fig. 44 – Experimental Vs Simulink Motor Response

Results

76Fig. 45 – Zoomed Experimental Vs Simulink Motor Response

•Overview

•Conclusion

Future Work

February

15-22 25 29 2-6 9-13 16-20 23 27-30 3 6-17 20-31 3-28

Efficiency Model

Controller Model

November December JanuaryTask Name

Fig. 46 – Alex’s Future Gantt Chart

Conclusion

•Kevin has completed:•Serial Communication•Input Command•Disturbance Command•I2C

Conclusion

•Timothy has completed:•H-Bridge Model•PWM Model•PWM Frequency Optimization•Kinematic Model•Dynamic Model

Conclusion

•Benjamin has completed:•Generator Torque Disturbance Control Circuitry

Conclusion

•Alexander has completed:•Motor Analysis•Cogging Torque Analysis•Cogging Torque Modeling•Simulink Testing

Objectives Completed:

•Cogging Torque Modeled ✓

•Current Source Developed and Modeled ✓

•Kinematic Model Finished ✓

•Dynamic Models Finished ✓

•Input Commands Communicated ✓

•Disturbance Commands Communicated ✓

•I2C Communication Established with DAC ✓

Summary

•On schedule for project completion

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

November 24, 2015

Appendix Slides

•Kevin Block•Timothy De Pasion•Benjamin Roos•Alexander Schmidt

Input and Disturbance Commands: Baud Rate

UBRR: USART Baud Rate Registers

𝐵𝐴𝑈𝐷 =𝑓𝑂𝑆𝐶

16 𝑈𝐵𝑅𝑅+1[1]

I2C Communication: Clock Speed

TWBR: TWI Bit Rate RegisterTWPS: TWI Bit Rate Prescalar

𝑓𝑆𝐶𝐿 =𝑓𝑂𝑆𝐶

16+2 𝑇𝑊𝐵𝑅 ∗4𝑇𝑊𝑃𝑆 [2]

I2C Communication: MCU Limitations

•2 8-bit Timers•1 PWM Channel Apiece

•2 16-bit Timers•3 PWM Channels Apiece

I2C Communication: Project Requirements

•2 8-bit Timers for Rotary Encoders

•2 16-bit Timers for 4 PWM Channels

•1 Timer for Interrupt Generation

Appendix Slides

Theoretical Vehicle Design

•Battery Calculations•Part Choices•Force Calculations•Wheel Size Calculations

Battery Calculations

•Sum of the current required from each of the components•Motor Current: 2.5 A each•Other components: 1,064 mA

•Use three batteries•7.2 Volt, 2800 mAh•Two 12 Volt, 1600 mAh

•Gives a test length of 38.4 minutes

Part Choices

•These choices were purely theoretical•Interfacing all of the parts was not considered•Goal was to get a realistic theoretical vehicle to model

Parts:• 2 Motors• BeagleBone Black• Xbee• Compass• Pixy and pan/tilt

• 4 Ultrasonic Sensors• 2 12 Volt batteries• 7.2 Volt battery• ATmega128 development board

Wheel Size Calculations

•Mass of the Vehicle: 3,876 g

•Maximum incline: 15 degrees

•Maximum Velocity: 20 ft/s

•Calculated wheel radius: 24.78 mm

Wheel Size: Equations

𝑅𝑅 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 × 𝐶𝑟𝑟 [3]

𝐺𝑅 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 × sin ∝ [4]

𝐹𝐴 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 ×𝑉𝑚𝑎𝑥

𝑓𝑡

32.2𝑓𝑡

𝑠2×𝑡𝑎[𝑠]

𝑇𝑇𝐸 𝑙𝑏 = 𝑅𝑅 𝑙𝑏 + 𝐺𝑅 𝑙𝑏 + 𝐹𝐴 𝑙𝑏 [6]

𝑅𝑤 𝑖𝑛 =𝑇𝑤 𝑙𝑏−𝑖𝑛

𝑇𝑇𝐸 𝑙𝑏 ×𝑅𝑓[7]

Final Vehicle Design

98Fig. 47 – Theoretical Vehicle Design

•Specification: Model the physical rotary encoder output to within ±20%

•Approach: Convert the internal velocity input to internal shaft position, use the internal shaft position to estimate the frequency of the rotary encoder output

Fig. 48– Rotary Encoder Model

Rotary Encoder Model: Conversion

Fig. 49 – Conversion Subsystem

Rotary Encoder Model: Rounding

Fig. 50 – Rounding Subsystem

Rotary Encoder Model: Frequency Creation

Fig. 51 – Frequency Creation Subsystem

Rotary Encoder Model: Index Creation

Fig. 52 – Index Creation Subsystem

Rotary Encoder Model: Channel B

105Fig. 53 – Channel B Creation

Rotary Encoder Model: Pulse Generator

106Fig. 54 – Pulse Generator Subsystem

Rotary Encoder Model: Channel A

Fig. 55 –Channel A Creation Subsystem

•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 3.84% over the whole range, maximum instantaneous error of 21.73%•Meets the specification

Command Conditioning Model

•Used to convert an input velocity command into something that the system will recognize

•Convert velocity in RPM into pulses

109Fig. 56 – Command Conditioning Model

•Test to find a frequency where the rotary encoder error is minimal

•Frequency swept from 8 kHz to 40 kHz at 20% and 80% duty cycles

•Found that there was little error (1.7%) due to the PWM Frequency

•Choose to stick with a 15,625 Hz frequency that the microcontroller can easily generate

