Mathematics

Research

22 pages, 829 KiB

Open AccessArticle

Coalitional Control Strategy for a Heterogeneous Platoon Application

by Anca Maxim, Ovidiu Pauca, Romeo-Gabriel Amariei, Florin-Catalin Braescu and Constantin-Florin Caruntu

Mathematics 2024, 12(1), 7; https://doi.org/10.3390/math12010007 - 19 Dec 2023

Cited by 1 | Viewed by 881

Abstract

In this work, we propose a coalitional control solution for a multi-agent networked system. The idea is to use a flexible communication topology, in which the communication links are enabled or disabled between sub-systems, depending on their shared task. The control methodology is [...] Read more.

In this work, we propose a coalitional control solution for a multi-agent networked system. The idea is to use a flexible communication topology, in which the communication links are enabled or disabled between sub-systems, depending on their shared task. The control methodology is designed in an optimal control framework, by computing an optimal state feedback gain matrix corresponding to each communication topology. The proposed control algorithm was validated in simulation, and tested in real-time experiments using a heterogeneous vehicle platoon consisting of four mobile robots. Both simulation and experimental results illustrate the efficacy of our proposed methodology. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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16 pages, 2485 KiB

Open AccessArticle

Higher Order Sliding Mode Control of MIMO Induction Motors: A New Adaptive Approach

by Ali Karami-Mollaee and Oscar Barambones

Mathematics 2023, 11(21), 4558; https://doi.org/10.3390/math11214558 - 6 Nov 2023

Cited by 3 | Viewed by 1244

Abstract

In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition [...] Read more.

In this paper the objective is to force the outputs of nonlinear nonaffine multi-input multi-output (MIMO) systems to track those of a linear system with the desired properties. The approach is based on designing higher order sliding mode controller (HOSMC) with the definition of a new proportional-integral (PI) sliding surface. To this end, a linear state feedback with an adaptive switching gain (ASG) is applied to the nonlinear MIMO systems. Therefore, the switching gain can increase or decrease based on the system conditions. Then, the chattering is completely removed using a combination of HOSMC and ASG. Moreover, the proposed procedure is independent from the upper bound of the matched uncertainty, which is in the direction of system inputs. The finite time convergence to the sliding surface is also proved, which provides an invariance property in finite time. Note that invariance is the most important property of SMC. Finally, the general model of MIMO induction motors (IM) is used to address and to verify the proposed controller. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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24 pages, 1129 KiB

Open AccessArticle

Transfer-Matrix Method for Calculus of Long Cylinder Tube with Industrial Applications

by Luminita Codrea, Mihai-Sorin Tripa, Daniel Opruţa, Robert Gyorbiro and Mihaela Suciu

Mathematics 2023, 11(17), 3756; https://doi.org/10.3390/math11173756 - 31 Aug 2023

Viewed by 1112

Abstract

The Transfer-Matrix Method (TMM) is an original and relatively simple mathematical approach for the calculus of thin-walled cylindrical tubes presented in this work. Calculation with TMM is much less used than calculation with the Finite Elements Method (FEM), even though it is much [...] Read more.

The Transfer-Matrix Method (TMM) is an original and relatively simple mathematical approach for the calculus of thin-walled cylindrical tubes presented in this work. Calculation with TMM is much less used than calculation with the Finite Elements Method (FEM), even though it is much easier to apply in different fields. That is why it was considered imperative to present this original study. The calculus is based on Dirac’s and Heaviside’s functions and operators and on matrix calculation. The state vectors, the transfer-matrix, and the vector corresponding to the external efforts were defined, which were then used in the calculations. A matrix relation can be written, which gives the state vector of the last section depending on the state vector of the first section, a relation in which the conditions of the two end supports can be set. As an application, a heat exchanger was studied, with a large cylinder subjected to a uniformly distributed internal load, and from the inner cylinder bundle, a cylinder subjected to both uniform internal and external loads was considered. For the second cylinder, two possibilities of action for the external forces were considered, a successive action and a simultaneous action, achieving the same results in both situations. The TMM is intended to be used for iterative calculus in optimization problems where rapid successive results are required. In the future, we want to expand this method to other applications, and we want to develop related programs. This is an original theoretical study and is a complement to the research in the field on thin-walled cylinder tubes and their applications in heat exchangers. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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19 pages, 1486 KiB

