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Symmetry
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PID Control and Symmetry
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PID Control and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: closed (15 August 2022) | Viewed by 15821

Special Issue Editors

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
Prof. Dr. Damir Vrančić

E-Mail Website
Guest Editor
Department of Systems and Control, Jožef Stefan Institute, Jamova Cesta 39, 1000 Ljubljana, Slovenia
Interests: control; controller tuning;anti-windup;electronics
Dr. Paulo Moura Oliveira

E-Mail Website
Guest Editor
Department of Engineering, University of Trás-os-Montes e Alto Douro, 5001-911 Vila Real, Portugal
Interests: control engineering; evolutionary and nature inspired algorithms for single and multiple objective optimization problem solving
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The striking development in industrial automation and embedded computers has brought about the explosion of system control structures that are commonly referred to as PID control. The search for appropriate solutions often requires solving symmetric or asymmetric problems. These may relate, for example, to control constraints always present in optimal control design and relay identification to reconstruction and compensation of input and output disturbances, to finding the appropriate equilibrium between the set-point and disturbance-rejection response, to choosing the working point for systems with interval uncertainties and nonlinear dynamics, to asymmetries in dealing with different types of delays, etc.

For this Special Issue, we invite specialists that are active in the field of PID control design, including educational aspects.

Prof. Dr. Mikulas Huba
Prof. Dr. Damir Vrančić
Dr. Paulo Moura Oliveira 
Guest Editors

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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
  • control saturation
  • filtration
  • optimal control
  • robustness and uncertainties
  • set-point and disturbance-rejection optimization
  • time-delayed systems
  • dead time compensators

Published Papers (6 papers)

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Research

24 pages, 4420 KiB  
Article
The Regulation of an Electric Oven and an Inverted Pendulum
by Ricardo Balcazar, José de Jesús Rubio, Eduardo Orozco, Daniel Andres Cordova, Genaro Ochoa, Enrique Garcia, Jaime Pacheco, Guadalupe Juliana Gutierrez, Dante Mujica-Vargas and Carlos Aguilar-Ibañez
Symmetry 2022, 14(4), 759; https://doi.org/10.3390/sym14040759 - 06 Apr 2022
Cited by 27 | Viewed by 2793
Abstract
In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error [...] Read more.
In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error decays to zero after a convergence time; it has the problem of chattering in the output. A second-order sliding-mode regulator is a smooth method to counteract the chattering effect where the integral of the sign-mapping is used. A second-order sliding-mode regulator is presented as a new class of algorithm where the trajectory is asymptotic and stable; it is shown to greatly improve the convergence time in comparison with other regulators considered. Simulation and experimental results are described in which an electric oven is considered as a stable linear mathematical model, and an inverted pendulum is considered as an asymmetrical unstable non-linear mathematical model. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
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15 pages, 313 KiB  
Article
On PID Design Constraints in Relation to Control of Strictly Metzler Linear MIMO Systems
by Dušan Krokavec and Anna Filasová
Symmetry 2021, 13(9), 1589; https://doi.org/10.3390/sym13091589 - 29 Aug 2021
Cited by 3 | Viewed by 1088
Abstract
For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the [...] Read more.
For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
44 pages, 4717 KiB  
Article
Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise
by Mikulas Huba and Damir Vrancic
Symmetry 2021, 13(5), 798; https://doi.org/10.3390/sym13050798 - 04 May 2021
Cited by 15 | Viewed by 2684
Abstract
The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial [...] Read more.
The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial process identification and modelling and also to modify the target closed-loop transfer functions, which must remain causal. To attenuate high initial control signal peaks, appropriate pre-filters are introduced. In order to work with as few parameters as possible, all higher-order transfer functions (process models, target closed loops, pre-filters and noise-attenuation filters) are selected in the form of binomial filters with multiple time constants. Consequently, the so-called “half-rule”, used to reduce too complex process transfer functions, has been modified accordingly. Because derived controllers can lead to different transient dynamics depending on the context of use, the article recalls the need to introduce dynamic classes of control to clarify the mission of individual types of controllers. Consequently, also the performance evaluation using the total variation (TV) criterion had to be refined. Indeed, in its original version, TV is not suitable to distinguish between reasonable and excessive control effort due to improper tuning and noise. The modified TVs allow evaluating higher order systems with multiple changes in direction of their control signal increase without contributing to the excessive control increments. The advantages of the proposed modifications, compared to the traditional approaches, are made clear through simulation examples. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
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20 pages, 1204 KiB  
Article
Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant
by Mária Hypiusová and Danica Rosinová
Symmetry 2021, 13(1), 142; https://doi.org/10.3390/sym13010142 - 16 Jan 2021
Cited by 8 | Viewed by 2430
Abstract
Robust pole-placement based on convex DR-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is [...] Read more.
Robust pole-placement based on convex DR-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
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14 pages, 305 KiB  
Article
PID Control Design for SISO Strictly Metzlerian Linear Systems
by Dušan Krokavec and Anna Filasová
Symmetry 2020, 12(12), 1979; https://doi.org/10.3390/sym12121979 - 30 Nov 2020
Cited by 4 | Viewed by 1365
Abstract
For linear time-invariant Metzlerian systems, this paper proposes an original approach reflecting specific structural system constraints and positiveness in solving the problem of PID control. Refining parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with the control [...] Read more.
For linear time-invariant Metzlerian systems, this paper proposes an original approach reflecting specific structural system constraints and positiveness in solving the problem of PID control. Refining parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with the control law representation and is formulated as a linear matrix inequality feasibility problem. Taking into account structural restriction of Metzlerian positive systems, a characterization of PID control law parameters is permitted, to highlight dynamical properties of the closed-loop system solutions and the significant structural influence of derivative gain value of the control law parameters in design. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
19 pages, 631 KiB  
Article
Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter
by Józef Wiora and Alicja Wiora
Symmetry 2020, 12(11), 1898; https://doi.org/10.3390/sym12111898 - 19 Nov 2020
Cited by 14 | Viewed by 2793
Abstract
Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article [...] Read more.
Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system. Full article
(This article belongs to the Special Issue PID Control and Symmetry)
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