Mathematics

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16 pages, 8983 KiB

Open AccessArticle

A Finite-Time Disturbance Observer for Tracking Control of Nonlinear Systems Subject to Model Uncertainties and Disturbances

by Manh Hung Nguyen and Kyoung Kwan Ahn

Mathematics 2024, 12(22), 3512; https://doi.org/10.3390/math12223512 - 10 Nov 2024

Viewed by 417

Abstract

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, [...] Read more.

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, in which the estimation error only converges to the origin asymptotically under assumptions that the first and/or second derivatives are vanishing, the suggested DOB is able to estimate the disturbance exactly in finite time. Firstly, uncertainties (parametric and unstructured uncertainties), unknown dynamics, and external disturbances in system dynamics are lumped into a generalized disturbance term that is subsequently estimated by the proposed DOB. Based on this, a DOB-based backstepping controller is synthesized to ensure high-accuracy tracking performance under various working conditions. The stability analysis of not only the DOB but also the overall closed-loop system is theoretically confirmed by the Lyapunov stability theory. Finally, the advantages of the proposed FTDOB and the FTDOB-based controller over other DOBs and existing DOB-based controllers are explicitly simultaneously demonstrated by a series of numerical simulations on a second-order mechanical system and comparative experiments on an actual DC motor system. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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14 pages, 418 KiB

Open AccessArticle

Bi-Objective Optimization for Interval Max-Plus Linear Systems

by Cailu Wang, Jiye Zhang, Pengcheng Chen and Haichao Zhao

Mathematics 2024, 12(5), 653; https://doi.org/10.3390/math12050653 - 23 Feb 2024

Viewed by 777

Abstract

This paper investigates the interval-valued-multi-objective-optimization problem, whose objective function is a vector-valued max-plus interval function and the constraint function is a real-affine function. The strong and weak solvabilities of the interval-valued-optimization problem are introduced, and the solvability criteria are established. A necessary and [...] Read more.

This paper investigates the interval-valued-multi-objective-optimization problem, whose objective function is a vector-valued max-plus interval function and the constraint function is a real-affine function. The strong and weak solvabilities of the interval-valued-optimization problem are introduced, and the solvability criteria are established. A necessary and sufficient condition for the strong solvability of the multi-objective-optimization problem is provided. In particular, for the bi-objective-optimization problem, a necessary and sufficient condition of the weak solvability is provided, and all the solvable sub-problems are found out. The interval optimal solution is obtained by constructing the set of all optimal solutions of the solvable sub-problems. The optimal load distribution is used to demonstrate how the presented results work in real-life examples. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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20 pages, 6346 KiB

Open AccessArticle

Temperature-Controlled Laser Cutting of an Electrical Steel Sheet Using a Novel Fuzzy Logic Controller

by Dinh-Tu Nguyen, Yuan-Ting Lin, Jeng-Rong Ho, Pi-Cheng Tung and Chih-Kuang Lin

Mathematics 2023, 11(23), 4769; https://doi.org/10.3390/math11234769 - 25 Nov 2023

Viewed by 13424

Abstract

A novel PID-type fuzzy logic controller (FLC) with an online fuzzy tuner was created to maintain stable in situ control of the cutting front temperature, aiming to enhance the laser process for thin non-oriented electrical steel sheets. In the developed controller, the output [...] Read more.

A novel PID-type fuzzy logic controller (FLC) with an online fuzzy tuner was created to maintain stable in situ control of the cutting front temperature, aiming to enhance the laser process for thin non-oriented electrical steel sheets. In the developed controller, the output scaling factors and the universe of discourse were initially optimized using a hybrid of the particle swarm optimization and grey wolf optimization methods. The optimal parameters obtained were utilized in experiments involving the laser cutting of thin non-oriented electrical steel sheets, compared to an open-loop control system maintaining a constant cutting speed. The PID-type FLC with an online fuzzy tuner demonstrated a superior cutting quality, generating a smaller roundness and a reduced heat-affected zone (HAZ) through the in situ tuning of control parameters. Particularly, the HAZ width was significantly smaller than that reported in a previous study which used fuzzy gain scheduling for temperature control. Moreover, the cutting time was diminished by optimally adjusting the cutting speed using PID-type FLC with an online fuzzy tuner. Therefore, the accumulated heat in the steel sheet, particularly under high laser pulse frequencies, was effectively reduced, making it suitable for industrial applications. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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22 pages, 4341 KiB

Open AccessArticle

A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems

by Majid Roohi, Saeed Mirzajani and Andreas Basse-O’Connor

Mathematics 2023, 11(21), 4463; https://doi.org/10.3390/math11214463 - 27 Oct 2023

Cited by 16 | Viewed by 1669

Abstract

Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of different system classes. This paper introduces [...] Read more.

Over the past decade, fractional-order laser chaotic systems have attracted a lot of attention from a variety of fields, including theoretical research as well as practical applications, which has resulted in the development of a number of different system classes. This paper introduces a novel single-input finite-time PID sliding mode control (SMC) technique to stabilize a specific group of unknown 4-dimensional chaotic fractional-order (FO) laser systems. By combining the PID concept with the FO-version of the Lyapunov stability theory, a novel finite-time PID SMC strategy has been developed, which effectively mitigates chaotic behavior in the mentioned unknown 4-dimensional chaotic FO laser system. This method makes use of a characteristic of FO chaotic systems known as boundedness, which is used here. Notably, the control input’s sign function, which is responsible for undesirable chattering, is transformed into the fractional derivative of the control input. This transformation results in a smooth and chattering-free control input, further enhancing the method’s performance. To demonstrate the efficacy of the proposed chattering-free–finite-time PID SMC technique, two numerical scenarios are presented, showcasing its efficient performance in stabilizing the unknown 4-dimensional chaotic FO laser system. These scenarios serve as illustrations of the method’s potential for practical applications. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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20 pages, 5818 KiB

Open AccessFeature PaperArticle

Adaptively Learned Modeling for a Digital Twin of Hydropower Turbines with Application to a Pilot Testing System

by Hong Wang, Shiqi (Shawn) Ou, Ole Gunnar Dahlhaug, Pål-Tore Storli, Hans Ivar Skjelbred and Ingrid Vilberg

Mathematics 2023, 11(18), 4012; https://doi.org/10.3390/math11184012 - 21 Sep 2023

Cited by 7 | Viewed by 1629

Abstract

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of [...] Read more.