•Linear result at 15,625 Hz

111Fig. 57 – Rotary Encoder Output Due to PWM Input

In Depth View of Kinematic Model

•2 Subsystems

•Angle Calculation Subsystem

•Position Calculation Subsystem

Kinematic Model

Fig. 58 – Internal Kinematic Model

Angle Calculation

Fig. 59 – Angle Calculation Subsystem

Position Calculation

Fig. 60 – Position Calculation Subsystem

Dynamic Model: Velocity Torques

116Fig. 61 – Torques Affect by Velocity in Dynamic Model

Dynamic Model: Angle Torques

Fig. 62 – Torques Affected by Angles in Dynamic Model

In Depth View of Dynamic Model

•Rolling Torque

Fig. 63 – Rolling Torque Subsystem

•Gravitational Torque

Fig. 64 – Gravitational Torque Subsystem

•Aerodynamic Lift Torque

Fig. 65 – Aerodynamic Lift Torque Subsystem

•Aerodynamic Drag Torque

Fig. 66 – Aerodynamic Drag Torque

In Depth View of the Dynamic Model

•Acceleration Torque

Fig. 67 – Acceleration Torque Subsystem

H-Bridge Model

•Modeled as a variable gain

•Test the physical H-Bridge duty cycle and voltage output versus the Simulink model duty cycle and voltage output

•Results: •0.038% error for the duty cycle test•10.04% error for the voltage output test•Meets the ±20% Specification

H-Bridge Model

Fig. 68 – H-Bridge Model in Simulink

In Depth View of H-Bridge Model

Fig. 69 – Supply Limiting Function in H-Bridge

Fig. 70 – Normalize PWM Input Function

PWM Model

•Use an input frequency and an input duty cycle and generate a PWM waveform based off of those inputs

•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•This meets the ±20% specification

PWM Model

Fig. 71 – PWM Model in Simulink

Appendix Slides

Physical Current Source Testing

Fig. 72 – Gain Reduction Compensated Physical Current Source Circuit 1V Step Response

Compensated Circuit Schematic

Fig. 73 – Compensated Lead Network Current Source Circuit Schematic

Compensated Linear Frequency Response

Fig. 74 – Compensated Open Loop Linear Frequency Response of Current Source Circuit

Nonlinear Current Source Gain

Fig. 75 – Nonlinear Current Source Gain Adjustment for Better PSPICE Matching

Current Source Circuit Plant

𝐺𝑝𝑙𝑎𝑛𝑡 = 𝐺𝑜𝑝−𝑎𝑚𝑝 ∗ 𝐺𝐵𝐽𝑇−𝑔𝑒𝑛𝑠𝑒𝑡 ∗ 𝐺𝑔𝑎𝑖𝑛−𝑚𝑜𝑑 [8]

Current Source Circuit Plant: Op-Amp

𝐺𝑜𝑝−𝑎𝑚𝑝 𝑠 = (119 ∗ 103)1

2𝜋∗10𝑠+1)(

2𝜋∗1.22∗106𝑠+1)

𝐺𝐵𝐽𝑇−𝑔𝑒𝑛𝑠𝑒𝑡 𝑠 =1

2𝜋∗104𝑠+1)2(

2𝜋∗3∗105)2

Current Source Circuit Plant:Transistor and Generator

𝐺𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑜𝑟 𝑠 = 0.233(

2𝜋∗3.18∗104𝑠+1)

2𝜋∗15.9𝑠+1)(

2𝜋∗1.38∗105𝑠+1)(

2𝜋∗106𝑠+1)

Current Source Compensator

PSPICE Current Source Testing

Fig. 76 – Compensated PSPCE Current Source Circuit 0.5V Step Response

PSPICE Current Source Testing

Fig. 77 – Compensated PSPCE Current Source Circuit 0.25V Step Response and DC Offset

Physical Current Source Testing

Fig. 78 – Compensated Physical Current Source Circuit 0.25V Step Response and DC offset

Op-Amp: LMC6482

Maximum Ratings:

Supply Voltage: 15.5 V

Sourcing Output Current: 8 mA

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 Current (Continuous): 5 A

Total Power Dissipation: 65 W

Source: Motorola, Inc., “Plastic Medium-Power Complementary Silicon Transistors,” TIP120 Datasheet, 1995.

Appendix Slides

Top Level

143Fig. 79 – Full Motor Simulink Model

Motor Model

144Fig. 80 – Internal Motor Simulink Model

Coulomb Friction

145Fig. 81 – Coulomb Friction Block

Static Friction

146Fig. 82 – Static Friction Block

Static Friction Logic

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. 83 – Static Friction Code

Position

148Fig. 84 – Position Block

Cogging Torque

149Fig. 85 – Cogging Torque Block

Cogging Torque Logic

150Fig. 86 – Cogging Torque Internal Logic Block

Gear Reduction

151Fig. 87 – Gear Reduction Block

Power Loss Block

152Fig. 88 – Power Loss Block

Thermals

153Fig. 89 – Internal Of Power Loss Block

Electrical Power Loss

154Fig. 90 – Electrical Power Loss

12 Volt Simulink Output

155Fig. 91 – 12 V Simulink Motor Output

Frequency Method

Fig. 92 – Left Oscilloscope Side Fig. 93 – Right Oscilloscope Side

Scale Method

Fig. 94 – 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

TABLE III. Cogging Current Data

Average Thermal Loss

159Fig. 95 – Thermal Average Output

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