AI in Manufacturing and Green Technology

9 Eigenvalue Assignment for Control of Time-Delay System

A Lambert W Function-Based Approach

Jayanta Kumar Kar and Sovit Kumar Pradhan

National Institute of Technology

Contents

9.1   Introduction

9.2   Lambert W Function

9.2.1   Preliminary

9.2.2   Mathematical Form of Lambert W Function

9.3   Solution of Delay Differential Equations Using Lambert W Function

9.3.1   Free System of DDEs: Scalar Case

9.3.2   Matrix Case

9.4   Proportional-Integral Control of Systems with Time Delay

9.4.1   Illustrative Example

9.4.2   Lambert W Function–Based Approach

9.5   Result Analysis

9.6   Conclusion

References

9.1   Introduction

Most of the physical systems have time delay and are inherently nonlinear in nature. Time-delay systems (TDS) arise from inherent ...