Daniel M. Lofaro, Tony Truong Giang Le, Dr. Paul Oh ... › ... › files › Ballancing_Bot_FIRA2009_Presenta… · NXT-WhIP: NXT Wheeled Inverted Pendulum. Master’s Thesis, Drexel

Daniel M. Lofaro, Tony Truong Giang Le, Dr. Paul OhPresented By Daniel M. Lofaro

Overview

Getting people excited about controls Attract new talent to the field Retain students

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Overview

Issues with Control Systems Courses Fear of too much math Lack of accessible hands on learning Teaching techniques antiquated

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Proposed Class Real World Design

Required task Required performance Budget

Real World (Pre-existing) Tools CAD Control/Simulation Software Hardware

Control System Low Cost Small Modifiable

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Quanser Control Solutions The Good

Accurate Well Designed Compatible with Matlab, Simulink and LabVIEW

The Bad Large Expensive Black Box Un-Modifiable

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Modifiable Control System(Lego NXT)

The Good Inexpensive (Commercial Product) Powerful Arm7 Processor Compatible with Matlab, Simulink and

LabVIEW Small Reconfigurable Open Source

The Bad Not as accurate as Quanser

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• Hardware design (MLCAD)

• Software tutorial• Sensor integration• Virtual Reality model

Design

• Dynamic model• Control theory• MATLAB• Simulink

Simulation• Construction• Programming• LEGO

MINDSTORMS NXT

Experimentation

Class Outline

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• Hardware design (Lego CAD)

• Itemized parts list• Virtual Reality Model

Design

• Dynamic model• Control theory• MATLAB• Simulink

Simulation• Construction• Programming (Simulink

– ECRobot) [1]• LEGO MINDSTORMS

NXT

Prototype and Experimentation

Class WILL Work If:

Pre-Existing Tools Exist Lego CAD ECRobot MATLAB/Simulink

Reconfigurable Platform Exits Lego NXT Kit

IF ANY DOES NOT EXIST WILL NOT WORK

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Case Study

Objective Make a two (2) wheeled balancing robot Minimum forward speed 0.1m/s Minimum turning speed π/4 rad/sec Minimum floor angle ±15o

10Segway [7]

Case Study: Design

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Case Study: Simulation and Test

PID Balance Control Minimizes angular

pitch rate Gains manually tuned to

balance, peak between ±15º & 2 sec. settling time

Difficult to tune Moving average to

smooth calculation

120 2 4 6 8 10 12 14 16 18 20

-20

-15

-10

-5

0

5

10

15

20

Time [sec]

Pitc

h A

ngle

, θp [d

eg]

SimulationExperimental

Case Study: Simulation and Test

State Variable Feedback State feedback control using

linear quadratic regulator Weight matrices Q & R are

manually tuned Emphasis on wheel angle

and pitch angle

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0 2 4 6 8 10 12 14 16 18 20

-10

-5

0

5

10

Time [sec]

Pitc

h A

ngle

, θp [d

eg]

SimulationExperimental

Case Study: Simulation and Test

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Recap Class Designed to be

Fun Interactive Educational

Uses Pre-Existing Tools Lego NXT Lego CAD MATLAB/Simulink

Use Reconfigurable Small Low Cost Used for Multiple Design Problems

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References1. Yamamoto, Yorihisa: NXTway-GS Model-Based Design – Control of self-

balancing two-wheeled robot built with LEGO Mindstorm NXT. First Edition, 29 February 2008.

2. Nise, Norman S.: Control Systems Engineering Fourth Edition. John Wiley and Sons INC, 2004

3. Lofaro, Daniel M.: Control Design to Reduce the Effects of Torsional Resonance in Coupled Systems. Master’s Thesis, Drexel University Department of Electrical and Computer Engineering, May 2008.

4. Kwatny, Harry G. Blankenship Gilmer L. Nonlinear Control and Analytical Mechanics A Computational Approach. Birkhauser, Boston 2000.

5. Erkkinen, Tom: Embedded Coder Robot NXT Demo. Updated 18 December 2008 http://www.mathworks.com/matlabcentral/fileexchange/13399

6. Yamamoto, Yorihisa: NXTway-GS Model-Based Design – Control of self-balancing two-wheeled robot built with LEGO Mindstorm NXT. First Edition, 29 February 2008.

7. Le, Tony: NXT-WhIP: NXT Wheeled Inverted Pendulum. Master’s Thesis, Drexel University Department of Electrical and Computer Engineering, May 2008.

8. Greenwood, Donald T.: Principles Of Dynamics Second Edition. Prentice Hall, Upper Saddle River, New Jersey 1988.

9. Le Tony, Oh Paul: IDETC Presentation: System Integration Case Study: NXT-WhIP NXT Wheeled Inverted Pendulum. New York City, NY, 2008-04-08.

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Motor Controller Motor Controller

Friction Compensator Rotation, kδ’

Wheel sync, ksync

Motor velocity, kϕ’

Worked to balance, rotate, and keep wheels synchronized

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Motor Model Motors represented as rigid body Electrical & mechanical constants determined by

Hurbain & Watanabe trusted and validated

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Prototype and Simulation

MathWorks’ MATLAB Simulink ECRobot NXT

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