Open AccessArticle

Hidden Markov Model-Based Control for Cooperative Output Regulation of Heterogeneous Multi-Agent Systems under Switching Network Topology

by Gia-Bao Hong and Sung-Hyun Kim

Mathematics 2023, 11(16), 3481; https://doi.org/10.3390/math11163481 - 11 Aug 2023

Viewed by 1061

Abstract

This paper investigates the problem of stochastically cooperative output regulation of heterogeneous multi-agent systems (MASs) subject to hidden Markov jumps using observer-based distributed control. In order to address a more realistic situation than prior studies, this paper focuses on the following issues: (1) [...] Read more.

This paper investigates the problem of stochastically cooperative output regulation of heterogeneous multi-agent systems (MASs) subject to hidden Markov jumps using observer-based distributed control. In order to address a more realistic situation than prior studies, this paper focuses on the following issues: (1) asynchronous phenomena in the system mode’s transmission to the controller; (2) the impact of system mode switching on network topology; and (3) the emergence of coupled terms between the mode-dependent Lyapunov matrix and the control gain in control design conditions. Specifically, to reduce the complexity arising from the asynchronous controller-side mode, the leader–state observer is developed so that the solution pair of regulator equations can be integrated into the observer. Furthermore, a linear decoupling method is proposed to handle the emergence of the aforementioned coupled terms; this provides sufficient LMI conditions to achieve stochastically cooperative output regulation for heterogeneous MASs. Finally, the validity of the proposed method is shown through two illustrative examples. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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19 pages, 1040 KiB

Open AccessArticle

New Insights on Robust Control of Tilting Trains with Combined Uncertainty and Performance Constraints

by Fazilah Hassan, Argyrios Zolotas and George Halikias

Mathematics 2023, 11(14), 3057; https://doi.org/10.3390/math11143057 - 11 Jul 2023

Cited by 1 | Viewed by 1120

Abstract

A rigorous study on optimized robust control is presented for non-preview (nulling-type) high-speed tilting rail vehicles. The scheme utilizes sensors on the vehicle’s body, contrary to that of preview tilt (which uses prior rail track information). Tilt with preview is the industrial norm [...] Read more.

A rigorous study on optimized robust control is presented for non-preview (nulling-type) high-speed tilting rail vehicles. The scheme utilizes sensors on the vehicle’s body, contrary to that of preview tilt (which uses prior rail track information). Tilt with preview is the industrial norm nowadays but is a complex scheme (both in terms of inter-vehicle signal connections and when it comes to straightforward fault detection). Non-preview tilt is simple (as it essentially involves an SISO control structure) and more effective in terms of (the localization of) failure detection. However, the non-preview tilt scheme suffers from performance limitations due to non-minimum-phase zeros in the design model (due to the compound effect of the suspension dynamic interaction and sensor combination used for feedback control) and presents a challenging control design problem. We proposed an optimized robust control design offering a highly improved non-preview tilt performance via a twofold model representation, i.e., (i) using the non-minimum phase design model and (ii) proposing a factorized design model version with the non-minimum phase characteristics treated as uncertainty. The impact of the designed controllers on tilt performance deterministic (curving acceleration response) and stochastic (ride quality) trade-off was methodically investigated. Nonlinear optimization was employed to facilitate fine weight selection given the importance of the ride quality as a bounded constraint in the design process. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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18 pages, 1852 KiB

Open AccessArticle

Exploring the Role of Sampling Time in String Stabilization for Platooning: An Experimental Case Study

by Felipe I. Villenas, Francisco J. Vargas and Andrés A. Peters

Mathematics 2023, 11(13), 2923; https://doi.org/10.3390/math11132923 - 29 Jun 2023

Cited by 2 | Viewed by 1028

Abstract

In this article, we investigate the behavior of vehicle platoons operating in a predecessor-following configuration, implemented through sampled-data control systems. Our primary focus is to examine the potential influence of the sampling time on the string stability of the platoon. To address this, [...] Read more.

