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Algorithms
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Algorithms for PID Controller 2024
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Algorithms for PID Controller 2024

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 15168

Special Issue Editors

Prof. Dr. Ramiro Barbosa

E-Mail Website
Guest Editor
Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Interests: control; simulation; optimization; fractional calculus; evolutionary algorithms; artificial intelligence
Special Issues, Collections and Topics in MDPI journals
Dr. Paulo Moura Oliveira

E-Mail Website
Guest Editor
INESC-TEC, University of Trás-os-Montes e Alto Douro, 5001-911 Vila Real, Portugal
Interests: PID control; intelligent control; control engineering education; evolutionary and natural inspired metaheuristics for single and multiple objective optimisation problem solving
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

To date, the PID controller is still the most commonly used algorithm for control applications. Since its first development, the PID algorithm has gone hand in hand with the evolution of science and engineering, and new methods and applications have been introduced over time. Advances in recent decades, provided by the area of fractional calculus and metaheuristic algorithms, and, more recently, by artificial intelligence, have given rise to a refreshing boost to PID control.

This Special Issue aims to present the most recent developments in the design, tuning, and applications of PID controllers. The focus is on reporting theoretical and applied research results in control structures, optimization techniques, metaheuristic algorithms, tuning methods, digital implementations, and applications of the PID algorithm, among others, and the use of current artificial intelligence techniques, such as machine learning, deep learning, and reinforcement learning.

Prof. Dr. Ramiro Barbosa
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. Algorithms 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 1600 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

  • fractional-order PID controller
  • fuzzy PID controller
  • neural PID controller
  • fuzzy logic
  • fractional-order control
  • predictive control
  • optimization
  • neural networks
  • metaheuristic algorithms
  • neural-fuzzy algorithms
  • evolutionary algorithms
  • machine learning
  • deep learning
  • digital implementation
  • reinforcement learning
  • artificial intelligence

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Published Papers (8 papers)

