After an introduction into goals and significance of modelling and simulation, numerical methods for solving ordinary differential equations (various implicit and explicit single step and multi-step methods, other methods) and their properties (numeric stability, local and global errors, suitability for stiff differential equations, for step inputs and for step width control) are considered. For the solution of partial differential equations, there is only a hint by an example with space and time discretization.
The chapter "experimental modelling" at first discusses principles and choice of test signals, followed by methods for gaining nonparametric models. For general parmeter estimation methods, as they are contained in the MATLAB system identification toolbox, the basic models are presented. For one method, the reduction to a least-squares problem is shown; for further details the lecture refers to another lecture ("state and parameter estimation"). Other methods are only mentioned as outlook.
A short overview over physical fundamentals from mechanics, thermodynamics and fluid dynamics is given. These fundamentals are applied for theoretical modelling (gaining rigorous models) for numerous examples, e.g.: DC drive, pump and compressor, valve, heat exchanger, heated vessel (liquid, gas, boiling liquid and vapour), stirring vessel reactor with chemical reaction.
The students should be able to apply numerical methods for the solution of ordinary differential equations and to evaluate their properties and suitability for a given application case. They are expected to apply various methods for experimental system identification. Also, they should be able to formulate rigorous (theoretical) models for some simple systems, which are important in process industry.
- Maier, Uwe: Vorlesungsskript "Modelling and Simulation of Dynamic Systems" (steht zum Download zur Verfügung).
- Thomas, Philip: Simulation of Industrial Processes for Control Engineers. Butterworth Heinemann, 1999.
- Weitere umfangreiche Literaturliste zu den einzelnen Kapiteln in den Vorlesungsunterlagen.