State Variables Of System Research Articles

A long-term power system state calculation method using sequential power and holomorphic embedding

Traditional Power Flow (PF) calculations struggle to support the data analysis requirements as the power system develops. Therefore, this paper introduces a non-sequential and non-iterative PF calculation method to enhance the computational speed and analytical efficiency of power system state variables over long time scales. Firstly, a Power Sequential Division (PSD) method is proposed, representing the power curve using hierarchical energy with temporal characteristics. Next, based on the Fast and Flexible Holomorphic Embedding (FFHE) method, the paper explores the incremental properties of Voltage Power Series Coefficients (VPSC) and proposes an Incremental Holomorphic Embedding (IHE) method. Finally, by combining PSD and IHE, this study introduces a Power Sequential Flow (PSPF) method for rapid computation of power system state variables over long time scales. Unlike traditional PF methods, PSPF method shifts away from time-series calculations and instead analyzes the distribution of power system state variables over long time scales from an energy perspective. Various test cases are set up to analyze the performance characteristics of IHE and PSPF from multiple perspectives. The results indicate that the proposed methods significantly outperform traditional PF methods in terms of computational speed, adaptability to test cases, and analytical efficiency.

Speed‐sensorless control for SPMSM via novel exponential super‐twisting ADRC

AbstractAlthough the conventional super‐twisting reaching law (CSTRL) maintains the desired tracking performance for disturbed systems, its implementation is challenging due to its dependence on accurate system dynamics. To mitigate this dependence and reduce chattering of CSTRL, a novel exponential super‐twisting reaching law (NESTRL) is proposed, leveraging the dynamic adaptability of the exponential reaching law and eliminating chattering. By using NESTRL, the proposed controller can achieve a fast response without chattering. Additionally, a comprehensive procedure for finite convergence time analysis is provided. The convergence conditions of the system's state variables are determined using a Lyapunov function, and the stability of system is proven using an algebraic Lyapunov function. Finally, simulations and experimental results demonstrate that the proposed approach is valid and effective, showing improvements compared to the traditional super‐twisting active disturbance rejection control and linear active disturbance rejection control in sensorless control.

Tracking performance and power quality enhancement of DFIG based wind turbine using robust integral terminal sliding mode control

The aim of this work is to develop a robust Integral Terminal Sliding Mode Control (ITSMC) strategy for a Doubly Fed Induction Generator (DFIG) wind turbine (WT) operating in challenging conditions. This controller is designed to manage the system's rotor side converter (RSC) and grid side converter (GSC), ensuring maximum power production, improved power quality, and accurate tracking of system state variables, even in the face of fluctuating wind conditions, parameter uncertainties, and external disturbances. The stability of the proposed controller is assured using the Lyapunov theory. The performance of ITSMC is compared with that of the conventional sliding mode controller (SMC) and backstepping controller through simulation tests, using the integral absolute error (IAE) as a performance metric. The results highlight the superiority of ITSMC, demonstrating its ability to precisely track reference values, eliminate static errors, and minimize chattering. ITSMC consistently achieves the lowest IAE for all tracked state variables and across all test scenarios. A comparative study analyzing the Total Harmonic Distortion (THD) of the proposed controller versus SMC, the backstepping controller, and other similar works in the literature shows a marked improvement in the THD of stator and filter currents by at least 24.53 % and 7.96 %, respectively. These findings underscore the controller's capability to enhance the power quality delivered to the grid.

Discrete adaptive sliding mode controller design for overhead cranes considering measurement noise and external disturbances

AbstractResearch on the motion control of overhead cranes, constrained by underactuated characteristics, helps improve the efficiency of payload transportation. Most studies require all system state variables (trolley displacement, payload swing angle, and their velocities). In practice, sensors measure and transmit these variables, but noise affects their accuracy, reducing control performance. Additionally, uncertainties in crane parameters, unmodeled friction, and unknown disturbances threaten the system's stability. Traditional methods struggle to address these issues effectively. To address these challenges, this article proposes an adaptive discrete sliding mode control (DSMC) method with a Kalman filter. By extending the state system and considering disturbances as new variables, the Kalman filter effectively eliminates signal noise, accurately estimates disturbances, and estimates system states simultaneously. The proposed method incorporates disturbance compensators into the adaptive DSMC, utilizing exponential terms to suppress oscillations caused by excessively high or low control gains, thus increasing control speed. Experimental comparisons demonstrate the superiority and robustness of the proposed control method under various disturbance conditions.

