Dynamics and Control with Jupyter Notebooks
  • 1. Introduction to Sympy and the Jupyter Notebook for engineering calculations
    • 1.1. A quick tour
    • 1.2. Math in text boxes
    • 1.3. Special symbols in variable names
    • 1.4. SymPy
    • 1.5. Calculus
    • 1.6. Limits
    • 1.7. Approximation
    • 1.8. Solving equations
  • 2. Python stuff not done in MPR
    • 2.1. List comprehensions
    • 2.2. Dictionaries
    • 2.3. Tuples
      • 2.3.1. Tuple expansion
    • 2.4. The for loop in Python
      • 2.4.1. zip
    • 2.5. lambda
  • 3. The Jupyter notebook cheat sheet
    • 3.1. Table of Contents
    • 3.2. Numeric
    • 3.3. Basic plotting functions
    • 3.4. Symbolic manipulation
      • 3.4.1. Imports
      • 3.4.2. Working with rational functions and polynomials
      • 3.4.3. Functions useful for discrete systems
    • 3.5. Equation solving
      • 3.5.1. Symbolic
      • 3.5.2. Numeric sympy
      • 3.5.3. Numeric
    • 3.6. Matrix math
      • 3.6.1. Symbolic
      • 3.6.2. Numeric
  • 1. The draining cup problem
    • 1.1. Volume-height relationship
    • 1.2. Dynamic model
  • 1. Equation solving tools
    • 1.1. Exact solution using sympy
    • 1.2. Special case: linear systems
    • 1.3. Nonlinear equations
      • 1.3.1. Numeric root finding
      • 1.3.2. Downsides of numerical solution
    • 1.4. Differential equations
      • 1.4.1. Analytic solution
      • 1.4.2. Numeric solution
        • 1.4.2.1. A note about odeint
  • 2. The problem with simple math on computers
    • 2.1. Computers use base 2 instead of base 10
    • 2.2. Solutions
      • 2.2.1. Built-in to Python
      • 2.2.2. Sympy
    • 2.3. Why isn’t math always done in base 10?
    • 2.4. Forcing rounding of exact representations
  • 3. Read simulation input from a file
  • 4. Fed Batch Bioreactor
  • 5. CSTR system
    • 5.1. Model
    • 5.2. Solve for steady state
    • 5.3. Nonlinear behaviour
  • 6. Mixing system
  • 7. Steady state calculation
    • 7.1. Flow rates
    • 7.2. Compositions
  • 8. Design
  • 9. Dynamic simulation
  • 1. Valve equation
    • 1.1. Rewriting in terms of devation variables
  • 2. A note about simplification
    • 2.1. Multiple variables
  • 3. Laplace transforms in SymPy
    • 3.1. Direct evaluation
    • 3.2. Library function
    • 3.3. What is that θ?
    • 3.4. Reproducing standard transform table
    • 3.5. More complicated inverses
  • 4. Convolution and transfer functions
    • 4.1. Numeric convolution
  • 5. Visualising complex functions
    • 5.1. One-dimensional functions
  • 1. Standard process inputs
    • 1.1. Step
    • 1.2. Laplace transform
    • 1.3. Scaling and translation
    • 1.4. Rectangular pulse
      • 1.4.1. Arbitrary piecewise constant functions
    • 1.5. Ramp
    • 1.6. Continuous piecewise linear functions
    • 1.7. Arbitrary piecewise linear functions
  • 2. First order systems
  • 3. Sinusoidal response
    • 3.1. First order
    • 3.2. Second order sinusoidal response
    • 3.3. Amplitude over frequency
  • 1. Random response generator
  • 2. Simulation of arbitrary transfer functions
    • 2.1. Convert to ODE and integrate manually
    • 2.2. LTI support in scipy.signal
      • 2.2.1. Step responses
      • 2.2.2. Responses to arbitrary inputs
      • 2.2.3. Manual integration using state space form
      • 2.2.4. Demonstration for higher order functions
      • 2.2.5. State space for higher order functions
      • 2.2.6. Systems in series
    • 2.3. 3. Control module
  • 3. Simplifying block diagrams
  • 4. Approximation
    • 4.1. Taylor approximation
    • 4.2. Padé approximation
      • 4.2.1. Further exploration
    • 4.3. Approximations based on response matching
    • 4.4. Skogestad’s “Half Rule”
  • 1. Transfer function matrices
    • 1.1. Representing matrices in SymPy
    • 1.2. Representing matrices using the control library
  • 2. Conversion to state space
  • 3. State space representation
    • 3.1. Converting between state space and transfer function forms
      • 3.1.1. Scipy.signal
      • 3.1.2. Control library
    • 3.2. Symbolic conversion
    • 3.3. Analysis
  • 1. Linear regression
  • 2. Create the design matrices
    • 2.1. Pseudoinverse solution
    • 2.2. Dedicated solvers
  • 3. Nonlinear regression
  • 4. Fitting step responses
  • 5. Neural network regression
    • 5.1. Scikit-learn
    • 5.2. Keras
  • 1. Fourier series
    • 1.1. Step function
    • 1.2. Step response via Frequency response
  • 2. What does a sinusoid sound like?
