Discrete Systems with Python

[Pages:54]

Discrete Systems with Python

Hans-Petter Halvorsen

Free Textbook with lots of Practical Examples



Additional Python Resources



Contents

? Differential Equations ? Simulation ? Discrete Systems ? Examples

Simulation of Discrete Systems

? Python has powerful features for simulation of continuous differential equations and dynamic systems.

? Sometimes we want to or need to discretize a continuous system and then simulate it in Python.

? This means we need to make a discrete version of our continuous differential equations.

? The built-in ODE solvers in Python use different discretization methods



Differential Equations

Hans-Petter Halvorsen

Differential Equations

Differential Equation on general form:

= , ,

! = !

Different notation is used:

Initial condition Example:

= ! =

= 3y + 2,

! = 0

ODE ? Ordinary Differential Equations

Differential Equations

Example:

=

Note that = !"

!#

Where ! = 0 = (!) is the initial condition

Where = - #", where is denoted as the time constant of the system

The solution for the differential equation is found to be (learned in basic Math courses and will not be derived here):

= !"#

Where $ = 0 = ($) is the initial condition

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