matlab & simulink for teaching and research in engineering ... · matlab/simulink solutions for...
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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