LEAD-LAG ALGORITHMS

Table of Contents

1.  Introduction

2.  Discrete-Time Simulation of First-Order Response

2.1  Background

2.2  Optimum First-Order Simulation

2.2.1  Basic Assumptions

2.2.2  General First-Order Recurrence Formulas

2.2.3  Optimum Recurrence Coefficients for Constant τ

2.2.4  Optimum Recurrence Coefficients for Variable τ

2.2.5  Discussion

2.3  Modified First-Order Simulation Methods

2.3.1  Simplifications Based on Approximations of e^z

2.3.2  Finite Differences and Bilinear Substitution

2.3.3  Pre-Warping

2.3.4  Composite Past Value Recurrence

2.3.5  Discussion

3.  Discrete-Time Simulation of Second-Order Response

3.1  Background

3.2  Optimum Second-Order Recurrence Formulas

3.2.1  Basic Assumptions

3.2.2  General Second-Order Recurrence Formulas

3.2.3  Optimum Recurrence Coefficients for Second-Order Interpolation

3.2.4  Optimum Recurrence Coefficients for Point-to-Point Interpolation

3.2.5  Discussion

3.3  Modified Methods for Second Order Simulation

3.3.1  Cascaded First-Order Simulations

3.3.2  Finite Difference Method

3.3.3  Bilinear Substitution

3.3.4  Simplifications Based on Approximations of e^z

3.3.5  Discussion

APPENDIX A:  Recursive Simulation of Feedback Loops

APPENDIX B:  Discrete-Time Simulation of Nth-Order Response

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