Finite-Time Neural Network-Based Hierarchical Sliding Mode Antiswing Control for Underactuated Dual Ship-Mounted Cranes With Unmatched Sea Wave Disturbances Suppression.

As typical mechanical transportation equipment, cooperative dual ship-mounted cranes are widely used to transport large goods or containers in the marine environment. However, the control problem of the dual ship-mounted crane system is much more complex due to its underactuated characteristic and persistent unmatched disturbances. To solve these problems, we propose a novel neural network (NN)-based hierarchical sliding mode adaptive (HSMA) control method in this article. More specifically, an appropriate hierarchical sliding mode surface is first designed to connect the actuated and underactuated system state variables effectively. At the same time, the NNs are constructed to compensate for the unmatched interference of ship motions induced by sea waves simultaneously. Not only can the booms and the rope lengths reach their desired positions in finite time, but also the synchronous swing angles of the payload can be effectively eliminated. The asymptotic convergence of the closed-loop system's equilibrium points is achieved through rigorous mathematical proofs. Furthermore, the stability of each sliding mode surface is also analyzed utilizing the Lyapunov technique and Barbalat's lemma. Finally, numerous groups of compared numerical simulation results are investigated to further show the effectiveness and strong robustness of the proposed NN-based HSMA controller.

Nonstandard finite difference schemes for some epidemic optimal control problems

We construct and analyse nonstandard finite difference (NSFD) schemes for two epidemic optimal control problems. Firstly, we consider the well-known MSEIR system that can be used to model childhood diseases such as the measles, with the vaccination as a control intervention. The second optimal control problem is related to the 2014–2016 West Africa Ebola Virus Disease (EVD) outbreak, that came with the unprecedented challenge of the disease spreading simultaneously in three different countries, namely Guinea, Liberia and Sierra Leone, where it was difficult to control the considerable migrations and travels of people inbound and outbound. We develop an extended SEIRD metapopulation model modified by the addition of compartments of quarantined and isolated individuals. The control parameters are the exit screening of travelers and the vaccination of the susceptible individuals. For the two optimal control problems, we provide the results on: (i) the (global) stability of the disease-free and/or endemic equilibria of the state variable systems; (ii) the positivity and boundedness of solutions of the state variables systems; (iii) the existence, uniqueness and characterization of the optimal control solutions that minimizes the cost functional. On the other hand: (iv) we design Euler-based nonstandard finite difference versions of the Forward-Backward Sweep Method (NSFD-FBSM) that are dynamically consistent with the state variable systems; (v) we provide numerical simulations that support the theory and show the superiority of the nonstandard approach over the classical FBSM. The numerical simulations suggest that significantly increasing the coverage of the vaccine with its implementation for adults as well is essential if the recurrence of measles outbreaks is to be stopped in South Africa. They also show that the optimal control vaccination for the 2014-2016 EVD is more efficient than the exit screening intervention.

Free-will arbitrary time adaptive chaos control for permanent magnet synchronous motor

Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system, which is prone to chaotic behavior during actual operation. In order to suppress the chaotic behavior of the PMSM, this work designs a free-will arbitrary time adaptive controller based on the inverse step derivation, adaptive control theorem and Lyapunov stability theory. Firstly, the corresponding coordination transformations are designed according to the PMSM. Secondly, the bounded problem of the controlled system is analyzed by using the Lyapunov stability theory, and the free-will arbitrary time adaptive controller is designed by backstepping derivation. Finally, numerical simulation verifies that the designed controller quickly stabilizes the system state variables to the output signals and proves that the controller is free-will arbitrary time stable for all closed-loop signals.

