2. Mechatronic group at UiA 15 full time employed in teaching and labs. Mechatronic profile at UiA characterized by: High power / Power Mechatronics Dynamic systems Off Shore applications Mechatronic profile at UiA, programmes: 3 years B.Sc., since 1988 2 years M.Sc., since 2008 3 years Ph.D., since 2010 Agenda: - Background - Modeling and simulation at UiA engng. - Mathematical challenges - Conclusions Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

3. Modeling and Simulation at the Engineering MSc educations at UiA Mechatronics and Renewable Energy Dedicated course (10SP) Used in subsequent courses on mechanics, hydraulics, electrical drives, control, instrumentation, industrial information technology, product development. Used in multidisciplinar project works (across individual courses) Used extensively in graduate projects Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

4. Simulation Mainly time domain simulation and numerical methods Why time domain simulation ? - Investigate dynamic characteristics - Avoid or minimize physical testing - Gain insight into non-linear behavior - Gain insight into parameters that are difficult to measure physically - Extensively used in industry to predict and verify design Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

5. Simulation Mainly time domain simulation and numerical methods Why time domain simulation ? - Investigate dynamic characteristics - Avoid or minimize physical testing Simulation - Gain insight into non-linear behavior - Gain insight into parameters that are difficult to measure physically - Extensively used in industry to predict and verify design Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

6. Simulation Mainly time domain simulation and numerical methods Why numerical methods ? - Practical problems typically outside the scope of analytical solutions - Allows for the handling of large scale problems - Allows for design optimization Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

7. Simple system with no analytical solution MATHEMATICAL CHALLENGES: - WHITE BOX MODELING, DIFFERENTIAL EQUATION OF MOTION - GRAY BOX MODELING, IMPACT WITH WALL - NUMERICAL SOLUTION, TIME INTEGRATION Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

8. FURTHER MATHEMATICAL CHALLENGES: - TRIGONOMETRY. - BLACK BOX MODELING, TIRE MODEL, BUMP IN ROAD. Simple system with no analytical solution Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

9. MATHEMATICAL CHALLENGE: FORMULATE DESIGN PROBLEM (INVERSE ANALYSIS) Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14

10. MAIN MATHEMATICAL CHALLENGES: - WHITE BOX MODELING, PURELY PHYSICAL (Newtons 2nd law, Ohms law). - GRAY BOX MODELING, PARTLY PHYSICAL - PARTLY EMPIRICAL (Parameter identification, friction, impact, damping). - BLACK BOX MODELING, PURELY EMPIRICAL RELATIONSHIPS (Forcing mathematical expressions on observations, measurements, or assumed dependencies). - SETTING UP NUMERICAL SOLUTIONS (Time integration, nonlinear equations, optimization). - TRIGONOMETRY. IN CONCLUSION Michael R. Hansen, MatRIC meeting, Grimstad 27/5-14