In this article, we investigate the behavior of vehicle platoons operating in a predecessor-following configuration, implemented through sampled-data control systems. Our primary focus is to examine the potential influence of the sampling time on the string stability of the platoon. To address this, we begin by designing a string-stable platoon in continuous time. Subsequently, we consider the controller discretization process and proceed to simulate and implement the designed control strategy on an experimental platform at a scaled-down level. Through experimental testing and some theoretical results, we analyze the effects of different sampling times on the string stability performance of the platoon. We observe that an inappropriate selection of the sampling time can lead to a degradation in string stability within the platoon, making the choice of the sampling time crucial in maintaining the desired string stability properties. These findings highlight the importance of carefully considering the sampling time in the implementation of control systems for platooning applications. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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20 pages, 4456 KiB

Open AccessArticle

Optimized Cooperative Control of Error Port-Controlled Hamiltonian and Adaptive Backstepping Sliding Mode for a Multi-Joint Industrial Robot

by Xiaoyu Yang and Haisheng Yu

Mathematics 2023, 11(6), 1542; https://doi.org/10.3390/math11061542 - 22 Mar 2023

Cited by 2 | Viewed by 1395

Abstract

Robot joints driven by permanent magnet synchronous motors (PMSM) often cannot have both superior accuracy and rapidity when they track target signals. The robot joints have fine dynamic characteristics and poor steady-state characteristics when the signal controller is used, or they have fine [...] Read more.

Robot joints driven by permanent magnet synchronous motors (PMSM) often cannot have both superior accuracy and rapidity when they track target signals. The robot joints have fine dynamic characteristics and poor steady-state characteristics when the signal controller is used, or they have fine steady-state characteristics and poor dynamic characteristics when the energy controller is used. It is hard to make robot joints that have both superior dynamic and steady-state characteristics at once using a single control method. In order to solve this problem, the strategy of optimized cooperative control is proposed. First, an error port-controlled Hamiltonian (EPCH) energy controller and an adaptive backstepping sliding mode (ABSM) signal controller are designed. Second, an optimized cooperative control coefficient based on the position error of a robot joint is designed; this enables the system to switch smoothly between the EPCH energy controller and ABSM signal controller. Next, the strategy of optimized cooperative control is designed. In this way, robot systems can combine the advantages of the EPCH energy controller and the ABSM signal controller. Finally, simulation results demonstrate that using the strategy of optimized cooperative control gives robot joints outstanding control performance in terms of tracking accuracy and response rapidity. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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26 pages, 9714 KiB

Open AccessArticle

A Kalman-Based Compensation Strategy for Platoons Subject to Data Loss: Numerical and Empirical Study

by Felipe I. Villenas, Francisco J. Vargas and Andrés A. Peters

Mathematics 2023, 11(5), 1228; https://doi.org/10.3390/math11051228 - 2 Mar 2023

Cited by 5 | Viewed by 1421

Abstract

This article considers a homogeneous platoon with vehicles that communicate through channels prone to data loss. The vehicles use a predecessor-following topology, where each vehicle sends relevant data to the next, and data loss is modeled through a Bernoulli process. To address the [...] Read more.

