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Advances in Nonlinear Dynamical Systems and Control Systems
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Advances in Nonlinear Dynamical Systems and Control Systems

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

Deadline for manuscript submissions: 10 May 2025 | Viewed by 4122

Special Issue Editor

Prof. Dr. Mikulas Huba

E-Mail Website
Guest Editor
Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, SK-812 19 Bratislava, Slovakia
Interests: control; e-learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Surprisingly, after several waves of innovation, which were reflected in the technological basis of automatic control, it can be stated with that the basic structure of the most used control algorithms remains essentially at the level of solutions from the first half of the 20th century. However, the explanation of the reasons themselves is even more surprising; until now, we have not really understood them. Currently, however, development in industrial automation, embedded computers, different programmable devices, or field-programmable analog arrays has created conditions that allow exceeding these traditional technologies that are commonly referred to as PID control. The search for appropriate solutions on the one hand welcomes their innovation; on the other hand, it requires a reliable design using strict mathematical procedures. These can reflect completely new ideas, but also dusting off older inventions, which, at the time of their discovery, were technologically ahead of their time. As one of the possible examples, we could mention constrained controllers with higher-order derivatives proposed using criteria to guarantee the absolute stability of nonlinear systems, but the calculation of such possibilities could be much wider. Meanwhile, the field of application has grown significantly from traditional process control, servo systems, power electronics, or robotics. Let us mention only new solutions from the field of automotive, autonomous vehicles, or renewable energy sources. There are an awful lot of incoming challenges from practice—you just have to get hold of them!

Prof. Dr. Mikulas Huba
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • PID control
  • automatic reset
  • predictive control
  • nonlinear control
  • constrained control
  • adaptive control
  • intelligent control
  • optimal control
  • filtration
  • multilevel optimization
  • measurement and quantization noise
  • robustness and uncertainties
  • set-point and disturbance rejection optimization
  • time-delayed systems
  • dead-time compensators
  • digitalization
  • Industry 4.0

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Published Papers (3 papers)

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Research

17 pages, 1463 KiB  
Article
Adaptive Backstepping Time Delay Control for Precision Positioning Stage with Unknown Hysteresis
by Zhifu Li, Jiawei Li, Tao Weng and Ziyang Zheng
Mathematics 2024, 12(8), 1197; https://doi.org/10.3390/math12081197 - 17 Apr 2024
Cited by 1 | Viewed by 806
Abstract
Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the [...] Read more.
Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the positioning accuracy of the system. In addition, it is challenging to identify the model parameters for hysteresis. In this paper, an adaptive backstepping time delay control method is proposed for piezoelectric devices system with unknown hysteresis. Firstly, the Bouc–Wen model is used to describe the hysteresis characteristics, and the model is interpreted as a linear term and a bounded uncertain hysteresis term. Then, the time delay estimation technique is used to estimate the hysteresis term of the Bouc–Wen model online, and the unknown parameters of the system and hysteresis model are obtained through adaptive updating laws. Furthermore, the stability of the control scheme is proved based on Lyapunov stability theory. Finally, the effectiveness and superiority of the proposed control scheme are demonstrated by comparing it with two typical hysteresis compensation control algorithms through three different sets of input signals. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Control Systems)
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16 pages, 2571 KiB  
Article
Event-Triggered Second-Order Sliding Mode Controller Design and Implementation
by Andrej Sarjaš and Dušan Gleich
Mathematics 2023, 11(20), 4314; https://doi.org/10.3390/math11204314 - 16 Oct 2023
Viewed by 1150
Abstract
The paper presents an event-triggered higher-order sliding mode controller design. The event-triggering technique is the alternative approach to real-time controller execution, unlike the classic time-triggering technique, which is not time-dependable and is governed by the triggering policy. The technique is suitable for system [...] Read more.
The paper presents an event-triggered higher-order sliding mode controller design. The event-triggering technique is the alternative approach to real-time controller execution, unlike the classic time-triggering technique, which is not time-dependable and is governed by the triggering policy. The technique is suitable for system resource relaxation in case of computation burden or network usage mitigation. The paper describes the stability analysis of the super-twisted sliding mode controller based on input-to-state stability notation. The stability analysis introduces a triggering policy related directly to the ultimate boundness of the system states and preselected sliding variables. The controller time execution with the selected triggering condition prevents the exhibition of the Zeno phenomena, where the minimal inter-event time of the controller has a positive non-zero lower bound. The minimal value of the inter-event time is related directly to the controller parameters and triggering bound, the selection of which is given with the derived stability conditions regarding the designer’s objective. Preventing the fast nonlinear controller execution, especially close to the sliding manifold, also alleviates the chattering phenomena effectively, which is a primal drawback, and limits the usage of the controller on various systems. The method’s efficiency is verified with the hardware-in-the-loop system, where the dynamic and robustness of the triggering approach are compared to the standard time-triggered execution technique. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Control Systems)
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32 pages, 2379 KiB  
Article
Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models
by Mikulas Huba, Pavol Bistak and Damir Vrancic
Mathematics 2023, 11(20), 4229; https://doi.org/10.3390/math11204229 - 10 Oct 2023
Cited by 9 | Viewed by 1588
Abstract
The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) [...] Read more.
The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamical Systems and Control Systems)
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