# Lecture: System Modeling

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## Overview

This lecture provides an overview of modeling for control systems. We discuss what a model is and what types of questions it can be used to answer. The concepts of state, dynamics, inputs and outputs are described, including running examples to demonstrate the concepts. Several different modeling techniques are summarized, with emphasis on differential equations. Two examples are included to demonstrate the main concepts.

## Lecture Materials

Caltech CDS 101/110, Fall 2008:

Caltech CDS 101/110, Fall 2004:

- System Modeling lecture: pdf
- MATLAB files: L2_1_modeling.m, springmass.m

## Frequently Asked Questions

- FAQ: Can we get more information about state space formulation?
- FAQ: How can I go from a continuous linear ODE to a discrete representation?
- FAQ: How do we learn how to translate MATLAB equations into the Simulink diagrams?
- FAQ: How do you know when your model is sufficiently complex?
- FAQ: In a difference equation, how is the state continuous even though the time is discrete?
- FAQ: In the mass-spring system modelling the car, one of the springs is fixed to a wall. How does that model the car when that "spring" on the car is connected to the chassis?
- FAQ: In the predator prey example, where is the fox birth rate term?
- FAQ: What is a state? How does one determine what is a state and what is not?
- FAQ: What is a stochastic system?
- FAQ: What is the advantage of having a model?
- FAQ: Why is the parameter "a" in the predator-prey problem used as both death of rabbit and birth of foxes?
- FAQ: Why isn't there a term for the rabbit death rate besides being killed by the foxes?