This article considers a homogeneous platoon with vehicles that communicate through channels prone to data loss. The vehicles use a predecessor-following topology, where each vehicle sends relevant data to the next, and data loss is modeled through a Bernoulli process. To address the lossy communication, we propose a strategy to estimate the missing data based on the Kalman filter with intermittent observations combined with a linear extrapolation stage. This strategy enables the followers to better deal with data dropouts. We compare this approach to one purely based on the linear extrapolation of previous data. The performance of both strategies is analyzed through Monte Carlo simulations and experiments in an ad hoc testbed, considering various data loss and transmission loss probabilities depending on the inter-vehicle distance. The results show that for the considered cases, the proposed strategy outperforms the linear extrapolation approach in terms of tracking and estimation error variances. Our results also show that the proposed strategy can achieve string stability for the mean and variance for both the tracking and estimation errors in scenarios where the basic extrapolation strategy cannot. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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23 pages, 5698 KiB

Open AccessArticle

Intelligent Global Fast Terminal Sliding Mode Control of Active Power Filter

by Jiahao Yang, Xiangguo Li and Juntao Fei

Mathematics 2023, 11(4), 919; https://doi.org/10.3390/math11040919 - 11 Feb 2023

Cited by 2 | Viewed by 1274

Abstract

Faced with serious harmonic pollution, a global fast terminal sliding mode control (GFTSMC) based on a novel recurrent fuzzy neural network (NRFNN) strategy for an active power filter (APF) with uncertainty is proposed in this article, which is aimed at improving the power [...] Read more.

Faced with serious harmonic pollution, a global fast terminal sliding mode control (GFTSMC) based on a novel recurrent fuzzy neural network (NRFNN) strategy for an active power filter (APF) with uncertainty is proposed in this article, which is aimed at improving the power quality and realizing harmonic suppression. First, the GFTSMC is adopted due to its advantages in finite-time convergence and faster convergence rate of tracking error in the system. Second, NRFNN is adopted to approximate the unknown model and lump the uncertainty of the APF system. Because the values of base width, center vector and feedback gain of NRFNN can be adjusted adaptively according to adaptive laws, the accurate approximation of the unknown model can be achieved, and the robustness and accuracy of the APF system can be guaranteed. Finally, the validity and feasibility of the proposed GFTSMC-NRFNN scheme is fully verified by simulation results, showing it has better steady-state and dynamic performance than other existing methods. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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21 pages, 39108 KiB

Open AccessArticle

Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation

by Omer Saleem, Faisal Abbas and Jamshed Iqbal

Mathematics 2023, 11(4), 913; https://doi.org/10.3390/math11040913 - 10 Feb 2023

Cited by 25 | Viewed by 2406

Abstract

This article presents a systematic approach to formulate and experimentally validate a novel Complex Fractional Order (CFO) Linear Quadratic Integral Regulator (LQIR) design to enhance the robustness of inverted-pendulum-type robotic mechanisms against bounded exogenous disturbances. The CFO controllers, an enhanced variant of the [...] Read more.

This article presents a systematic approach to formulate and experimentally validate a novel Complex Fractional Order (CFO) Linear Quadratic Integral Regulator (LQIR) design to enhance the robustness of inverted-pendulum-type robotic mechanisms against bounded exogenous disturbances. The CFO controllers, an enhanced variant of the conventional fractional-order controllers, are realised by assigning pre-calibrated complex numbers to the order of the integral and differential operators in the control law. This arrangement significantly improves the structural flexibility of the control law, and hence, subsequently strengthens its robustness against the parametric uncertainties and nonlinear disturbances encountered by the aforementioned under-actuated system. The proposed control procedure uses the ubiquitous LQIR as the baseline controller that is augmented with CFO differential and integral operators. The fractional complex orders in LQIR are calibrated offline by minimising an objective function that aims at attenuating the position-regulation error while economising the control activity. The effectiveness of the CFO-LQIR is benchmarked against its integer and fractional-order counterparts. The ability of each controller to mitigate the disturbances in inverted-pendulum-type robotic systems is rigorously tested by conducting real-time experiments on Quanser single-link rotary pendulum system. The experimental outcomes validate the superior disturbance rejection capability of the CFO-LQIR by yielding rapid transits and strong damping against disturbances while preserving the control input economy and closed-loop stability of the system. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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29 pages, 17571 KiB

Open AccessArticle

Model-Free VRFT-Based Tuning Method for PID Controllers

by Damir Vrančić, Paulo Moura Oliveira, Pavol Bisták and Mikuláš Huba

Mathematics 2023, 11(3), 715; https://doi.org/10.3390/math11030715 - 31 Jan 2023

Cited by 1 | Viewed by 2037

Abstract

The main objective of this work was to develop a tuning method for PID controllers suitable for use in an industrial environment. Therefore, a computationally simple tuning method is presented based on a simple experiment on the process without requiring any input from [...] Read more.

