Dimensional Dynamical Systems and Control Theory in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 2448

Special Issue Editor


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Guest Editor
Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, 812 19 Bratislava, Slovakia
Interests: smith predictor; internal model control; PID controller

Special Issue Information

Dear Colleagues,

The modern control theory of dynamical systems has gradually been applied in engineering practices, even though the vast majority of industrial control systems still rely on the proven classical control theory that is often represented by proportional–integral–derivative controllers. However, challenges created by new technologies, processes and their products, where the application of classical control theory can no longer guarantee the required control quality, must be met with more sophisticated mathematical methods to obtain adequate control algorithms. Thus, higher-order controllers, fractional-order controllers, and adaptive and intelligent control have become more important, where the quality is ensured by criteria formulated in the optimization process. Robust controllers are resistant to parameter changes, and emphasis should also be placed on disturbance attenuation. Control is implemented at the lowest level using embedded computers, and network infrastructures are used at higher control levels. Controlled objects must work together in a common space, while many of them must work autonomously at the same time. To fulfil all these particular goals, new mathematical approaches should be applied so that this development of automation is in line with the revolutionary principles of Industry 4.0 and 5.0.

Dr. Pavol Bistak
Guest Editor

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Keywords

  • linear control systems
  • nonlinear control systems
  • system identification
  • mathematical and computer modelling
  • optimization and optimal control
  • adaptive control
  • robust control
  • intelligent control systems
  • cooperative control
  • networked and embedded controls
  • autonomous systems
  • systems and automation
  • testbeds and digital twins
  • Industry 4.0 and 5.0

Published Papers (1 paper)

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Research

24 pages, 1144 KiB  
Article
Robust Stability Analysis of Filtered PI and PID Controllers for IPDT Processes
by Mikulas Huba, Pavol Bistak and Damir Vrancic
Mathematics 2023, 11(1), 30; https://doi.org/10.3390/math11010030 - 21 Dec 2022
Cited by 6 | Viewed by 1853
Abstract
The paper discusses the stability and robustness of the proportional-integral (PI), proportional-integral-derivative (PID), and proportional-integral-derivative-accelerative (PIDA) controller for the integral-plus-dead-time (IPDT) plants. To enable the implementation and measurement of noise attenuation, binomial low-pass filters are added to the traditional design of controllers with [...] Read more.
The paper discusses the stability and robustness of the proportional-integral (PI), proportional-integral-derivative (PID), and proportional-integral-derivative-accelerative (PIDA) controller for the integral-plus-dead-time (IPDT) plants. To enable the implementation and measurement of noise attenuation, binomial low-pass filters are added to the traditional design of controllers with ideal transfer functions, and the impact of the low-pass filters on the robust stability of the circuit is studied in detail. The proposed controller tuning, which integrates the suboptimal controller and filter design, is based on explicit tuning formulas derived by using the multiple real dominant pole (MRDP) method. It is shown that by combining derivative actions with possibly higher-order low-pass filters, it is possible to either accelerate the transients or increase the closed loop robustness and that the problem of defining the robust stability area should be addressed at the stage of determining the process model. In addition, if wishing to maintain the closed loop robustness of unfiltered PI control, while increasing the degree of the derivative components, one needs to increase the filtering properties of the low-pass filter used accordingly. Simple analytical relations for setting filtered PI, PID, and PIDA controllers with equivalent robustness are derived. Full article
(This article belongs to the Special Issue Dimensional Dynamical Systems and Control Theory in Engineering)
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