Chaos synchronization of two coupled map lattice systems using safe reinforcement learning

When synchronizing two continuous typical chaotic systems, the state variables of the response system are usually bounded and satisfy the Lipschitz condition. This permits a universal synchronization method. In the synchronization of two high-dimensional discrete chaotic systems such as the coupled map lattice systems, the state variables of the response system often diverge, which makes it difficult to seek a universal synchronization method. To overcome this difficulty, bounded and hard constraints, which correspond to the concept of safety level III in reinforcement learning terms, on the state variables must be imposed, when the discrete response system is perturbed. We propose a universal method for synchronizing two discrete systems based on safe reinforcement learning (RL). In this method, the RL agent’s policy is used to reach the goal of synchronization and a safety layer added directly on top of the policy is used to satisfy safety level III. The safety layer consists of a one-step predictor for the perturbed response system and an action correction formulation. The one-step predictor, based on a next generation reservoir computing, is used to identify whether the next state of the perturbed system is within the chaotic domain, and if not, the action correction formula is activated to modify the corresponding perturbing force component to zero. In this way, the state of the perturbed system will remain in the bounded chaotic domain. We demonstrate that the proposed method succeeds in synchronization without divergence through a numerical example with two coupled map lattice systems, and the average synchronization time is 12.66 iteration steps over 1000 different initial conditions. The method works even when parameter mismatches and disturbances exist in the system. We compare the performance in both cases with and without the safety layer and find that successful synchronization is only possible in the former case, emphasizing the significance of the safety layer. The performance of the algorithm with optimal hyper-parameters obtained by Bayesian optimization is robust and stable.

Understanding Childhood Victimization Experiences and Mental Health Outcomes in a Sample of Prison Inmates in Northern Chile

In this paper, the weak points have been investigated, the proposal to solve them, the application of the solution and the comparison of the results in the mode of simulation and experimental testing have been discussed. For this purpose, a four-wheel mobile robot has been considered for simulation and implementation, and a linear quadratic regulator controller and a nonlinear model predictive controller have been used to control it. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Also, in order to reduce the existing time delays, especially in the implementation of the nonlinear controller on the robot in the experimental mode, by training other neural networks to optimally extract the benefit of the forecast horizon, reducing the calculations and increasing the speed of the solution has been achieved. In the hardware part, by examining and using operators such as the pixy camera and the U2D2 interface, which are faster than the usual method, the solution time has been reduced.

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Robust topology and discrete fiber orientation optimization under principal material uncertainty

This paper introduces a formulation of the robust topology optimization problem that is tailored for designing fiber-reinforced composite structures with spatially varying principal mechanical properties. Specifically, a methodology is developed that incorporates the spatial variability in the engineering constants of the composite lamina into the concurrent topology (i.e., material distribution) and morphology (i.e., fiber orientation distribution) optimization problem for the minimization of the robust compliance function. The spatial variability in the mechanical properties of the lamina is modeled as a homogeneous random field within the design domain by means of the Karhunen-Loe´ve series expansion, and is thereafter intrusively propagated into the stochastic finite element analysis of the composite structure. To carry out the stochastic finite element analysis per iteration of the optimization cycle, the first-order perturbation method is utilized for approximating the current state variables of the physical system. The resulting robust topology and fiber orientation optimization problem is formulated step-by-step for the minimization of the robust compliance function. With the view of solving the optimization problem at hand by means of gradient-based solution algorithms, the first-order derivatives of the involved design functions w.r.t. the associated design variables are analytically derived. The present work concludes with a series of numerical examples, focusing on the benchmark academic case studies of the 2D cantilever and the half part of the Messerschmitt-Bölkow-Blohm beam, aiming to demonstrate the developed methodology as well as to explore the effect that different parameterization instances of the random field bear on the predicted topology and morphology of the beams.

Adaptive sliding mode and RBF neural network based fault tolerant attitude control for spacecraft with unknown uncertainties and disturbances

Taking the external disturbance, model uncertainty, actuator failure, and actuator saturation into consideration, this paper investigates the nonlinear fault-tolerant attitude control problem for the spacecraft. First, to deal with the disturbance and uncertainty with unknown boundaries, an adaptive sliding mode control method is proposed to stabilize the state variables of the spacecraft attitude control system. Then the actuator failure and saturation are further considered, and the second spacecraft fault-tolerant attitude controller is derived based on adaptive sliding mode control and radial basis function (RBF) neural networks. The adaptive control gains reduction technique is applied in the design process, which can weaken the chattering phenomenon of the controller to some extent, and the stability of the attitude control system is analyzed through Lyapunov theory. In the proposed controller, model information and external disturbance are not required and only the system states are needed. Furthermore, the boundaries of the model uncertainty, external disturbance, actuator fault and saturation are assumed to be existing but unknown by the proposed controllers. These features make the proposed attitude controllers need few modeling information of the spacecraft, or maintain strong robustness even if the model or external environment occurs significant changes. Finally, numerical simulations demonstrate the great performance of the proposed fault-tolerant attitude control method.

