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

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

•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

4

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%

5

Division of Labor

6

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

8

MCUMotor

Platform

Generator Set/Current

Source

Rotary Encoder

Power

User Input

Motor PWM

Encoder Feedback

Motor/Gen Coupling

H-Bridge Interface2 2 2

2

D/A

Rotational Motion

I2C Debug

Rotational Motion

RS-232

Motor PWM

Debug Signal

2

Generator PWM

Fig. 2 – Experimental Platform Block Diagram

Simulink System

9

Fig. 3 – Simulink System Block Diagram



10


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

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

11

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




13

Input and Disturbance Commands: Limitations and Requirements

14

•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

15

Legend:Command – CMDAcknowledge – ACK

Atmega128 MATLAB

CMD1ACK1

CMD2ACK2

CMD3ACK3

Etc…

Time

Fig. 6 – ATmega128/MATLAB Acknowledgements

Input and Disturbance Commands: Baud Rate

16

•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




17

I2C Communication

18

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

0

2

4

6

SC

L [V

]

I2C Communication

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

0

2

4

6

SD

A [V

]

Time

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-4

0

2

4

6

PO

RT

B [V

]

Time




20

Future Work

21

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



22


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

•Benjamin Roos•Alexander Schmidt•Conclusion

23

Overview

24

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




25

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

27




28

Simulink System: Kinematic Model

29

Motor Coupling

Differential Motor Model

Motor Coupling

x

Vehicle Dynamic Model

Rotary Encoder Model

Vehicle Kinematic

Model

VelocityPosition XPosition Y

AccelerationOrientation

5

x

User Input

User Input

Rotational Velocity2

Pulses per Rotation

Controller

2

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

32

Fig. 15 – Simulink Kinematic System

Kinematic Model: Results

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




34

Simulink System: Dynamic Model

35Fig. 17 – Simulink System Block Diagram

Dynamic Model

•Torque inputs into the Simulink motor model

36

Fig. 18 – Dynamic Model Connection to Motor Model

Dynamic Model: Forces

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

37

Dynamic Model

38

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




41

Future Work

42

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



43


•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

44

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

46

Fig. 24 – Current Source Located in the Experimental Platform




47

Generator Current Control Design

48

•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

49

Fig. 26 – Current Source Testing Schematic

Initial Circuit Testing: Generator Load

50

Fig. 27 – Physical Circuit Step Response




51

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




54

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

56

Fig. 31 – Compensated Physical Circuit Step Response




57

Future Work

58

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



59


•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

60

Overview

61

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

62

Motor Model

63

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

67

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

68

Current Probe Method

69Fig. 38 – Cogging Torque Current Scope Waveform



•Overview


•Conclusion

70

Adjusting For Current Variations

•How do we handle Cogging Torque?

•Adjusting with Nonlinear Gain

71Fig. 39 – Flowchart for Cogging Torque



•Overview


•Conclusion

72

Without Nonlinear Gain

73

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

With Nonlinear Gain

74

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

77

Future Work

78

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



79

Conclusion

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

80

Conclusion

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

81

Conclusion

•Benjamin has completed:•Generator Torque Disturbance Control Circuitry

82

Conclusion

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

83

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 ✓

84

Summary

•On schedule for project completion

85

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

87

Input and Disturbance Commands: Baud Rate

88

UBRR: USART Baud Rate Registers

𝐵𝐴𝑈𝐷 =𝑓𝑂𝑆𝐶

16 𝑈𝐵𝑅𝑅+1[1]

I2C Communication: Clock Speed

89

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

90

I2C Communication: Project Requirements

•2 8-bit Timers for Rotary Encoders

•2 16-bit Timers for 4 PWM Channels

•1 Timer for Interrupt Generation

91

Appendix Slides


92

Theoretical Vehicle Design

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

93

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

94

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

95

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

96

Wheel Size: Equations

𝑅𝑅 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 × 𝐶𝑟𝑟 [3]

𝐺𝑅 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 × sin ∝ [4]

𝐹𝐴 𝑙𝑏 = 𝐺𝑉𝑊 𝑙𝑏 ×𝑉𝑚𝑎𝑥

𝑓𝑡

𝑠

32.2𝑓𝑡

𝑠2×𝑡𝑎[𝑠]

[5]

𝑇𝑇𝐸 𝑙𝑏 = 𝑅𝑅 𝑙𝑏 + 𝐺𝑅 𝑙𝑏 + 𝐹𝐴 𝑙𝑏 [6]

𝑅𝑤 𝑖𝑛 =𝑇𝑤 𝑙𝑏−𝑖𝑛

𝑇𝑇𝐸 𝑙𝑏 ×𝑅𝑓[7]

97

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

99


100

Fig. 48– Rotary Encoder Model

Rotary Encoder Model: Conversion

101

Fig. 49 – Conversion Subsystem

Rotary Encoder Model: Rounding

102

Fig. 50 – Rounding Subsystem

Rotary Encoder Model: Frequency Creation

103

Fig. 51 – Frequency Creation Subsystem

Rotary Encoder Model: Index Creation

104

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

107

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

108

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

110


•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

112

Kinematic Model

113

Fig. 58 – Internal Kinematic Model

Angle Calculation

114

Fig. 59 – Angle Calculation Subsystem

Position Calculation

115

Fig. 60 – Position Calculation Subsystem

Dynamic Model: Velocity Torques

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

Dynamic Model: Angle Torques

117

Fig. 62 – Torques Affected by Angles in Dynamic Model

In Depth View of Dynamic Model

•Rolling Torque

118

Fig. 63 – Rolling Torque Subsystem


•Gravitational Torque

119

Fig. 64 – Gravitational Torque Subsystem


•Aerodynamic Lift Torque

120

Fig. 65 – Aerodynamic Lift Torque Subsystem


•Aerodynamic Drag Torque

121

Fig. 66 – Aerodynamic Drag Torque

In Depth View of the Dynamic Model

•Acceleration Torque

122

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

123

H-Bridge Model

124

Fig. 68 – H-Bridge Model in Simulink

In Depth View of H-Bridge Model

125

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

126

PWM Model

127

Fig. 71 – PWM Model in Simulink

Appendix Slides


128

Physical Current Source Testing

129

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

Compensated Circuit Schematic

130

Fig. 73 – Compensated Lead Network Current Source Circuit Schematic

Compensated Linear Frequency Response

131

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

Nonlinear Current Source Gain

132

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

Current Source Circuit Plant

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

133

Current Source Circuit Plant: Op-Amp

𝐺𝑜𝑝−𝑎𝑚𝑝 𝑠 = (119 ∗ 103)1

(1

2𝜋∗10𝑠+1)(

1

2𝜋∗1.22∗106𝑠+1)

[9]

134

135

𝐺𝐵𝐽𝑇−𝑔𝑒𝑛𝑠𝑒𝑡 𝑠 =1

(1

2𝜋∗104𝑠+1)2(

1

2𝜋∗3∗105)2

[10]

Current Source Circuit Plant:Transistor and Generator

136

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)

[11]

Current Source Compensator

PSPICE Current Source Testing

137

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

PSPICE Current Source Testing

138

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

Physical Current Source Testing

139

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

140

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

141

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

Appendix Slides


142

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

147

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

156

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

Scale Method

157

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

158

TABLE III. Cogging Current Data

Average Thermal Loss

159Fig. 95 – Thermal Average Output

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