A comparative evaluation of digital redesign techniques for LTI systems

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A comparative evaluation of digital redesign techniques for LTI systems

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Abstract

In this paper, a comparative evaluation of various redesign techniques is available in the literature of LTI control system. The redesign techniques like Tustin transform, step invariant method and Euler's method are evaluated based on the Energy Resemblance Index (ERI) at different sampling times which indicate the closeness of the Integral Square Error (ISE) of the continuous-time system with the Error Sequence Energy (ESE) of the redesigned system. It is found that the performance of the redesigned digital system depends on the discretisation method used, the controlled process and the sampling time chosen. There is no specific discretisation technique that out performs the others in all cases. The comparative study is illustrated using standard bench mark problem.

Index Terms – Digital redesign, Energy Resemblance Index, Integral Square Error, Error Sequence Energy

Abstract
Introduction
Calculation preliminaries
1. Continuous signal energy
2. Discrete sequence energy
3. Error Sequence Energy (ESE) and Energy Resemblance Index (ERI)
Illustrative example
Simulation and results
Conclusion
References

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[...] The energy resemblance index (ERI) is defined as ERI = ISE / ESE = η which can be used either in the performance evaluation of the redesigned digital system using different discretisation methods or in the determination of sampling time required for the digital controller ILLUSTRATIVE EXAMPLE Consider the normalized model of a motor which has the following controlled process Gp(s) = 1 / The following analogue controller can meet the performance specifications Gc(s) = / The closed-loop system becomes = 4 / (s2+2s+4) which has the damping ratio of ξ = 0.5 and natural frequency of ωn = 2 rad/sec The objective is to first the system performance of the redesigned digital control systems using different discretisation methods within the stable sampling-time range, and second to determine the sampling time required Trq based on a user-specified ERI constraint. [...]

[...] Vol.150,No.4, July 2003. 5.Chang,W.,Park,J.B.,Lee,H.J. and Joo,Y.H. approach to digital redesign of linear time invariant systems”, IEE.Proc.Control Theory Appl.Vol.149,No.4, pp 297- Rabbath,C.A. and Hori, N., a comparative study of Digital Redesign methods”, Proc. American Control Conference , Chicago, June Wang , C.H., Hsu, C.C. “Digital redesign and performance evaluation using the energy resemblance index”, IEE. Proc. Control Theory Appl [...]

[...] CONCLUSION In this paper, new quantitative ERI to address the performance evaluation and design issues of the redesigned digital system using conventional discretisation method is proposed. The performance of the redesigned digital control system using different discretisation methods at different sampling tmes can be evaluated using ERI indications. This ERI approach provides a global view of how well the digital system works using different discretisation methods. The discretisation method that provides highest ERI index within the desired sampling range can be chosen to implement the digital controller, so that the best system performance can be acheived. [...]

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