1© 2014 The MathWorks, Inc.© 2014 The MathWorks, Inc.

MATLAB & Simulink for Teaching and Research inEngineering Education

Stefano OlivieriEducation Technical Marketing

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Two-Wheeled Inverted Pendulum Motion Equations

Side view Plane view

휃: average angle of left and right wheel휙: body yaw angle휓: body pitch angle

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Lagrangian expression

푇 : translational kinetic energy 푇 : rotational kinetic energy 푈: potential energy 퐿: Lagrangian

퐿 = 푇 + 푇 − 푈

Rotation kinetic energy of an armature in left and right DC motor

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Lagrange equations

휃: average angle of left and right wheel 휙: body yaw angle 휓: body pitch angle

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Generalized force expressions

푣 ,푣 : left and right DC motor voltage

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State Equations

Linearizing motion equations at a balance point Considering limit 휓 → 0(sin휓 → 휓,cos휓 → 1) Neglecting second order terms (휓 )

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State Equations

State variables and inputs

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Controller design

Two-wheeled inverted pendulum balancing position is not stable May be considered as a mass-spring-damper system A control system is designed accordingly

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Project-Based Learning

Motivating Project-Based Learning: Sustaining the Doing, Supporting the Learning, Educational Psychologist Volume 26, Issue 3-4, 1991

Project-based learning is a comprehensive approach to classroom teaching and learning that is designed to engage students in

investigation of authentic problems.

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Physical Interaction Benefits

Accessible

High Fidelity

Hands-On Learning

Unexpected Scenarios

Engaging

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Physical Interaction

Simulation

MATLAB/Simulink Solutions for Project-Based Learning

Project-Based Learning – Learning by Doing

MATLAB and Simulink:-Both simulation and hardware solutions-Target affordable hardware platforms-Industry-standard workflow for engineering education

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Get Simulink Hardware Support Packages

Get from the MATLAB Toolstrip: Add-Ons Get Hardware Support Packages

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LEGO MINDSTORMS NXT Support from Simulink

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LEGO Mindstorms NXT Simulink Support Package

Inputs, sensors

Outputs, actuators

Examples