Saturation Function Research Articles

Minimum loss optimization of flywheel energy storage systems via distributed adaptive dynamic programming

AbstractIn this article, a distributed controller based on adaptive dynamic programming is proposed to solve the minimum loss problem of flywheel energy storage systems (FESS). We first formulate a performance function aiming to reduce total losses of FESS in power distribution applications. Then we use the Hamilton–Jacobi–Bellman (HJB) equation to solve this optimal control problem. The solution of the HJB equation is approximated by neural networks. To achieve distributed control, we estimate the global variables in the HJB equation by using the dynamic average consensus algorithm. A barrier Lyapunov function and a saturation function are introduced to handle the issue of state and input constraints, respectively. Then the stability of the system is proved through the Lyapunov stability analysis. Finally the effectiveness of the proposed strategy is verified by simulations. Simulation results show that FESS can track the power command while minimizing total power losses by interacting with neighbors. The proposed algorithm leads to a loss reduction of compared to the equal power distribution strategy.

Robust output regulation of a class of uncertain nonlinear minimum phase systems perturbed by unknown external disturbances

This paper addresses the problem of robust output regulation for uncertain nonlinear minimum phase systems affected by an unknown external disturbance. We present a novel unknown input observer (UIO)-embedded high-gain stabilizer to completely reconstruct the disturbance in a finite time. A new saturation function is introduced to prevent finite time escape of the closed-loop trajectories. This allows us to achieve a semi-globally exponential regulation of the regulated output. The proposed method features the exact cancellation rather than approximate cancellation, for both structured and/or unstructured external disturbance. The presented controller is finite-dimensional and does not require the nominal model of the plant. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Optimal treatment and stochastic stability on a fractional-order epidemic model incorporating media awareness

Infectious diseases have become a severe concern in our society in recent times. In this respect, conducting a qualitative investigation of infectious disease systems is very crucial. Nowadays, developing a mathematical model and its analysis for disease control has been very popular. Our present study has formulated a SIR-type epidemic model by considering a saturated incidence function with media impact. To account for the influence of memory, we have modified the model by employing a system of fractional-order differential equations of Caputo’s notion. We have determined all the system equilibrium points and discussed their stability criteria based on the basic reproduction number (R0) as the threshold parameter. It is observed that for the threshold R0<1, disease-free equilibrium becomes both locally and globally asymptotically stable. A transcritical bifurcation occurs at the threshold R0=1. Further, as the threshold R0 exceeds unity, the endemic equilibrium becomes asymptotically stable. A fractional-order optimal control problem with treatment as the control parameter is developed to reduce the impact of disease. Using Pontryagin’s Maximum Principle yields a theoretical and numerical solution to the fractional order optimal control problem. It is observed that both the media and memory effect dramatically reduces infection rates. Considering environmental variations, the stochastic stability of the endemic equilibrium point has also been studied. Sensitivity analysis is carried out to comprehend how the parameters impact the threshold value (R0). Finally, extensive numerical simulations are performed to demonstrate our theoretical examination.

Design of ABS sliding mode control system for in-wheel motor vehicle based on road identification

Aiming at the problem that the current Anti-lock Braking System (ABS) control algorithm can not make full use of the ground friction to complete the braking when emergency braking on complex roads, an ABS sliding mode control method based on road surface identification is proposed. Combined with the in-wheel motor of in-wheel motor electric vehicle, a coordinated control method of motor regenerative braking and mechanical friction braking is designed. Based on the neural network control method, the road friction coefficient is estimated to realize the identification of typical roads and dynamically obtain the optimal slip ratio of different roads. The ABS sliding mode controler is designed with the optimal slip ratio and the actual slip ratio as input, and the saturation function is used to replace the symbol function in the traditional sliding mode control to weaken the chattering problem, and then the ABS controller is designed. The research results show that compared with the traditional ABS sliding mode controller, the designed ABS neural network sliding mode controller has the following advantages: 1. Through the identification of tire-road friction coefficient by neural network, the real-time performance and road adaptability of ABS controller are improved; 2. When the braking simulation is carried out at a given speed, the braking time is reduced by about 1.03 % and the braking distance is shortened by about 1.01%; 3. The identification of tire-road friction coefficient is realized, which weakens the chattering problem of traditional sliding mode control and improves the stability and robustness of ABS controller.

