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The Towers of Hanoi as a CyberPhysical System Education Case Study
Pieter J. Mosterman, Justyna Zander, Zhi Han
© 2013 The MathWorks, Inc. 1
Teaching
Conceive, design, implement, operate (CDIO)
– Deep learning of disciplinary content – Grow professional skills of engineers
R. Niewoehner, E. Crawley, J. Koster, and T. Simpson, ―A Learning Science Foundation for Project-Based Learning in Engineering,‖ 7th International CDIO Conference, Copenhagen, Denmark, June 2011
Project-based learning (PBL)
– Is central to the teaching strategy and is reflected as the main element in the curriculum – Brings out desired questions and learning experiences about specific domains and their principles – Actively develops new knowledge in a constructive manner – Facilitates autonomous exploration by the students – Is authentic, implementable, and proposes to solve a problem that exists outside of the classroom
J. W. Thomas, ―A review of research on project-based learning,‖ The Autodesk Foundation, San Rafael, CA, March 2000
2
Virtual worlds
Virtual electronics laboratory with a physical supplement
– Students score as well on written and practical tests as those taking the physical laboratory only
J. O. Campbell, J. R. Bourne, P. J. Mosterman, and A. J. Brodersen, ―The effectiveness of learning simulations for electronics laboratories,‖ Journal of Engineering Education, no. 1, pp. 81–87, Jan. 2002
3
A distributed Towers of Hanoi virtual world
Smart blocks with local control
Authenticity with a detailed physics model
R I
parameters brkwy_frc = { 25, 'N' }; Col_frc = { 20, 'N' }; visc_coef = { 100, 'N*s/m' }; trans_coef = { 10, 's/m' }; vel_thr = { 1e-4, 'm/s' }; end parameters (Access=private) brkwy_frc_th = { 24.995, 'N' }; end
% % % % %
Breakaway friction force Coulomb friction force Viscous friction coefficient Transition approximation coefficient Linear region velocity threshold
% Breakaway force at threshold velocity
function setup % Computing breakaway friction force at threshold velocity brkwy_frc_th = visc_coef * vel_thr + Col_frc + (brkwy_frc - Col_frc) * exp(-trans_coef * vel_thr); end equations if (abs(v) <= vel_thr) % Linear region f == brkwy_frc_th * v / vel_thr; elseif v > 0 f == visc_coef * v + Col_frc + ... (brkwy_frc - Col_frc) * exp(-trans_coef * v); else f == visc_coef * v - Col_frc - ... (brkwy_frc - Col_frc) * exp(-trans_coef * abs(v)); end end
The overall distributed Towers of Hanoi model
http://www.mathworks.com/matlabcentral/fileexchange/38515-smart-manufacturing-robotics-cyber-physical-system http://www.mathworks.com/matlabcentral/fileexchange/38515-smart-manufacturing-robotics-cyber-physical-system
Example—multi-rate timing issues
8
Conclusions
Problem authenticity is crucial—Virtual worlds work! A distributed Towers of Hanoi virtual world includes
– – – – Physics modeling Image processing Control Communication Distributed control on concurrent resources Multirate and timing issues Feature interaction Design across multiple disciplines
CPS challenges to study
– – – –
Helps guide toward multi-domain inquiry
9
®
10
Pieter J. Mosterman, Justyna Zander, Zhi Han
© 2013 The MathWorks, Inc. 1
Teaching
Conceive, design, implement, operate (CDIO)
– Deep learning of disciplinary content – Grow professional skills of engineers
R. Niewoehner, E. Crawley, J. Koster, and T. Simpson, ―A Learning Science Foundation for Project-Based Learning in Engineering,‖ 7th International CDIO Conference, Copenhagen, Denmark, June 2011
Project-based learning (PBL)
– Is central to the teaching strategy and is reflected as the main element in the curriculum – Brings out desired questions and learning experiences about specific domains and their principles – Actively develops new knowledge in a constructive manner – Facilitates autonomous exploration by the students – Is authentic, implementable, and proposes to solve a problem that exists outside of the classroom
J. W. Thomas, ―A review of research on project-based learning,‖ The Autodesk Foundation, San Rafael, CA, March 2000
2
Virtual worlds
Virtual electronics laboratory with a physical supplement
– Students score as well on written and practical tests as those taking the physical laboratory only
J. O. Campbell, J. R. Bourne, P. J. Mosterman, and A. J. Brodersen, ―The effectiveness of learning simulations for electronics laboratories,‖ Journal of Engineering Education, no. 1, pp. 81–87, Jan. 2002
3
A distributed Towers of Hanoi virtual world
Smart blocks with local control
Authenticity with a detailed physics model
R I
parameters brkwy_frc = { 25, 'N' }; Col_frc = { 20, 'N' }; visc_coef = { 100, 'N*s/m' }; trans_coef = { 10, 's/m' }; vel_thr = { 1e-4, 'm/s' }; end parameters (Access=private) brkwy_frc_th = { 24.995, 'N' }; end
% % % % %
Breakaway friction force Coulomb friction force Viscous friction coefficient Transition approximation coefficient Linear region velocity threshold
% Breakaway force at threshold velocity
function setup % Computing breakaway friction force at threshold velocity brkwy_frc_th = visc_coef * vel_thr + Col_frc + (brkwy_frc - Col_frc) * exp(-trans_coef * vel_thr); end equations if (abs(v) <= vel_thr) % Linear region f == brkwy_frc_th * v / vel_thr; elseif v > 0 f == visc_coef * v + Col_frc + ... (brkwy_frc - Col_frc) * exp(-trans_coef * v); else f == visc_coef * v - Col_frc - ... (brkwy_frc - Col_frc) * exp(-trans_coef * abs(v)); end end
The overall distributed Towers of Hanoi model
http://www.mathworks.com/matlabcentral/fileexchange/38515-smart-manufacturing-robotics-cyber-physical-system http://www.mathworks.com/matlabcentral/fileexchange/38515-smart-manufacturing-robotics-cyber-physical-system
Example—multi-rate timing issues
8
Conclusions
Problem authenticity is crucial—Virtual worlds work! A distributed Towers of Hanoi virtual world includes
– – – – Physics modeling Image processing Control Communication Distributed control on concurrent resources Multirate and timing issues Feature interaction Design across multiple disciplines
CPS challenges to study
– – – –
Helps guide toward multi-domain inquiry
9
®
10