This is the table of contents, arranged by topic.

If you are looking for the use of a particular function, try the Function index.

There is also a set of YouTube videos linked to the course.

0. Getting Started

• Notebook introduction
• Extra Python
• Cheatsheet

1. Dynamics

1.1 Modelling

• Draining cup

1.2 Time domain simulation

• Equation solving tools
• Numeric representation
• Read input from file
• Example: Fed batch bioreactor
• Example: Nonlinear CSTR
• Example: Mixing system

1.3 Linear systems

• Linearisation
• Laplace transforms
• Convolution
• Visualising complex functions

1.4 First and second order system dynamics

• Standard process inputs
• First order systems
• Second order systems
• Sinusoidal response

1.5 Complex system dynamics

• Random response generator
• Simulation of arbitrary transfer functions
• Block diagram simplification
• Approximation

1.6 Multivariable system representation

• Transfer function matrices
• State space

1.7 System identification

• Regression
• Dynamic model parameter estimation
• Neural networks
• Identifying discrete-time models

1.8 Frequency domain

• Fourier series
• Sound and frequency
• Frequency response plots
• Asymptotic Bode diagrams

1.9 Sampled systems

• Aliasing
• Filtering
• The z transform
• The z domain and continuous systems

2. Control

2.1 Conventional feedback control

• Control game
• PID controller step responses
• Effect of Proportional Control
• PID control on TCLab
• Closed loop controlled responses

2.2 Laplace domain analysis of control systems

• Stability analysis
• SymPy Routh Array
• Root locus diagrams

2.3 PID controller design, tuning and troubleshooting

• Direct synthesis PID design
• Optimal control - minimal integral measures
• ITAE parameters for FOPDT system

2.4 Frequency domain analysis of control systems

• Frequency domain stability

2.5 Advanced control methods

• Dead time compensation

2.6 Discrete control and analysis

• Discrete control
• Discrete PI
• Dahlin controller
• Simple discrete controller simulation
• Noise models

2.7 Multivariable control

• Multivariable closed loop transfer functions
• Multivariable stability analysis
• Multivariable pairing (RGA)
• Eigenvalues and Eigenvectors
• Decoupling
• Simple MPC

2.8 Control Practice

• Control valve design

Simulation

• Timing study
• Hybrid system simulation
• Classes
• Special functions in classes
• Object-Oriented simulation
• Object-Oriented simulation - Discrete
• Blocksim

TCLab

• FOPDT fit
• Interactive PID simulation
• Frequency domain

tbcontrol

The tbcontrol module contains functions helpful to students learning to solve control problems. It is broken up into submodules.

symbolic

• linearise attempt to linearise a symbolic expression
• routh construct a Routh-Hurwitz array
• pade pade approximation
• ss2tf determine the transfer function version of a state space realisation
• sampledvalues invert the Z transform symbolically
• evaluate_at_times evaluate a sympy expression at numeric times (useful for plotting responses)

numeric

• skogestad_half find an approximation of a high order system by Skogestad's half rule

plotting

• cross_axis create an axis in Matplotlib which has spines going through the origin like a Nyquist diagram would

loops

• feedback calculate the result of having two blocks in a feedback loop

responses

Step responses of certain systems

• fopdt first order plus dead time
• sopdt second order plus dead time