Modified Nested Saturated Control for Uncertain Multiple Integrators With High-Order Nonlinear Perturbation.

This article studies the global asymptotic stability problem of multiple integrators subject to uncertain parameters and high-order nonlinear perturbation. By introducing a modified saturation function with positive tunable parameters, three types of modified nested saturated controllers with different parameter assignments are proposed to handle the uncertain integrators with high-order nonlinear perturbation. The specific mechanism of the modified nested saturated controllers with different parameter assignments, in which control parameters appear before states, saturation functions, or saturation levels, is comprehensively analyzed. With the help of a modified saturation function, the global convergence domain of each state can be kept invariable in the saturation reduction analysis. Meanwhile, a large saturation level is obtained by adjusting positive tunable parameters. Combining with derivatives calculation and M -matrix-based comparison theory, proposed saturated control schemes are utilized to handle the considered system. Finally, an active magnetic bearing (AMB) system is revisited as an uncertain mechanical system and used to verify the feasibility of the proposed control designs.

Adaptive control of robotic manipulator with input deadzone and disturbances/uncertainties

This work address the problem of trajectory tracking for robotic manipulator while encountering external disturbances and internal uncertainties. Robotic manipulators have been widely used in various industrial and research applications due to their versatility and efficiency. The precise control of these manipulators is essential for their proper functioning. However, due to the presence of uncertainties and disturbances in the system, it is often challenging to achieve accurate control. The proposed controller is capable of handling the uncertainties and disturbances present in the system, making it robust and efficient for practical applications. The controller is designed based on the concept of second-order nonsingular terminal sliding mode control (SNTSMC), which ensures that the system tracks the desired trajectory accurately. The substitution of the sign function with the saturation function effectively reduces the chattering that is caused by the high-frequency switching element in the conventional SMC approach. By utilizing an adaptive technique, uncertainties can be effectively mitigated without relying on any prior knowledge of an upper limit. Moreover, the Lyapunov stability criterion is used to prove the stability of the closed-loop system. The simulation results show the effectiveness of the proposed algorithm in terms of tracking accuracy and robustness.

Adaptive integral sliding-mode finite-time control with integrated extended state observer for uncertain nonlinear systems

For the typical uncertain nonlinear systems subjected to controller gain variation and disturbances, an integrated adaptive robust controller, called integral sliding-mode finite-time controller with an integrated extended state observer (ISFC-IESO), is proposed. The designed controller mainly consists of an integrated ESO (IESO) unit and an integral sliding-mode control (ISMC) unit. The IESO unit is composed of improved linear and nonlinear ESOs which are designed to automatically switch each other, with the aim of enhancing disturbance estimation capability. Moreover, the ISMC unit produces an integral sliding-mode control law (SMCL) based on the newly designed integral sliding-mode surface function (SMSF) and sliding-mode reaching law (SMRL). The integral SMSF is developed based on the n-th estimated state and a designed convergence function of tracking error to suppress the influence of the disturbance estimation error. On this basis, SMRL is further presented by combining integral SMSF with a specially designed variable boundary layer thickness saturation function, for the purpose of eliminating chattering and enhancing robustness. Finally, fourteen control methods are compared to illustrate the effectiveness and superiority of the proposed ISFC-IESO.

Relating permeability and electrical conductivity in partially saturated porous media by means of the Johnson–Koplik–Schwartz characteristic length

SUMMARY In this work, we revisit the seminal concept of Johnson–Koplik–Schwartz (JKS) length Λ, that is a characteristic length representing an effective pore size which controls various transport-related properties of porous media, such as, the permeability and the electrical conductivity. We present a novel closed-form equation that predicts the behaviour of Λ in partially saturated media, for different saturation states. Using previous models in the literature that predict the intrinsic and relative electrical conductivities under partially saturated conditions, we infer the JKS length Λ and the electrical formation factor F as functions of water saturation and properties associated with the pore-size distribution of the probed porous medium. The proposed method permits to estimate the effective permeability and the relative permeability directly from electrical conductivity measurements, thus opening new-avenues for the remote characterization of partially saturated media. We believe that this new model will prove useful for various characterization and modelling applications from reservoir (CO2 or hydrogen storage) to vadose zone studies.

