Noise Induced Switching in Delayed Systems

Background and Introduction: The proposed control law is designed to provide fast reference tracking with minimal overshoot and to minimize the effect of unknown nonlinearities and external disturbances. Methods: In this work, an enhanced composite nonlinear feedback technique using adaptive control is developed for a nonlinear delayed system subjected to input saturation and exogenous disturbances. It ensures that the plant response is not affected by adverse effect of actuator saturation, unknown time delay and unknown nonlinearities/ disturbances. The analysis of stability is done by Lyapunov-Krasovskii functional that guarantees asymptotical stability. Results: The proposed control law is validated by its implementation on exothermic chemical reactor. MATLAB figures are provided to compare the results. Conclusion: The simulation results of the proposed controller are compared with the conventional composite nonlinear feedback control which illustrates the efficiency of the proposed controller.

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A Razumikhin approach to exponential admissibility of switched descriptor delayed systems

Applied Mathematical Modelling ◽

10.1016/j.apm.2013.09.007 ◽

2014 ◽

Vol 38 (5-6) ◽

pp. 1647-1659 ◽

Cited By ~ 9

Author(s):

Xiu Liu ◽

Shouming Zhong ◽

Xiuyong Ding

Keyword(s):

Delayed Systems

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Dead-Time Compensation for the First-Order Dead-Time Processes: Towards a Broader Overview

Mathematics ◽

10.3390/math9131519 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1519

Author(s):

Mikulas Huba ◽

Pavol Bistak ◽

Damir Vrancic ◽

Katarina Zakova

Keyword(s):

Degrees Of Freedom ◽

Dead Time ◽

Feedforward Control ◽

Structural Instability ◽

Smith Predictor ◽

Actual Process ◽

Delayed Systems ◽

First Order ◽

Plant Modelling ◽

Dead Time Compensation

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice.

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New Observer-Based Controller Design for Delayed Systems Subject to Input Saturation and Disturbances

Iranian Journal of Science and Technology Transactions of Electrical Engineering ◽

10.1007/s40998-019-00298-0 ◽

2019 ◽

Vol 44 (3) ◽

pp. 1081-1092 ◽

Cited By ~ 3

Author(s):

Nabil El Fezazi ◽

Ouarda Lamrabet ◽

Fatima El Haoussi ◽

El Houssaine Tissir

Keyword(s):

Controller Design ◽

Input Saturation ◽

Delayed Systems

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Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2018.0131 ◽

2019 ◽

Vol 377 (2153) ◽

pp. 20180131 ◽

Cited By ~ 2

Author(s):

Luca Giuggioli ◽

Zohar Neu

Keyword(s):

Langevin Equation ◽

Complex Dynamics ◽

Probability Distributions ◽

Delay Systems ◽

Langevin Equations ◽

Delayed Systems ◽

Temporal Features ◽

Fokker Planck Equations ◽

Random Fluctuations ◽

Fokker Planck

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker–Planck equations for the n -time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker–Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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