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Intro to modelling_wur
- 1. Intro to modeling April 22 2011
- 3. Today’s goal: Learn how to solve ODE models in MATLAB
- 4. Example: Heating of water
- 7. Fit the experimental data with the model
- 8. P1 = 1 P2 = 1 SS = 350 P1 = 1.1 P2 = 3 SS = 55 P1 = 1.13 P2 = 4 SS = 12 Manual estimation of the parameters
- 12. What’s a model?
- 14. How do we build a model? Grey box White box: First principles Black box: Measurements
- 17. True or false? TRUE Only valid when x is the independent variable.
- 18. Are these ODEs? YES YES Independent Dependent; Third order Independent Dependent; First order
- 19. How to solve ODEs? General Solution Particular Solution
- 23. Taylor’s series example 1
- 24. Taylor’s series example 2
- 25. Euler’s method Under which condition is this valid?
- 26. Euler’s method Solution in multiple time-steps. Iterate: Solution in one time-step:
- 27. Example # Time steps 1 5 f(x)
- 28. What does it have to do with my ODE model? Model Initial value Step Time step
- 32. From paper to MATLAB Identify state variables, parameters, inputs. Define equations and parameter values. Define initial values, call functions, plot results.
- 33. Example: an irreversible reaction
- 37. Now the language details…
- 38. 20 x0 = 30 0 0 time = 0.1 0.2 … 1
- 39. Magic word: Function 0.5 p = 0.02 20 x0 = 30 0 0 time = 0.1 0.2 … 1 dxdt = 3x11 t0 t1 t2 x1 x2 x3 t3 … t10
- 40. Summary: model function data IN OUT Row vector Row vector Matrix 20 x0 = 30 0 0 time = 0.1 0.2 … 1 dxdt = 11x3 x1 x2 x3 t0 t1 t2 t3 … t10
- 41. 0 t = 0.1 0.2 … 1 x = 11x3 x1 x2 x3 t0 t1 t2 t3 … t10
- 42. Summary: script data IN OUT Row vector Row vector Matrix Row vector 20 x0 = 30 0 0 time = 0.1 0.2 … 1 x = 11x3 x1 x2 x3 t0 t1 t2 t3 … t10 0 t = 0.1 0.2 … 1
- 43. From paper to MATLAB Identify state variables, parameters, inputs. Define equations and parameter values. Define initial values, call functions, plot results.
- 44. Break
Notes de l'éditeur
- Lumped parameters
- I’ll give an example on using experimental data.
- White box: Derive a model from first principles. If not possible then we have to do system identification: Black box: No prior model available. Grey box: you understand the physics of your system: you can specify an explicit mathematical model but you don’t know the parameters values
- An ODE describes the rate of change of a dependant variable with respect to an independent variable. The unknown element is a function. The information we have is on its derivatives.
- An analytical method gives the solution as a mathematical formula, which is an advantage. From this we can gain insight in the behavior and the properties of the solution, and with a numerical solution (that gives the function as a table) this is not the case
- Write it on the blackboard
- Show in blackboard how it would be if passing individual variables.
- Interested?