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 ez

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 ez

3.3.5  Discussion

 

APPENDIX A:  Recursive Simulation of Feedback Loops

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

 

Return to MathPages Main Menu