lec1.pdf - State-Space Model Mathematical Modeling Basic...

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8/28/2016 1 State-Space Model Mathematical Modeling Basic Definitions State Equations Illustrative Example System Definition in MATLAB Mathematical Modeling (MM) Mathematical model of a dynamic system is a set of mathematical equations (e.g., differential eqs.) that describes the input-output behavior of the system. A model is primarily used to simulate the behavior of the system. The structure (e.g, order) of the model is often obtained by applying physical laws such as Newton's law, Ohms law, etc. The numerical values of the model parameters are often approximated from experimental data by curve fitting.
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8/28/2016 2 Mass-Spring-Damper Example Derive a mathematical model for the mass- spring-damper system shown: FBD What type of model is this? what are the inputs and outputs? How can the output(s) be predicted? What are the alternative models? How are the parameters m, c, and k estimated? m f x k c x m x c kx f F x m kx x c f x k c f kx x c x m Basic Terminology System : An aggregation or assemblage of things so combined by man or nature to form an integral and complex whole. From engineering point of view, a system is defined as an interconnection of many components or functional units act together to perform a certain objective Examples: automobile, machine tool, robot, aircraft, human cell, etc.
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8/28/2016 3 System Variables Every system is associated with 3 variables: Input variables (u) originate outside the system and are not affected by what happens in the system
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