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

• 9

This preview shows pages 1–4. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '08
• Staff

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern