Process Control and Dynamics

  1. Laplace Transforms and Transfer Functions
    1. Laplace Transform Theory
      1. Definition of Laplace Transform
        1. Transform Properties
          1. Linearity Property
            1. Time Shifting Property
              1. Frequency Shifting Property
                1. Scaling Property
                2. Common Function Transforms
                  1. Unit Step Function
                    1. Unit Impulse Function
                      1. Exponential Functions
                        1. Sinusoidal Functions
                          1. Polynomial Functions
                          2. Transform of Derivatives
                            1. Transform of Integrals
                              1. Initial Value Theorem
                                1. Final Value Theorem
                                2. Inverse Laplace Transforms
                                  1. Partial Fraction Decomposition
                                    1. Residue Method
                                      1. Convolution Theorem
                                      2. Transfer Function Concepts
                                        1. Definition and Derivation
                                          1. Physical Interpretation
                                            1. Transfer Function Properties
                                              1. Poles and Zeros
                                                1. Definition and Calculation
                                                  1. Pole-Zero Maps
                                                    1. Effect on System Behavior
                                                  2. Block Diagram Analysis
                                                    1. Block Diagram Elements
                                                      1. Block Diagram Algebra
                                                        1. Series Combination
                                                          1. Parallel Combination
                                                            1. Feedback Combination
                                                            2. Signal Flow Graphs
                                                              1. Mason's Gain Formula
                                                                1. Block Diagram Reduction

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                                                              2. Mathematical Modeling of Dynamic Systems

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                                                              4. Dynamic Response Analysis