Distribution of gas hydrate in fractured reservoirs: implications from anisotropic elastic and electrical numerical simulations

SUMMARY Fractured hydrate-bearing reservoirs are extensively discovered worldwide and show notable anisotropic geophysical properties. Hydrate distribution in fractures significantly affects the anisotropic properties, and hence plays an important role in the accurate assessment of hydrate resources. However, the knowledge about how the hydrate distribution impacts the anisotropic geophysical properties of fractured reservoirs, which is the premise for the identification and quantification of hydrate in fractured reservoirs, is still poorly understood. To obtain such knowledge, we forward study the effects of various hydrate distribution (including floating, bridging and evolving hydrate distribution) in aligned fractures on the anisotropic elastic, electrical and joint elastic–electrical properties of a digital core using validated numerical methods. We show that for all the hydrate distribution, the anisotropic velocities increase, while the conductivities decrease with increasing hydrate saturation, with the effects of the floating and bridging distribution being the least and greatest, respectively. We also show that the anisotropic velocities and conductivities for the floating and bridging distribution vary approximately linearly with hydrate saturation, leading to linear correlations between the elastic and electrical properties. Further investigation illustrates that the difference in the slopes of the linear joint correlations between the two distribution is significantly greater than that of the individual properties as a function of hydrate saturation. The results have revealed the distinct effects of hydrate distribution on the anisotropic elastic and electrical properties of fractured reservoirs, and have confirmed the superiority of the joint elastic–electrical properties for the distinguishment of hydrate distribution in fractures over individual physical properties.

Stabilization and Energy Consumption Estimation of Discontinuous Fuzzy Inertial CGNNs via Saturation Function Approach

Stabilization and Energy Consumption Estimation of Discontinuous Fuzzy Inertial CGNNs via Saturation Function Approach

Probabilistic Forecast of Multiphase Transport Under Viscous and Buoyancy Forces in Heterogeneous Porous Media

AbstractWe develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length.

The Effects of Health Care Providers Night Shift on Cerebral Oxygen Saturation and its Relationship to Cognitive Function

Background: In-training physicians frequently experience acute periods of sleep deprivation due to the extended durations of on-call shifts. To safeguard the well-being of residents, ensure patient safety, and optimize their performance, it becomes imperative to thoroughly assess and evaluate the cerebral function of in-training physicians subsequent to their shifts. Objective: To elucidate the effects of the nightshifts on regional cerebral oxygen saturation (rScO₂) and cognitive function of 50 in-training pediatricians. Materials and Methods: The rScO₂ was monitored using Near-infrared spectroscopy at specific intervals, pre-on-call (H0), post-call (H16), 24-hours from pre-on-call (H24), and 48-hours from pre-on-call (H48). All physicians continued their duties without a post-call day. The mathematical tests were performed at H0, H16, H24, and H48, while the Montreal cognitive assessment (MoCA) test was conducted at H0 and H24. Results: The mean rScO₂ at post-call at 65.8±5.3% and 24-hours from pre-on-call at 64.6±6.4%, were significantly declined from pre-on-call at 68.2±5.6% (p&lt;0.001), and then returned to baseline at 48-hours from pre-on-call at 68.9±5.5%. The mathematical test scores were not different. The mean MoCA score was significantly decreased at 24-hours from pre-on-call at H0 with 28.4±1.4 to H24 with 27.7±1.8 (p&lt;0.001). Conclusion: The 16-hours nightshifts and continuous working among residents might cause a transient reduction of rScO₂, which could lead to decreased cognitive function scores. Understanding the effects of stress, fatigue, and sleep deprivation on the cognitive performance of medical residents not only benefits each individual resident, but also promotes a culture of continuous improvement and excellence in medical education. Keywords: Cerebral oxygen saturation; In-training physicians; Sleep deprivation; Work-hours; Cognitive function

Trajectory-Tracking Control for Quadrotors Using an Adaptive Integral Terminal Sliding Mode under External Disturbances

