System Dynamics
System Dynamics
1 Introduction
1.1 The systems approach
1.2 State-determined systems
1.3 Energy, power, and lumping
1.4 Mechanical translational elements
1.5 Mechanical rotational elements
1.6 Electronic elements
1.7 Generalized through- and across-variables
1.8 Generalized one-port elements
1.9 Problems
2 Linear graph models
2.1 Introduction to linear graphs
2.2 Sign convention
2.3 Element interconnection laws
2.4 Systematic linear graph modeling
2.5 Problems
3 State-space models
3.1 State variable system representation
3.2 State and output equations
3.3 Normal trees
3.4 Normal tree to state-space
3.5 State-space model of a translational mechanical system
3.6 State-space model of a rotational mechanical system
3.7 Problems
4 Electromechanical systems
4.1 Ideal transducers
4.2 Modeling with transducers
4.3 DC motors
4.4 Modeling a real electromechanical system
4.5 DC motor performance in steady-state
4.6 Transient DC motor performance
4.7 Simulating the step response
4.8 Estimating parameters from the step response
4.9 Driving motors
4.10 Problems
5 Linear time-invariant system properties
5.1 Superposition, derivative, and integral properties
5.2 Equilibrium and stability properties
5.3 Vibration isolation table analysis
5.4 When gravity ghosts you
5.5 Problems
6 Qualities of transient response
6.1 Characteristic transient responses
6.2 First-order systems in transient response
6.3 Second-order systems in transient response
6.4 Problems
7 State-space response
7.1 Solving for the state-space response
7.2 Linear algebraic eigenproblem
7.3 Computing eigendecompositions
7.4 Diagonalizing basis
7.5 A vibration example with two modes
7.6 Analytic and numerical output response example in Matlab
7.7 Simulating state-space response
7.8 Problems
8 Lumped-parameter modeling fluid and thermal systems
8.1 Fluid system elements
8.2 Thermal system elements
8.3 Fluid transducers
8.4 State-space model of a hydroelectric dam
8.5 Thermal finite element model
8.6 Problems
9 Fourier series and transforms
9.1 Fourier series
9.2 Complex Fourier series example
9.3 Fourier transform
9.4 Discrete and fast Fourier transforms
9.5 Problems
10 Laplace transforms
10.1 Introduction
10.2 Laplace transform and its inverse
10.3 Properties of the Laplace transform
10.4 Inverse Laplace transforming
10.5 Solving io ODEs with Laplace
10.6 Problems
11 Transfer functions
11.1 Introducing Transfer Functions
11.2 Poles and zeros
11.3 Transfer Functions in Python
11.4 Exploring transfer functions in Matlab
11.5 ZPK transfer functions in Matlab
11.6 Problems
12 Impedance-based modeling
12.1 Input impedance and admittance
12.2 Impedance with two-port elements
12.3 Transfer functions via impedance
12.4 Impedance modeling example in Matlab
12.5 Norton and Thévenin theorems
12.6 The divider method
12.7 Problems
13 Frequency response
13.1 Frequency and impulse response
13.2 Sinusoidal input, frequency response
13.3 Bode plots
13.4 Bode plots for simple transfer functions
13.5 Sketching Bode plots
13.6 Periodic input, frequency response
13.7 Problems
14 Nonlinear systems and linearization
14.1 Linearization
14.2 Nonlinear system characteristics
14.3 Nonlinear Systems in Python
14.4 Nonlinear systems in Matlab
14.5 Nonlinear fluid system example
14.6 Problems
A Math Reference
A.1 Quadratic Forms
A.2 Trigonometry
A.3 Matrix Inverses
A.4 Euler's Formulas
A.5 Laplace Transforms
B Advanced topics
B.1 Systems with repeated eigenvalues
C Summaries
C.1 Summary of system representations
C.2 Summary of one-port elements
C.3 Laplace transforms
C.4 Fourier transforms
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Summary of one-port elements
The one table to rule them all,
table C.1
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Online Resources for Section C.2
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