Low conservative stability criteria for discrete-time Lur’e systems with sector and slope constrained nonlinearities

Lur’e system is an important nonlinear system in engineering, which is composed of a feedback connection of a linear dynamic system and a nonlinear system that satisfies the sector constraint. In this paper, for nominal and uncertain discrete Lur’e systems with time-varying delays, the absolute and robustly absolute stability are studied in detail with the nonlinearity satisfying the sector and slope constraints. Firstly, an augmented Lyapunov–Krasovskii functional (LKF) is designed, in which some augmented vectors are selected to increase the coupling information between the delay intervals and other system state variables. At the same time, some effective integral terms of nonlinear state variables are extended in the LKF according to the characteristics of sector constraint and slope constraint. Secondly, a general lemma of summation inequality for free-weighted matrices is given, which adds some coupling information between vectors and extends the search range for solving linear matrix inequalities (LMIs). Thirdly, by synthesizing the general summation inequality and the newly constructed LKF, different absolute stability criteria are derived respectively, and the absolute stability criteria are extended to robustly absolute stability cases with uncertain parameters. The stability criteria reduce the conservatism of some previously proposed results. Finally, some common numerical examples and simulations are used to verify the results of this paper.

Learning model predictive controller for wheeled mobile robot with less time delay

The weak spots have been examined, a solution has been suggested, the solution has been applied, and a comparison between the simulation and experimental test results has been given in this work. In order to do this, a nonlinear model predictive controller and a linear quadratic regulator controller have been utilized to control a four-wheel mobile robot during modeling and implementation. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Additionally, by training additional neural networks to optimally extract the benefit of the forecast horizon, fewer calculations and faster solution times have been achieved, helping to reduce the current time delays, particularly in the implementation of the nonlinear controller on the robot in the experimental mode. In the hardware section, the solution time has been shortened by looking at and utilizing operators like the U2D2 interface and the pixy camera, which are quicker than the standard procedure. The information indicates that the proposed intelligence technology reacts 40%–50% quicker than the NMPC standard procedure. The suggested algorithm has also minimized the path tracking error since it extracts the optimal gain at each stage. Moreover, a hardware mode solving speed comparison between the recommended and conventional methods is given. In this domain, a 33% increase in solving speed has been noted.

A novel observer-based neural-network finite-time output control for high-order uncertain nonlinear systems

Due to the difficulty encountered in dealing with unstructured system dynamics with unmeasured system state variables, this paper presents a novel observer-based neural network finite-time output control strategy for general high-order nonlinear systems (HNSs). The suggested technique is performed based on the backstepping-like control (BSC) scheme with a hybrid nonlinear disturbance-state observer and norm estimation-based radial basis function neural network (RBFNN). This helps not only reduce the number of estimated parameters but also relax the restriction of using inequality when exploiting the norm estimation concept in a conventional way; thus, retaining the same properties of the original system. Therefore, an observer-based finite-time output feedback control is established to deal with the unstructured dynamical behaviors and satisfying the output tracking regulation with the semi-global practically finite-time stability (SGPFS) guaranteed for the closed-loop system. The effectiveness and workability of the proposed algorithm is verified by a numerical simulation on a specific practical application.

Distributed moving horizon fusion estimation for linear constrained uncertain systems

AbstractIn this paper, the distributed moving horizon fusion estimation of uncertain systems with constraints of system noise and state variables is studied. Firstly, relying on the basic idea of consensus algorithm, the cost function in the performance index is reconstructed by weighted fusion of the state prediction values. Secondly, considering the performance index with uncertain parameters, the min‐max optimization problem of the algorithm is transformed into the least squares optimization problem based on 2‐norm regularization method. Thirdly, the scalar‐weighted linear minimum variance fusion estimation strategy is used to realize the weighted fusion of local state estimation values. Then, on the premise of minimum network connectivity and collective observability, the stability of the proposed algorithm is studied, and the sufficient conditions for the expected convergence of the fused estimation error norm square are given. Finally, the effectiveness of the algorithm is verified by numerical simulation.