In the face of external disturbances affecting the trajectory tracking of quadrotors, a control scheme targeted at accurate position and attitude trajectory tracking was designed. Initially, a quadrotor dynamic model, essential for control design, was derived. Adaptive integral backstepping control (AIBS) was then employed within the position loop, enabling the upper boundaries of disturbances to be estimated through adaptive estimation. Subsequently, a new adaptive backstepping fast nonsingular integral terminal sliding mode control (ABFNITSM) was proposed to enable adherence to the desired Euler angles. Rapid convergence and accurate tracking were facilitated by the incorporation of the nonsingular terminal sliding mode and an integral component. The dead zone technique was deployed to curtail estimation errors, while a saturation function was used to eradicate the phenomenon of chattering. Finally, to validate the proposed control scheme, simulation experiments were conducted in the Simulink environment, and the results were contrasted with those obtained from traditional integral terminal sliding mode control (ITSM) and integral backstepping control (IBS), providing evidence of the effectiveness of the proposed method.

Three‐dimensional path following control of underactuated autonomous underwater vehicles with nonzero roll dynamics: A novel line‐of‐sight‐guided approach

AbstractMost existing path following control approaches for underactuated Autonomous underwater vehicles (AUVs) assumed that the roll angle can be passively stabilized at zero, and simplified the problem to the 5‐degree‐of‐freedom model. However, in practice, the roll motion suffers from undesirable oscillations induced by environmental disturbances, unbalanced propeller torque, etc. To preserve the stability of the system under nonzero roll dynamics, this paper proposes a novel line‐of‐sight‐ (LOS) guided path following control approach. Firstly, the spatial path following error dynamics model is derived to comprehensively reveal the negative effect of roll dynamics. Secondly, an improved LOS guidance law is designed to compensate for the nonzero roll angle. A salient feature is that the proposed guidance law can be applied to the underwater vehicle no matter it is underactuated in the roll motion or not. Thirdly, by assigning the guidance angles to the desired attitude angles, a robust attitude tracking controller is developed, in which the adaptive estimation technique is employed to handle the lumped uncertainties. The tanh‐based saturation function is incorporated such that the resultant control signals are inherently bounded. The closed‐loop path following and attitude tracking errors are proved to be globally asymptotically stable at the origin. Comparative simulation results are provided to substantiate the effectiveness and superiority of the proposed method.

Trajectory Planning for Spacecraft Formation Reconfiguration Using Saturation Function and Difference-of-Convex Decomposition

Trajectory Planning for Spacecraft Formation Reconfiguration Using Saturation Function and Difference-of-Convex Decomposition

Leader-Following Consensus of Discrete-Time Nonlinear Multi-Agent Systems with Asymmetric Saturation Impulsive Control

Impulsive control is an effective approach for coordinating multi-agent systems in practical environments due to its high robustness and low cost. However, impulsive control exhibits characteristics such as high amplitude and rapid variation, potentially presenting threats to the equipment. Additionally, multi-agent systems are constrained by input saturation due to limitations in physical controller structures and information-processing capabilities. These saturation constraints may be asymmetrical. Therefore, it is necessary to consider the saturation constraint when implementing impulsive control, as it can also mitigate the threats posed by the impulse to agents. This paper investigates the leader-following consensus for a class of discrete-time nonlinear multi-agent systems, proposing an asymmetric saturation impulsive control protocol to reduce the energy consumption and damage to the equipment. Regarding the handle of asymmetric saturation, an approach is proposed that eliminates the need for transformation from the asymmetric case to the symmetric case, which retains the saturation function and directly introduces the sector condition to deal with saturation nonlinearity. Furthermore, based on Lyapunov stability theory and matrix theory, sufficient conditions for leader-following consensus in discrete-time nonlinear multi-agent systems under asymmetric saturation impulsive control are established, and the admissible region of the system is estimated. Finally, numerical simulations are provided to verify the validity of the theoretical results.