The main objective of this work was to develop a tuning method for PID controllers suitable for use in an industrial environment. Therefore, a computationally simple tuning method is presented based on a simple experiment on the process without requiring any input from the user. Essentially, the method matches the closed-loop response to the response obtained in the steady-state change experiment. The proposed method requires no prior knowledge of the process and, in its basic form, only the measurement of the change in the steady state of the process in the manually or automatically performed experiment is needed, which is not limited to step-like process input signals. The user does not need to provide any prior information about the process or any information about the closed-loop behavior. Although the control loop dynamics is not defined by the user, it is still known in advance because it is implicitly defined by the process open-loop response. Therefore, no exaggerated control signal swings are expected when the reference signal changes, which is an advantage in many industrial plants. The presented method was designed to be computationally undemanding and can be easily implemented on less powerful hardware, such as lower-end PLC controllers. The work has shown that the proposed model-free method is relatively insensitive to process output noise. Another advantage of the proposed tuning method is that it automatically handles the tuning of highly delayed processes, since the method discards the initial process response. The simplicity and efficiency of the tuning method is demonstrated on several process models and on a laboratory thermal system. The method was also compared to a tuning method based on a similar closed-loop criterion. In addition, all necessary Matlab/Octave files for the calculation of the controller parameters are provided online. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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16 pages, 1013 KiB

Open AccessFeature PaperArticle

An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus

by Mihaela Suciu

Mathematics 2023, 11(2), 450; https://doi.org/10.3390/math11020450 - 14 Jan 2023

Cited by 1 | Viewed by 1447

Abstract

This paper presents an original approach for mandible bone calculus by the Transfer Matrix Method (TMM). The role of the mandible bone is very important due to the three functions that it has: mastication, phonation and aesthetics. Due to these functions, there are [...] Read more.

This paper presents an original approach for mandible bone calculus by the Transfer Matrix Method (TMM). The role of the mandible bone is very important due to the three functions that it has: mastication, phonation and aesthetics. Due to these functions, there are many studies in this regard. The mandible bone is an unpaired bone and the only movable bone in the skull. For our studies, we separated a part of the mandible bone assimilated with a spring, and due to the symmetry we can only study a quarter of the circle, embedded at the two ends, charged perpendicular to its plane by a concentrated vertical load corresponding to a tooth which is on the studied side. This mandible side under study has eight teeth: two incisors, one canine, two premolars and three molars. The approach by the TMM is very easy to program, especially for extreme cases, when a quick calculus is needed to optimize the shape of the mandible. In the future we hope to be able to publish the calculation and shape optimization program and a related case study. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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28 pages, 5515 KiB

Open AccessArticle

Modeling and Simulation of High Voltage Power Lines under Transient and Persistent Faults

by Marius Fișcă, Mihail Abrudean, Vlad Mureșan, Iulia Clitan, Mihaela-Ligia Ungureșan, Roxana Motorga and Emilian Ceuca

Mathematics 2023, 11(1), 21; https://doi.org/10.3390/math11010021 - 21 Dec 2022

Cited by 2 | Viewed by 2519

Abstract

The work proposes an original method for modeling and simulating the triggering of 110 kV interconnection power lines in case of common faults, such as transient or persistent faults. Urban and industrial areas, surrounding urban areas, require a high energy consumption that is [...] Read more.