    • 2.1. But signals aren’t pure sinusoids
    • 2.2. Numeric Fourier Transform
    • 2.3. But that sounds terrible
  • 3. Frequency response plots
  • 4. Bode
  • 5. Phase unwrapping
  • 6. Nyquist
  • 7. With the control library
  • 8. Asymptotic Bode diagrams
  • 9. Systems with real poles
  • 10. Systems with complex poles
  • 11. Dead time
  • 1. Strategies for filtering out noise from a sampled signal
    • 1.1. Pandas
  • 2. Moving averages
    • 2.1. Exponentially weighted moving average
  • 3. The \(z\)-transform
    • 3.1. Definition
    • 3.2. Direct calculation in SymPy
    • 3.3. Transfer functions from difference equations
    • 3.4. Responses and inversion
    • 3.5. Calculation using scipy
    • 3.6. Calculation using the control libary
  • 1. Instructions
  • 2. PID step responses
    • 2.1. PI
    • 2.2. PID
    • 2.3. PD
  • 3. First-order system with proportional control
    • 3.1. Offset as function of gain
    • 3.2. Second order system with proportional control
  • 4. PID control on TCLab
  • 5. Programmatic interaction
  • 6. Advanced usage
  • 7. Accessing the historian
  • 8. More detailed analysis
  • 9. Closed loop controlled responses
  • 1. Closed loop stability
  • 2. Using the control library
    • 2.1. Direct substitution
  • 3. Why do we need the Routh Array
  • 4. A better way
  • 5. Root locus diagrams
  • 1. Direct synthesis PID design
    • 1.1. Alternate solution
  • 2. Minimal integral measures
  • 3. ITAE parameters for FOPDT system
  • 4. Interactive version
  • 1. Stability in the frequency domain
    • 1.1. Locating poles and zeros of a complex function
    • 1.2. Closed loop stability
    • 1.3. Nyquist stability criterion
    • 1.4. Bode stability criterion
  • 1. Dead time reduces control performance
  • 2. Smith Predictor
  • 1. Numeric simulation
  • 2. Symbolic calculation
  • 3. Discrete PI with ITAE parameters
    • 3.1. Reconstruction
    • 3.2. Discrete responses
    • 3.3. With output limits
    • 3.4. With setpoint tracking
  • 4. Dahlin controller
  • 5. Discretise the system
  • 6. Dahlin Controller
  • 7. Continuous response
  • 8. Simple discrete simulation: Dahlin controller
    • 8.1. Simple discretisation
    • 8.2. Do discrete transfer function math
    • 8.3. Convert from positive to negative powers of z
    • 8.4. Simple blocksim simulation
  • 9. Noise models
  • 1. Multivariable control
    • 1.1. Closed loop transfer functions for multivariable systems
    • 1.2. Characteristic equation
  • 2. Multivariable Stability analysis
  • 3. Multivariable pairing (RGA)
    • 3.1. Simulation results
  • 4. Eigenvalue problem
  • 5. Decoupling
    • 5.1. 1. Inverse-based
    • 5.2. 2. Zero off-diagonals
    • 5.3. 3. Adjugate method
  • 6. Model Predictive Control
  • 1. Control valve design
  • 1. No delays
    • 1.1. Normal way
    • 1.2. Preallocation
  • 2. Dead time
    • 2.1. Lists and interp
    • 2.2. Approximate indexing
  • 3. Nonlinear tank system
  • 4. PI Control
  • 5. Classes
    • 5.1. What is this good for?
    • 5.2. Objects must be “like” things
  • 6. Taking off the engine cover
  • 7. Objects
    • 7.1. Tank system
    • 7.2. PI Controller
    • 7.3. Generic integration
    • 7.4. Re-using the interface
  • 8. A discrete controller class
  • 9. Blocksim
    • 9.1. Re-using parts of a diagram
  • 10. Disturbances
  • 11. Algebraic equations
  • 1. FOPDT fit
  • 4. PID control on TCLab
  • 5. Programmatic interaction
  • 6. Advanced usage
  • 7. Accessing the historian
  • 8. More detailed analysis
  • 2. TCLab in the frequency domain
    • 2.1. Direct frequency domain tests
    • 2.2. FFT based bode diagram
Dynamics and Control with Jupyter Notebooks
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© Copyright 2018, Carl Sandrock.

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