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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19 pages, 3760 KiB

Open AccessArticle

Automatic Piston-Type Flow Standard Device Calibration System

by Xinming Song, Xiaoli Wang and Min Ma

Mathematics 2023, 11(18), 3802; https://doi.org/10.3390/math11183802 - 5 Sep 2023

Viewed by 1538

Abstract

Measurement of flow is crucial for assuring product quality, increasing manufacturing effectiveness, and promoting the development of science and technology. With the advancement of calibration and automation, standard devices using the mass method, volumetric method, and master meter method have limitations, such as [...] Read more.

Measurement of flow is crucial for assuring product quality, increasing manufacturing effectiveness, and promoting the development of science and technology. With the advancement of calibration and automation, standard devices using the mass method, volumetric method, and master meter method have limitations, such as low calibration efficiency and automation, large size, and complex operation. Innovations in this area are desperately needed. To realize the automation of calibrating ultrasonic water meters, a piston-type flow standard device calibration system with a high degree of automation, high calibration efficiency, small size, and easy operation was designed. A piston-type flow standard device was designed, the standard device was modeled, the selection of the main hardware and the design of the automated control of the hardware parts were completed; an automation control system adapted to the flow standard device was developed; and, furthermore, a water meter flow point calibration algorithm integrating the start–stop method and the dual-time method, as well as a water meter flow correction algorithm, was devised to improve the efficiency of ultrasonic water meter calibration. An uncertainty assessment of the designed system was completed; the standard uncertainty and expanded uncertainty of the device were 0.013% and 0.026%. Meanwhile, flow calibration tests were conducted, validating the rationality of the automated calibration algorithm for ultrasonic water meters. The results show that ultrasonic water meters calibrated with flow correction have a flow error within ±3% in the “low flow range” and within ±2% in the “high flow range”, with a repeatability of less than 0.05%. This indicates that a piston-type flow standard device, coupled with an automation calibration control system, can efficiently, accurately, and conveniently perform water meter calibration, and the system has good practical value. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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14 pages, 6015 KiB

Open AccessArticle

Mathematical Modelling of Fused Deposition Modeling (FDM) 3D Printing of Poly Vinyl Alcohol Parts through Statistical Design of Experiments Approach

by Mahmoud Moradi, Mojtaba Karamimoghadam, Saleh Meiabadi, Giuseppe Casalino, Mohammad Ghaleeh, Bobymon Baby, Harikrishna Ganapathi, Jomal Jose, Muhammed Shahzad Abdulla, Paul Tallon, Mahmoud Shamsborhan, Mohammad Rezayat, Satyam Paul and Davood Khodadad

Mathematics 2023, 11(13), 3022; https://doi.org/10.3390/math11133022 - 7 Jul 2023

Cited by 13 | Viewed by 2465

Abstract

This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input [...] Read more.

This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input parameters for the response surface methodology (DOE) while measuring modulus, elongation at break, and weight as experimental responses. To determine the optimal parameters, a regression equation analysis was conducted to identify the most significant parameters. The results indicate that both input parameters significantly impact the output responses. The Design Expert software was utilized to create surface and residual plots, and the interaction between the two input parameters shows that increasing the infill percentage (IP) leads to printing heavier samples, while the patterns do not affect the weight of the parts due to close printing structures. On the contrary, the discrepancy between the predicted and actual responses for the optimal samples is below 15%. This level of error is deemed acceptable for the DOE experiments. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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18 pages, 487 KiB

Open AccessArticle

Echo State Network-Based Adaptive Event-Triggered Control for Stochastic Nonaffine Systems with Actuator Hysteresis

by Shuxian Lun, Zhenkai Qin, Xiaodong Lu, Ming Li and Tianping Tao

Mathematics 2023, 11(8), 1884; https://doi.org/10.3390/math11081884 - 16 Apr 2023

Viewed by 1137

Abstract

This paper studies the problem of the event-triggered control of nonaffine stochastic nonlinear systems with actuator hysteresis. The echo state network (ESN) is introduced to approximate an unknown nonlinear function. The command filtering technology is used to avoid the derivation of the virtual [...] Read more.

This paper studies the problem of the event-triggered control of nonaffine stochastic nonlinear systems with actuator hysteresis. The echo state network (ESN) is introduced to approximate an unknown nonlinear function. The command filtering technology is used to avoid the derivation of the virtual controller in the controller design process and tries to solve the problem of complexity explosion in the traditional method. Based on Lyapunov’s finite-time stability theory, the proposed method verifies the stability of non-affine stochastic nonlinear systems. It is proved that the proposed controller method can guarantee that all of the signals in the closed-loop system are bounded, and the tracking error can converge to a minimal neighborhood of zero even if there exists an actuator hysteresis. The effectiveness of the proposed method is demonstrated by the simulation example. The simulation results show that the proposed method is effective. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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