Dynamics and control

Contents:

• 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
• 3. List comprehensions
  • 3.1. Dictionaries
• 4. Tuples
  • 4.1. Tuple expansion
• 5. The for loop in Python
  • 5.1. zip
• 6. lambda
• 7. The Jupyter notebook cheat sheet
  • 7.1. Table of Contents
  • 7.2. Numeric
  • 7.3. Basic plotting functions
  • 7.4. Symbolic manipulation
  • 7.5. Equation solving
  • 7.6. Matrix math
• 8. The draining cup problem
  • 8.1. Volume-height relationship
  • 8.2. Dynamic model
• 9. Equation solving tools
  • 9.1. Exact solution using sympy
  • 9.2. Special case: linear systems
  • 9.3. Nonlinear equations
  • 9.4. Differential equations
• 10. The problem with simple math on computers
  • 10.1. Computers use base 2 instead of base 10
  • 10.2. Solutions
  • 10.3. Why isn’t math always done in base 10?
  • 10.4. Forcing rounding of exact representations
• 11. Read simulation input from a file
• 12. Fed Batch Bioreactor
• 13. CSTR system
  • 13.1. Model
  • 13.2. Solve for steady state
  • 13.3. Nonlinear behaviour
• 14. Mixing system
• 15. Steady state calculation
  • 15.1. Flow rates
  • 15.2. Compositions
• 16. Design
• 17. Dynamic simulation
• 18. Valve equation
  • 18.1. Rewriting in terms of devation variables
• 19. A note about simplification
  • 19.1. Multiple variables
• 20. Laplace transforms in SymPy
  • 20.1. Direct evaluation
  • 20.2. Library function
  • 20.3. What is that θ?
  • 20.4. Reproducing standard transform table
  • 20.5. More complicated inverses
• 21. Convolution and transfer functions
  • 21.1. Numeric convolution
• 22. Visualising complex functions
  • 22.1. One-dimensional functions
• 23. Standard process inputs
  • 23.1. Step
  • 23.2. Laplace transform
  • 23.3. Scaling and translation
  • 23.4. Rectangular pulse
  • 23.5. Ramp
  • 23.6. Continuous piecewise linear functions
  • 23.7. Arbitrary piecewise linear functions
• 24. First order systems
• 25. Sinusoidal response
  • 25.1. First order
  • 25.2. Second order sinusoidal response
  • 25.3. Amplitude over frequency
• 26. Random response generator
• 27. Simulation of arbitrary transfer functions
  • 27.1. Convert to ODE and integrate manually
  • 27.2. LTI support in scipy.signal
  • 27.3. 3. Control module
• 28. Simplifying block diagrams
• 29. Approximation
  • 29.1. Taylor approximation
  • 29.2. Padé approximation
  • 29.3. Approximations based on response matching
  • 29.4. Skogestad’s “Half Rule”
• 30. Transfer function matrices
  • 30.1. Representing matrices in SymPy
  • 30.2. Representing matrices using the control library
• 31. Conversion to state space
• 32. State space representation
  • 32.1. Converting between state space and transfer function forms
  • 32.2. Symbolic conversion
  • 32.3. Analysis
• 33. Linear regression
• 34. Create the design matrices
  • 34.1. Pseudoinverse solution
  • 34.2. Dedicated solvers
• 35. Nonlinear regression
• 36. Fitting step responses
• 37. Neural network regression
  • 37.1. Scikit-learn
  • 37.2. Keras
• 38. Fourier series
  • 38.1. Step function
  • 38.2. Step response via Frequency response
• 39. What does a sinusoid sound like?
  • 39.1. But signals aren’t pure sinusoids
  • 39.2. Numeric Fourier Transform
  • 39.3. But that sounds terrible
• 40. Frequency response plots
• 41. Bode
• 42. Phase unwrapping
• 43. Nyquist
• 44. With the control library
• 45. Asymptotic Bode diagrams
• 46. Systems with real poles
• 47. Systems with complex poles
• 48. Dead time
• 49. Strategies for filtering out noise from a sampled signal
  • 49.1. Pandas
• 50. Moving averages
  • 50.1. Exponentially weighted moving average
• 51. The \(z\)-transform
  • 51.1. Definition
  • 51.2. Direct calculation in SymPy
  • 51.3. Transfer functions from difference equations
  • 51.4. Responses and inversion
  • 51.5. Calculation using scipy
  • 51.6. Calculation using the control libary
• 52. Instructions
• 53. PID step responses
  • 53.1. PI
  • 53.2. PID
  • 53.3. PD
• 54. First-order system with proportional control
  • 54.1. Offset as function of gain
  • 54.2. Second order system with proportional control
• 55. PID control on TCLab
• 56. Programmatic interaction
• 57. Advanced usage
• 58. Accessing the historian
• 59. More detailed analysis
• 60. Closed loop controlled responses
• 61. Closed loop stability
• 62. Using the control library
  • 62.1. Direct substitution
• 63. Why do we need the Routh Array
• 64. A better way
• 65. Root locus diagrams
• 66. Direct synthesis PID design
  • 66.1. Alternate solution
• 67. Minimal integral measures
• 68. ITAE parameters for FOPDT system
• 69. Interactive version
• 70. Stability in the frequency domain
  • 70.1. Locating poles and zeros of a complex function
  • 70.2. Closed loop stability
  • 70.3. Nyquist stability criterion
  • 70.4. Bode stability criterion
• 71. Dead time reduces control performance
• 72. Smith Predictor
• 73. Numeric simulation
• 74. Symbolic calculation
• 75. Discrete PI with ITAE parameters
  • 75.1. Reconstruction
  • 75.2. Discrete responses
  • 75.3. With output limits
  • 75.4. With setpoint tracking
• 76. Dahlin controller
• 77. Discretise the system
• 78. Dahlin Controller
• 79. Continuous response
• 80. Simple discrete simulation: Dahlin controller
  • 80.1. Simple discretisation
  • 80.2. Do discrete transfer function math
  • 80.3. Convert from positive to negative powers of z
  • 80.4. Simple blocksim simulation
• 81. Noise models
• 82. Multivariable control
  • 82.1. Closed loop transfer functions for multivariable systems
  • 82.2. Characteristic equation
• 83. Multivariable Stability analysis
• 84. Multivariable pairing (RGA)
  • 84.1. Simulation results
• 85. Eigenvalue problem
• 86. Decoupling
  • 86.1. 1. Inverse-based
  • 86.2. 2. Zero off-diagonals
  • 86.3. 3. Adjugate method
• 87. Model Predictive Control
• 88. Control valve design
• 89. No delays
  • 89.1. Normal way
  • 89.2. Preallocation
• 90. Dead time
  • 90.1. Lists and interp
  • 90.2. Approximate indexing
• 91. Nonlinear tank system
• 92. PI Control
• 93. Classes
  • 93.1. What is this good for?
  • 93.2. Objects must be “like” things
• 94. Taking off the engine cover
• 95. Objects
  • 95.1. Tank system
  • 95.2. PI Controller
  • 95.3. Generic integration
  • 95.4. Re-using the interface
• 96. A discrete controller class
• 97. Blocksim
  • 97.1. Re-using parts of a diagram
• 98. Disturbances
• 99. Algebraic equations
• 100. FOPDT fit
• 55. PID control on TCLab
• 56. Programmatic interaction
• 57. Advanced usage
• 58. Accessing the historian
• 59. More detailed analysis
• 101. TCLab in the frequency domain
  • 101.1. Direct frequency domain tests
  • 101.2. FFT based bode diagram

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