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Research

19 pages, 756 KiB  
Article
Analytical MPC Algorithm Using Steady-State Process Model
by Piotr M. Marusak
Algorithms 2025, 18(2), 79; https://doi.org/10.3390/a18020079 - 2 Feb 2025
Viewed by 719
Abstract
For some classes of control plants (e.g., large time delay or inverse response), the PID controllers may offer unsatisfactory results; on the other hand, a Model Predictive Control (MPC) algorithm based on a linear model may offer insufficient control quality when applied to [...] Read more.
For some classes of control plants (e.g., large time delay or inverse response), the PID controllers may offer unsatisfactory results; on the other hand, a Model Predictive Control (MPC) algorithm based on a linear model may offer insufficient control quality when applied to nonlinear control plants. To improve the MPC algorithm operation, one can use a steady-state process model; this paper describes how to do this skillfully. The obtained algorithm, based on the popular Dynamic Matrix Control (DMC) algorithm, is detailed. The proposed approach consists in modifying the analytical version of the DMC algorithm in such a way that it can still be expressed as the control law. Thus, the algorithm can still be applied to fast control plants, requiring short sampling times. Though the proposed approach does not modify the DMC algorithm much, it offers improvement in the control quality when the algorithm is employed in a nonlinear control plant. Experiments illustrating the efficiency of the proposed approach were conducted in the control system of a nonlinear chemical reactor. The results show improvement in the control quality compared to a case when the classical MPC algorithm is used. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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31 pages, 11725 KiB  
Article
Evaluation of PID-Based Algorithms for UGVs
by Tiago Gameiro, Tiago Pereira, Hamid Moghadaspoura, Francesco Di Giorgio, Carlos Viegas, Nuno Ferreira, João Ferreira, Salviano Soares and António Valente
Algorithms 2025, 18(2), 63; https://doi.org/10.3390/a18020063 - 24 Jan 2025
Viewed by 1014
Abstract
The autonomous navigation of unmanned ground vehicles (UGVs) in unstructured environments, such as agricultural or forestry settings, has been the subject of extensive research by various investigators. The navigation capability of a UGV in unstructured environments requires considering numerous factors, including the quality [...] Read more.
The autonomous navigation of unmanned ground vehicles (UGVs) in unstructured environments, such as agricultural or forestry settings, has been the subject of extensive research by various investigators. The navigation capability of a UGV in unstructured environments requires considering numerous factors, including the quality of data reception that allows reliable interpretation of what the UGV perceives in a given environment, as well as the use these data to control the UGV’s navigation. This article aims to study different PID control algorithms to enable autonomous navigation on a robotic platform. The robotic platform consists of a forestry tractor, used for forest cleaning tasks, which was converted into a UGV through the integration of sensors. Using sensor data, the UGV’s position and orientation are obtained and utilized for navigation by inputting these data into a PID control algorithm. The correct choice of PID control algorithm involved the study, analysis, and implementation of different controllers, leading to the conclusion that the Vector Field control algorithm demonstrated better performance compared to the others studied and implemented in this paper. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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26 pages, 2476 KiB  
Article
Control of a Mobile Line-Following Robot Using Neural Networks
by Hugo M. Leal, Ramiro S. Barbosa and Isabel S. Jesus
Algorithms 2025, 18(1), 51; https://doi.org/10.3390/a18010051 - 17 Jan 2025
Viewed by 1456
Abstract
This work aims to develop and compare the performance of a line-following robot using both neural networks and classical controllers such as Proportional–Integral–Derivative (PID). Initially, the robot’s infrared sensors were employed to follow a line using a PID controller. The data from this [...] Read more.
This work aims to develop and compare the performance of a line-following robot using both neural networks and classical controllers such as Proportional–Integral–Derivative (PID). Initially, the robot’s infrared sensors were employed to follow a line using a PID controller. The data from this method were then used to train a Long Short-Term Memory (LSTM) network, which successfully replicated the behavior of the PID controller. In a subsequent experiment, the robot’s camera was used for line-following with neural networks. Images of the track were captured, categorized, and used to train a convolutional neural network (CNN), which then controlled the robot in real time. The results showed that neural networks are effective but require more processing and calibration. On the other hand, PID controllers proved to be simpler and more efficient for the tested tracks. Although neural networks are very promising for advanced applications, they are also capable of handling simpler tasks effectively. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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34 pages, 3047 KiB  
Article
Stability Analysis and Experimental Validation of Standard Proportional-Integral-Derivative Control in Bilateral Teleoperators with Time-Varying Delays
by Marco A. Arteaga, Evert J. Guajardo-Benavides and Pablo Sánchez-Sánchez
Algorithms 2024, 17(12), 580; https://doi.org/10.3390/a17120580 - 16 Dec 2024
Cited by 1 | Viewed by 1065
Abstract
The control of bilateral teleoperation systems with time-varying delays is a challenging problem that is frequently addressed with advanced control techniques. Widely known controllers, like Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID), are seldom employed independently and are typically combined with other approaches, or at [...] Read more.
