System Dynamics (24.509)

III. The State Space Equations and Their Time Domain Solution

Introduction

This section of notes concentrates on three areas:

1. A general notation for the state variable treatment of dynamic systems (the so-called* *standard state space form).

2. Techniques for putting general systems into standard form.

3. Methods for the time domain solution of the state equations, including both analytical methods and numerical methods.

Several examples are used to illustrate these techniques and a final numerical example in Matlab contrasts three different solution methods.

This information is organized into the following subsections:

- The State Space Representation
- Conversion to State Form
- Nth Order Linear Differential Equations
- Mixed Algebraic and Differential Equations
- Linearization of Nonlinear Systems
- Analytic Solution to Linear Stationary Systems
- Discretization of Linear Stationary Systems
- Numerical Integration of the State Equations
- An Example Illustrating Various Solution Schemes

24.509 Lecture Notes by Dr. J. R. White, UMass-Lowell (Spring 1997).