Current Controller Design of Grid-Connected Inverter with Incomplete Observation Considering L-/LC-Type Grid Impedance

This paper presents a current control design for stabilizing an inductive-capacitive-inductive (LCL)-filtered grid-connected inverter (GCI) system under uncertain grid impedance and distorted grid environment. To deal with the negative impact of grid impedance, LC-type grid impedance is considered in both the system model derivation and controller design process of an LCL-filtered GCI system. In addition, the integral and resonant control terms are also augmented into the system model in the synchronous reference frame to guarantee the reference tracking of zero steady-state error and good harmonic disturbance compensation of the grid-injected currents from GCI. By considering the effect of grid impedance on the control design process, an incomplete state feedback controller will be designed based on the linear-quadratic regulator (LQR) without damaging the asymptotic stabilization and robustness of the GCI system under uncertain grid impedance. By means of the closed-loop pole map evaluation, the asymptotic stability, robustness, and resonance-damping capability of the proposed current control scheme are confirmed even when all the system states are not available. In order to reduce the number of required sensors for the realization of the controller, a discrete-time current-type full-state observer is employed in this paper to estimate the system state variables with high precision. The feasibility and effectiveness of the proposed control scheme are demonstrated by the PSIM simulations and experiments by using a three-phase GCI prototype system under adverse grid conditions. The comprehensive evaluation results show that the designed control scheme maintains the stability and robustness of the LCL-filtered GCI when connecting to unexpected grids, such as harmonic distortion and L-type and LC-type grid impedances. As a result, the proposed control scheme successfully stabilizes the entire GCI system with high-quality grid-injected currents even when the GCI faces severe grid distortions and an extra grid dynamic caused by the L-type or LC-type grid impedance. Furthermore, low-order distortion harmonics come from the background grid voltages and are maintained as acceptable limits according to the IEEE Std. 1547-2003. Comparative test result with the conventional one also confirms the effectiveness of the proposed control scheme under LC-type grid impedance thanks to the consideration of LC grid impedance in the design process.

Estimator-based neural adaptive event-triggered control for strict-feedback nonlinear systems with incomplete measurements

This article addresses a neural adaptive event-triggered tracking control for a class of strict-feedback nonlinear dynamics with incomplete measurements, which is novel on the research of Cyber-physical Systems. The incomplete measurement problem caused by packet loss, saturation, and other issues during data transmission can lead to the unavailability of system state variables, which can degrade system performance and even lead to instability. To solve these problems, a state estimator for data-losing case and two controllers for normal and data-losing cases are designed utilising event-triggered strategies which can reduce the burden of calculation and data transmission. Radial basis function neural networks are adopted to approximate the unknown nonlinear system functions. A strict stability analysis in probability shows that the control laws for the considered strict-feedback nonlinear system can guarantee all the closed-loop to be uniformly ultimately bounded in mean square. Two examples are performed to demonstrate the effectiveness of the provided control method.

Ambient data-driven participation factors related to oscillation modes based on subspace dynamic mode decomposition

Analyzing the connection between the variables participating in the oscillation and modes in electromechanical oscillation is particularly important for maintaining system stability. This paper proposes an ambient data-driven method based on Subspace Dynamic Mode Decomposition (Sub-DMD) to extract the Participation Factors (PFs) related to system state and algebraic variables in electromechanical oscillation modes. This method uses ambient data to calculate the low-dimensional approximate matrix of the system, and the PFs is extracted by using eigen-decomposition and mode energy. Compare the extracted PFs with the results of power generation dispatch. The effectiveness of the proposed method is demonstrated by using simulation data from IEEE 4-generator 2-area test system and IEEE 16-generator 68-bus test system.

The Adaptive Optimal Output Feedback Tracking Control of Unknown Discrete-Time Linear Systems Using a Multistep Q-Learning Approach

This paper investigates the output feedback (OPFB) tracking control problem for discrete-time linear (DTL) systems with unknown dynamics. To solve this problem, we use an augmented system approach, which first transforms the tracking control problem into a regulation problem with a discounted performance function. The solution to this problem is derived using a Bellman equation, based on the Q-function. In order to overcome the challenges of unmeasurable system state variables, we employ a multistep Q-learning algorithm that surpasses the advantages of the policy iteration (PI) and value iteration (VI) techniques and state reconstruction methods for output feedback control. As such, the requirement for an initial stabilizing control policy for the PI method is removed and the convergence speed of the learning algorithm is improved. Finally, we demonstrate the effectiveness of the proposed scheme using a simulation example.