The control of bilateral teleoperation systems with time-varying delays is a challenging problem that is frequently addressed with advanced control techniques. Widely known controllers, like Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID), are seldom employed independently and are typically combined with other approaches, or at least with gravity compensation. This work aims to address a gap in the analysis of bilateral systems by demonstrating that the standard PID control law alone can achieve regulation in these systems when a human operator moves any of the robots while exchanging delayed positions. Experimental results are consistent with the theoretical analysis. Additionally, to illustrate the high degree of robustness of the standard PID, further experiments are conducted in constrained motion, both with and without force feedback. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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16 pages, 579 KiB  
Article
Fuzzy Modelling Algorithms and Parallel Distributed Compensation for Coupled Electromechanical Systems
by Christian Reyes, Julio C. Ramos-Fernández, Eduardo S. Espinoza and Rogelio Lozano
Algorithms 2024, 17(9), 391; https://doi.org/10.3390/a17090391 - 3 Sep 2024
Cited by 1 | Viewed by 1257
Abstract
Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system’s components, thermal effects, mechanical vibrations, [...] Read more.
Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system’s components, thermal effects, mechanical vibrations, electrical noise, and the dynamic and transient impacts of electrical loads. In this study, we introduce a fuzzy modelling identification approach utilizing the Takagi–Sugeno (T–S) structure, wherein model and control parameters are optimized. This methodology circumvents the need for deriving a mathematical model through energy balance considerations involving thermodynamics and the non-linear representation of the electric generator. Initially, a non-linear mathematical model for the electrical power system is obtained through the fuzzy c-means algorithm, which handles both premises and consequents in state space, utilizing input–output experimental data. Subsequently, the Particle Swarm Algorithm (PSO) is employed for optimizing the fuzzy parameter m of the c-means algorithm during the modelling phase. Additionally, in the design of the Parallel Distributed Compensation Controller (PDC), the optimization of parameters pertaining to the poles of the closed-loop response is conducted also by using the PSO method. Ultimately, numerical simulations are conducted, adjusting the power consumption of an inductive load. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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24 pages, 8519 KiB  
Article
Fractional-Order Fuzzy PID Controller with Evolutionary Computation for an Effective Synchronized Gantry System
by Wei-Lung Mao, Sung-Hua Chen and Chun-Yu Kao
Algorithms 2024, 17(2), 58; https://doi.org/10.3390/a17020058 - 29 Jan 2024
Cited by 4 | Viewed by 2100
Abstract
Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between [...] Read more.
Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup’s recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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17 pages, 4102 KiB  
Article
A Shadowed Type-2 Fuzzy Approach for Crossover Parameter Adaptation in Differential Evolution
by Patricia Ochoa, Cinthia Peraza, Oscar Castillo and Zong Woo Geem
Algorithms 2023, 16(6), 279; https://doi.org/10.3390/a16060279 - 31 May 2023
Cited by 2 | Viewed by 2118
Abstract
The shadowed type-2 fuzzy systems are used more frequently today as they provide an alternative to classical fuzzy logic. The primary purpose of fuzzy logic is to simulate reasoning in a computer. This work aims to use shadowed type-2 fuzzy systems (ST2-FS) to [...] Read more.
The shadowed type-2 fuzzy systems are used more frequently today as they provide an alternative to classical fuzzy logic. The primary purpose of fuzzy logic is to simulate reasoning in a computer. This work aims to use shadowed type-2 fuzzy systems (ST2-FS) to dynamically adapt the crossing parameter of differential evolution (DE). To test the performance of the dynamic crossing parameter, the motor position control problem was used, which contains an interval type-2 fuzzy system (IT2-FS) for controlling the motor. A comparison is made between the original DE and the algorithm using shadowed type-2 fuzzy systems (DE-ST2-FS), as well as a comparison with the results of other state-of-the-art metaheuristics. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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21 pages, 5841 KiB  
Article
Real-Time Interval Type-2 Fuzzy Control of an Unmanned Aerial Vehicle with Flexible Cable-Connected Payload
by Fethi Candan, Omer Faruk Dik, Tufan Kumbasar, Mahdi Mahfouf and Lyudmila Mihaylova
Algorithms 2023, 16(6), 273; https://doi.org/10.3390/a16060273 - 29 May 2023
Cited by 7 | Viewed by 2456
Abstract
This study presents the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system on an unmanned aerial vehicle (UAV) with a flexible cable-connected payload in comparison to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The IT2-FPID control has [...] Read more.
This study presents the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system on an unmanned aerial vehicle (UAV) with a flexible cable-connected payload in comparison to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The IT2-FPID control has significant stability, disturbance rejection, and response time advantages. To prove and show these advantages, the DJI Tello, a commercial UAV, is used with a flexible cable-connected payload to test the robustness of PID, T1-FPID, and IT2-FPID controllers. First, the optimal coefficients of the compared controllers are found using the Big Bang–Big Crunch algorithm via the nonlinear UAV model without the payload. Second, once optimised, the controllers are tested using several scenarios, including disturbing the payload and the coverage path planning area to examine their robustness. Third, the controller performance results are evaluated according to reference achievement and point-based tracking under disturbances. Finally, the superiority of the IT2-FPID controller is shown via simulations and real-time experiments with a better overshoot, a faster settling time, and good properties of disturbance rejection compared with the PID and the T1-FPID controllers. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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