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

April 5, 2016

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

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

Overview

4Fig. 1 – High Level Block Diagram

Vehicle

5Fig. 2 – Theoretical Vehicle Design



6

Transient Motor Testing

•Settling Time Error = 96.7%

•Overshoot Error = 228.1%

•Steady-State Error = 56.6%

7

Simulink Vs Experimental Error

8Fig. 3 – Simulink Vs Experimental Step Waveform

RPM Motor Testing

9Fig. 4 – Simulink Vs Experimental Final Values

Cogging Torque Experimental Waveform

10Fig. 5 – Cogging Torque from Experimental

Cogging Torque Specification

•Cogging Torque Percent Error = 14.5%

11Fig. 6– Cogging Torque Span



12

High Level Block Diagram

13Fig. 7– High Level Block Diagram

Simulink System

14

Fig. 8– Simulink System Block Diagram

Simulink System

15

Fig. 9– Simulink System Block Diagram

Functions and Specifications

•Function: Model Accuracy

•Specification: Within ±20% for average error

16

H-Bridge: Average Error of 10.046%

17

Fig. 10– H-Bridge Average Error

Rotary Encoder: Average Error of 3.47%

18

Fig. 11– Rotary Encoder Average Error

PWM: Average Error of 0.24%

19

Fig. 12– PWM Average Error



20

Experimental Platform


Experimental Platform

22

Fig. 14– Experimental Platform Block Diagram

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

23

Current Source Torque Disturbance Matching

24

Fig. 15– The Experimental Platform Disturbance Input should match that of the Simulink Model

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

25

Generator Specification: Settling Time

26Fig. 16– Experimental Platform Open Loop Settling Time Error as compared to Simulink

Generator Specification: Overshoot

27Fig. 17– Experimental Platform Open Loop Overshoot Error as compared to Simulink

Generator Specification: Steady-State

28Fig. 18– Experimental Platform Open Loop Steady State Error as compared to Simulink

Generator : Average Absolute Error

29Fig. 19– Experimental Platform Absolute Error as compared to Simulink

Generator Load: Open Loop Response

30Fig. 21–Open Loop Response with Vin = 16v and Current Load = 0 A

Generator Load: Open Loop Response

31Fig. 22–Open Loop Response with Vin = 16v and Current Load = 1.5 A

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

32

Velocity Comparison

33

Fig. 23– Velocity Output Comparison

Position Comparison

34

Fig. 24– Vehicle Position Comparison

Zoomed Position Comparison

35

Fig. 25– Vehicle Position Comparison



36

Vehicle Plant Bode Diagram

37Fig. 26– Vehicle Plant Bode Diagram

Controller and Plant Bode Diagram

38Fig. 27– Continuous Vehicle and Controller Bode with Controller Gain = 500

Discrete PI Controller Step Response

39Fig. 28– Simulink Controller Response to Worst Case Conditions,

Settling Time = 1 second

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%

40


•Simulink Test Measurements:•Max Instantaneous Error of 35.75% at 20 RPM•Spec has been met for the Simulink Model

41


42Fig. 29– Simulink Disturbance Response Curves with Disturbance Change at 2 seconds


43

•Experimental Platform Test Measurements:•Max Instantaneous Error of about 38% at 20 RPM•Spec has been met for the Experimental Platform


44Fig. 30– Simulink Disturbance Response Curves with Disturbance Change at 3 seconds


45Fig. 31– Average Instantaneous Error of Disturbance Tests in Experimental Platform

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

46


Simulink Test Measurements:•Max Error is about 14% at 400 RPM•Spec has been met for the Simulink Model

47


48Fig. 32– Average Error of Step Responses in Simulink


Experimental Platform Test Measurements:•Max Error is about 22% at 40 RPM•Spec has not been met for the Experimental Platform

49


50Fig. 33– Average Error of Step Responses in Experimental Platform

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

51


Simulink Test Measurements:•Max Error is about 35% at 400 RPM/s•Spec has not been met for Simulink

52


53Fig. 34– Average Error for Ramp Responses in Simulink


54Fig. 35– Simulink Ramp Response Curve with a Ramp Input = 400 RPM/s


Experimental Platform Test Measurements:•Max Error is about 19% at 20 RPM/s•Spec has been met for the Experimental Platform

55


56Fig. 36– Average Error for Ramp Responses in Experimental Platform


57Fig. 37– 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

58


Simulink Test Measurements:•Max Error is about 20% at 400 RPM/s^2•Spec has been met for Simulink

59


60Fig. 38– Average Error for Parabolic Responses in Simulink


Experimental Platform Test Measurements:•Max Error is about 23% at 80 RPM/s^2•Spec has been met for Experimental Platform

61


62Fig. 39– 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%

63


•The drive control system shall reduce the effect of motor mismatch

•Performance Specification: Shaft RPM change less than or equal to 15%

64


Simulink Test Measurements:•Max Error is about 4.25% at 20 RPM•Spec has been met

65


66Fig. 40–Error for Motor Mismatch in the Simulink Model



67

Overview




69

Function and Specification

•Function: Graphical User Interface (GUI) Communication

•Specification: Successfully send and receive commands

70

Experimental Platform Software

•Design and MCU Resources•Interrupt Software•Communication Software

71

Experimental Platform Software: Design

72

• 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

Graphical User Interface Communication: Serial Communication

73

Legend:Command – CMDAcknowledge – ACK

Atmega128 MATLAB

CMD1ACK1

CMD2ACK2

CMD3ACK3

Etc…

Time

Fig. 43– Communication Protocol Diagram

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%)

74

Graphical User Interface Communication: Interrupt Contents

75

•Rate Limiting•Command Conditioning•Anti-Windup Software•Model Based PID Controller•Feed-Forward Controller•Dynamic Model •Taylor Series Expansion

•Torque Matching Software•I2C Communication

Graphical User Interface Communication: I2C Communication

76

I2C Hardware Execution Time: 300 μsI2C Software Execution Time: 20 μs

Fig. 44– I2C Communication Plot



77

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

78

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

Appendix Slides

•Benjamin Roos

80

Vehicle Plant Root Locus

81Fig. 7 – Vehicle Plant Root Locus

Plant and Controller Root Locus

82Fig.8– Vehicle and Controller Root Locus with Zero at s = -19.5 rad/s

Vehicle Plant

83

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

Continuous Feedback Controller

𝐺𝑐 𝑠 = 19.5𝑘

𝑠19.5

+ 1

𝑠

𝑤ℎ𝑒𝑟𝑒 𝑘 = 500

84

Eq. 102-1 – Continuous Feedback Controller in the Laplace Domain

Discrete Feedback Controller

85

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


86Fig. 54 – Step Response Curves in Simulink


87Fig. 54 – Step Response Curves in Experimental Platform


88Fig. 55 – Simulink Parabola Response Curve with a Parabola Input = 400 RPM/s^2


89Fig. 55 – Exp. Platform Parabola Response Curve with a Parabola Input = 400 RPM/s^2


90Fig. 11 –Open Loop Response with Vin = 16v and Current Load = 0 A and no filtering

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Design of a Simulink-Based Control Workstation for Mobile