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Rational Implementation of Distributed Delay using Extended Bilinear Transformations

Author:Zhong Qing-Chang, University of Glamorgan, United Kingdom
Topic:2.2 Linear Control Systems
Session:Frequency-domain Analysis and Design of Time-Delay Systems
Keywords: distributed delay, finite-spectrum assignment, modified Smith predictor, dead-time compensator, γ-operator, bilinear transformation, rational implementation, implementation error


Based on an extension of the bilinear transformation, a rational implementation for distributed delay in linear control laws is proposed. This implementation converges much faster than the rational implementation inspired from the δ-operator. The implementation has an elegant structure of chained bi-proper nodes cascaded with a strictly proper node. The stability of each node is determined by the choice of the total number N of the nodes. The H-infinity norm of the implementation error approaches 0 when N goes to ∞ and hence the stability of the closed-loop system can be guaranteed. In addition, the steady-state performance of the system is retained. Simulation examples are given to verify the results and to show comparative study with other implementations.