The work proposes an original method for modeling and simulating the triggering of 110 kV interconnection power lines in case of common faults, such as transient or persistent faults. Urban and industrial areas, surrounding urban areas, require a high energy consumption that is being supplied through 110 kV overhead power lines, responsible for distributing power to the industrial and domestic consumers. High voltage distribution power lines are most prone to failure, due to their exposure, affecting a large number of consumers if a fault occurs. Faults of power lines in service certify that currently there is no perfectly controllable operation mode in terms of load rating, environmental factors, insulation resistance, or mechanical resistance, which would allow total avoidance of faults, it is only possible to reduce the impact they have on the network as a whole. Mathematical models have been developed to determine the experimental voltage and current responses describing the fault propagation, expressed as a 7th-degree polynomial curve, as a second-order transfer function or as the Gaussian model type. By comparing these mathematical models, the most probable answers that can lead to the development of a control structure for rapid identification of a fault were obtained, with the possibility of triggering the line protection relay. In the final part of the manuscript, the viability of applying artificial intelligence techniques, for the approached fault management application, is proven. The developed control structure evaluates the nature of the fault and determines a faster reaction of the line protection causing an increase in the performance of the distribution service. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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24 pages, 4247 KiB

Open AccessArticle

Modelling, Simulation and Controlling of a Multi-Pump System with Water Storage Powered by a Fluctuating and Intermittent Power Source

by Dorin Bordeașu, Octavian Proștean, Ioan Filip, Florin Drăgan and Cristian Vașar

Mathematics 2022, 10(21), 4019; https://doi.org/10.3390/math10214019 - 29 Oct 2022

Cited by 9 | Viewed by 2715

Abstract

In recent years, many pumping systems have begun to be powered by renewable energy generators, including mostly photovoltaic generators and, less frequently, electrical wind generators. Because of the technology’s complexity and novelty (it has not yet reached its maturation), most of those systems [...] Read more.

In recent years, many pumping systems have begun to be powered by renewable energy generators, including mostly photovoltaic generators and, less frequently, electrical wind generators. Because of the technology’s complexity and novelty (it has not yet reached its maturation), most of those systems consist of single pumps powered by photovoltaic generators or electrical wind generators. For this reason, the current paper proposes a strategy for driving a multi-pump system with water storage powered by a fluctuating and intermittent power source, such as power grids, which are limited by price variation over different periods during the day, or photovoltaic generators and/or electrical wind generators. The current work begins by proposing a model of a multi-pump system with water storage, followed by the design of a control strategy for operating such a system powered by a fluctuating and intermittent power source in an energy-efficient manner, without sacrificing the reliability, robustness and lifetime of the plant. Finally, an analysis of two concrete situations encountered in practice is made: in one, the considered multi-pump system is powered only by a power grid limited by price variation over three periods; in the other, it is powered by a photovoltaic generator. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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18 pages, 878 KiB

Open AccessArticle

Smooth, Singularity-Free, Finite-Time Tracking Control for Euler–Lagrange Systems

by Nguyen Xuan-Mung and Mehdi Golestani

Mathematics 2022, 10(20), 3850; https://doi.org/10.3390/math10203850 - 17 Oct 2022

Cited by 6 | Viewed by 1470

Abstract

This paper investigates the problem of constrained finite-time tracking control of Euler–Lagrange systems subject to system uncertainties and external disturbances. Firstly, we introduce a nonsingular, fast, constrained terminal sliding manifold (NFCTSM) that contains a time-varying gain to deal with the output tracking error [...] Read more.

This paper investigates the problem of constrained finite-time tracking control of Euler–Lagrange systems subject to system uncertainties and external disturbances. Firstly, we introduce a nonsingular, fast, constrained terminal sliding manifold (NFCTSM) that contains a time-varying gain to deal with the output tracking error constraint. Therefore, the desired performance in steady-state and transience such as ultimate-tracking-error bound, maximum overshoot, and convergence speed are provided. Then, based on the proposed NFCTSM, a smooth adaptive finite-time control is designed such that the tracking errors converge to an arbitrary small region around the origin during a finite period of time. Moreover, the square of the upper bound of the lumped uncertainty is estimated by the adaptive law in order not to use the discontinuous signum function. The efficacy and usefulness of the proposed control methodology are demonstrated via simulation results and comparison with relevant works. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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28 pages, 1569 KiB

Open AccessArticle

A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications

by Obaid Alshammari, Mourad Kchaou, Houssem Jerbi, Sondess Ben Aoun and Víctor Leiva

Mathematics 2022, 10(18), 3309; https://doi.org/10.3390/math10183309 - 12 Sep 2022

Cited by 20 | Viewed by 2028

Abstract

Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time [...] Read more.

Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-economic system and a tunnel diode circuit are presented to show potential applications, as well as validating the effectiveness of the scheme proposed in the present investigation. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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20 pages, 1993 KiB

Open AccessArticle

An Output Feedback Controller for a Second-Order System Subject to Asymmetric Output Constraint Based on Lyapunov Function with Unlimited Domain

by Alejandro Rincón, Fredy E. Hoyos and John E. Candelo-Becerra

Mathematics 2022, 10(11), 1855; https://doi.org/10.3390/math10111855 - 28 May 2022

Viewed by 1724

Abstract

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on [...] Read more.

In this work, a new robust controller is designed for a second-order plant model, considering asymmetric output constraints. The tracking error convergence and output constraint are achieved by using a control law whose output feedback term is user-defined and bounded: it takes on large but finite and user-defined values for tracking error values equal to or higher than the constraint boundary, and it comprises a previously known user-defined function for tracking error values far from the constraint boundary. This is a significant contribution that remedies two important limitations of common output constraint control designs: the infinite control effort for tracking error equal to or higher than the constraint boundary, and the impossibility of using previously known user-defined functions in the output feedback function for tracking error values far from the constraint boundary. As another contribution, the control design is based on the dead-zone Lyapunov function, which facilitates the achievement of convergence to a compact set with user-defined size, avoidance of discontinuous signals in the controller, and robustness to model uncertainty or disturbances. The proposed output feedback term consists of the product between two functions of the tracking error, an increasing function and a sigmoid function, whose exact expressions are user-defined. Finally, the effectiveness of the developed controller is illustrated by the simulation of substrate concentration tracking in a continuous flow stirred bioreactor. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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29 pages, 435 KiB

Open AccessArticle

On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback

by Manuel De la Sen

Mathematics 2022, 10(7), 1066; https://doi.org/10.3390/math10071066 - 25 Mar 2022

Viewed by 1487

Abstract

This paper deals with the closed-loop stabilization of a network which consists of a set of coupled hybrid single-input single-output (SISO) subsystems. Each hybrid subsystem involves a continuous-time subsystem together with a digital (or, eventually, discrete-time) one being subject to eventual mutual couplings [...] Read more.

This paper deals with the closed-loop stabilization of a network which consists of a set of coupled hybrid single-input single-output (SISO) subsystems. Each hybrid subsystem involves a continuous-time subsystem together with a digital (or, eventually, discrete-time) one being subject to eventual mutual couplings of dynamics and also to discrete delayed dynamics. The stabilizing controller is static and based on linear output feedback. The controller synthesis method is of algebraic type and based on the use of a linear algebraic system, whose unknown is a vector equivalent form of the controller gain matrix, which is obtained from a previous algebraic problem version which is based on the ad hoc use of the matrix Kronecker product of matrices. As a first step of the stabilization, an extended discrete-time system is built by discretizing the continuous parts of the hybrid system and to unify them together with its digital/discrete-time ones. The stabilization study via static linear output feedback contains several parts as follows: (a) stabilizing controller existence and controller synthesis for a predefined targeted closed-loop dynamics, (b) stabilizing controller existence and its synthesis under necessary and sufficient conditions based on the statement of an ad hoc algebraic matrix equation for this problem, (c) achievement of the stabilization objective under either partial or total decentralized control so that the whole controller has only a partial or null information about couplings between the various subsystems and (d) achievement of the objective under small coupling dynamics between subsystems. Full article

(This article belongs to the Special Issue Control Theory and Applications)

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