Dynamic Systems

an introduction

This page contains fill-in notes on Dynamic Systems: an introduction lectures from the courses ME 345 and ME 370.

For corresponding source code (Jupyter, Matlab, Python, etc.), see the source page.

Single file

A single pdf with all lectures can be downloaded here.

Individual lecture files

Click the thumbnails on the notes below to get a pdf version.

01.00 Introduction

01.01 The systems approach

01.02 State determined systems

01.03 Energy power and lumping

01.04 Mechanical translational elements

01.05 Mechanical rotational elements

01.06 Electronic elements

01.07 Generalized through and across variables

01.08 Generalized one port elements

02.00 Linear graph models

02.01 Introduction to linear graphs

02.02 Sign convention

02.03 Element interconnection laws

02.04 Systematic linear graph modeling

03.00 State space models

03.01 State variable system representation

03.02 State and output equations

03.03 Graphs to state space I normal trees

03.04 Graphs to state space II the algorithm

03.05 State space model of a translational mechanical system

03.06 State space model of a rotational mechanical system

03.07 Between state space and io differential equations

03.08 Exercises

04.00 Electromechanical systems

04.01 Ideal transducers

04.02 Modeling with transducers

04.03 DC motors

04.04 A real electromechanical system

04.05 Steady DC motor performance

04.06 Transient DC motor performance

04.07 Driving motors

04.08 Problems for Chapter 04

05.00 Superposition stability etc.

05.01 Superposition derivative and integral properties

05.02 Equilibrium and stability properties

05.03 Vibration isolation table analysis

06.00 Transient response

06.01 Characteristic transient responses

06.02 First order systems

06.03 Second order systems

07.00 State space response

07.01 Solving for the state space response

07.02 Linear algebraic eigenproblem

07.03 Diagonalizing basis

07.04 Simulating state space response

08.00 Fluid and thermal systems

08.01 Fluid system elements

08.02 Thermal system elements

08.03 Fluid transducers

08.04 State space model of a hydroelectric dam

09.00 Transfer functions

09.01 Poles and zeros

10.00 Impedance based modeling

10.01 Input impedance and admittance

10.02 Impedance with two port elements

10.03 Transfer functions via impedance

10.04 Norton and Thevenin theorems

10.05 The divider method

11.00 Steady frequency domain

11.01 Fourier series

11.02 Fourier transform

11.03 Frequency and impulse response

11.04 Sinusoidal frequency response

11.05 Bode plots

11.06 Periodic frequency response

11.07 Design problem

11.08 Nonlinear fluid system example

A.00 Mathematics reference

A.01 Quadratic forms

A.02 Trigonometry

A.03 Matrix inverses

A.04 Laplace transforms

B.00 Advanced topics

B.01 Systems with repeated eigenvalues

C.00 Summaries

C.01 Summary of system representations

C.02 Summary of one port elements

C.03 Laplace transforms

C.04 Fourier transforms

D.00 Bibliography