Fault‐tolerant adaptive tracking control for spacecraft attitude with asymptotic convergence

AbstractIn this paper, we present a novel spacecraft attitude adaptive tracking control strategy that addresses the challenges posed by unknown inertia parameters, bounded unstructured uncertainties, and various actuator faults. To mitigate the adverse effects of these multiple uncertainties, our proposed control algorithm utilizes a simple tracking‐error feedback and compensation term, which only requires two adaptive parameters. This approach ensures asymptotic tracking convergence by employing an infinitely integrable inequality that incorporates saturation functions. As a result, the complexity of controller design and computational burden are significantly reduced. Finally, several numerical simulations are conducted to validate the feasibility and superiority of our proposed controller.

Effects of Early Mobilisation on Post Operative Pulmonary Complication in Patients with Open Abdominal Surgery

Background: Patients undergoing open abdominal surgery are the focus of this research, namely the effect of earlymobilisation on postoperative pulmonary problems. Early mobilization is proposed as a potential intervention toenhance respiratory function and reduce the risk of PPCs.Purpose: The purpose of this study is to evaluate the impact of pre-operative mobilisation on the incidence ofpulmonary complications in patients undergoing open abdominal surgery.Materials and Methods: This quasi-experimental study included 50 subjects who underwent open abdominalsurgery at Saveetha Medical Hospital, SIMTS. Convenient sampling was used to select the participants. Measuresof oxygen saturation (SPO2) and pulmonary function (FEV1) from a spirometer were employed as functionaloutcome indicators. After two weeks, participants were given a post-test to record their progress.Results: Data collected before and after early mobilisation exercise were analysed using a paired t-test. Theexperimental group showed significant improvements in SPO2, FIM, and FEV1 (P&lt;0.0001), indicating highervalues post-intervention. Post-test demonstrated higher statistical significance compared to pre-test.Conclusion: As a result, it was shown that early mobilisation Exercise is beneficial for reducing pulmonarycomplications after surgery.

Real-time optimal control for attitude-constrained solar sailcrafts via neural networks

This work is devoted to generating optimal guidance commands in real time for attitude-constrained solar sailcrafts in coplanar circular-to-circular interplanetary transfers. Firstly, a nonlinear optimal control problem is established, and the necessary conditions for optimality are derived by Pontryagin’s Minimum Principle. Under some mild assumptions, the attitude constraints are rewritten as control constraints, which are replaced by a saturation function so that a parameterized system is formulated. This allows one to generate an optimal trajectory via solving an initial value problem, making it efficient to collect a dataset containing optimal samples, which are essential for training Neural Networks (NNs) to achieve real-time implementation. However, the optimal guidance command may suddenly change from one extreme to another, resulting in discontinuous jumps that generally impair the NN’s approximation performance. To address this issue, we use two co-states that the optimal guidance command depends on, to detect discontinuous jumps. A procedure for preprocessing these jumps is then established, thereby ensuring that the preprocessed guidance command remains smooth everywhere. Meanwhile, the sign of one co-state is found to be sufficient to revert the preprocessed guidance command back into the original optimal guidance command. Furthermore, three NNs are built and trained offline, and they cooperate to precisely generate the optimal guidance command in real time. Finally, numerical simulations are presented to demonstrate the developments of the paper.

A bounding surface model of methane hydrate-bearing carbonate sand-silt mixtures

The geological environment of marine methane hydrate-bearing sediments (MHBS) is highly complex. Mastering the mechanical behavior of MHBS is crucial for analyzing geomechanical hazards and evaluating its stability. The marine sediment in the South China Sea (SCS) contains a significant amount of porous foraminifera shells, which serve as the primary storage space for natural gas hydrates and differ significantly from other sea areas. In the laboratory, porous carbonate sand (CS) and cohesion-less silt were utilized to prepare host sand of methane hydrate. In this paper, based on the analysis of experimental data, a bounding surface model was proposed to describe the mechanical behavior of artificial MHBS. The effect of methane hydrates on the elastic strain, normal consolidation and critical state of host sand is discussed, and corresponding equations for the model parameters are established, taking into consideration the cementing mechanism of hydrates. These equations are defined as functions of hydrate saturation, carbonate sand content (CSC), and initial void ratio. The increase in hydrate saturation significantly reduces the compressibility of the host sand and improves its strength. The proposed model is applied to predict the results of isotropic consolidation and drained triaxial tests on MHBS, demonstrating satisfactory performance.