Second-order Dynamic Model Research Articles

Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.

Preparation and Application of Degradable Lignin/Poly (Vinyl Alcohol) Polymers as Urea Slow-Release Coating Materials.

The massive amount of water-soluble urea used leads to nutrient loss and environmental pollution in both water and soil. The aim of this study was to develop a novel lignin-based slow-release envelope material that has essential nitrogen and sulfur elements for plants. After the amination reaction with a hydrolysate of yak hair keratin, the coating formulation was obtained by adding different loadings (2, 5, 8, 14 wt%) of aminated lignin (AL) to 5% polyvinyl alcohol (PVA) solution. These formulations were cast into films and characterized for their structure, thermal stability, and mechanical and physicochemical properties. The results showed that the PVA-AL (8%) formulation had good physical and chemical properties in terms of water absorption and mechanical properties, and it showed good degradation in soil with 51% weight loss after 45 days. It is suitable for use as a coating material for fertilizers. Through high-pressure spraying technology, enveloped urea particles with a PVA-AL (8%) solution were obtained, which showed good morphology and slow-release performance. Compared with urea, the highest urea release was only 96.4% after 30 days, conforming to Higuchi model, Ritger-Peppas model, and second-order dynamic model. The continuous nitrogen supply of PVA-AL coated urea to Brassica napus was verified by potting experiments. Therefore, the lignin-based composite can be used as a coating material to produce a new slow-release nitrogen fertilizer for sustainable crop production.

A Second-order Dynamic Model of the Mean Global Carbon Cycle

A significant research activity is ongoing about present and future stability of the Earth’s mean global carbon cycle, which plays a key role in climate dynamics, and is perturbed by the increasing carbon emission of the fossil-fuel combustion. The paper aims to provide an answer through a second-order state equation, which is tuned on global data of surface temperature, airborne carbon dioxide (CD) concentration, solar radiation and anthropogenic carbon emissions. The state variables are temperature and airborne CD perturbations from pre-industrial equilibriums. The equilibriums, taken as unknown, are expected to approach historical estimates, thus providing a tuning validation criterion. Since state variables are linked in a closed loop, carbon cycle stability can be assessed through loop stability criteria. The state equations, being linear time invariant, neglect time variability and nonlinearity. They are revealed by a rolling time regression, whose time interval shrinks from industrial era to recent decades, when data become more accurate. The paper concludes with preliminary predictions tuned on recent data. Comparison with predictions of the well-known MAGICC model show discrepancies that are briefly discussed.

Leaching of heavy metals from tungsten mining tailings: A case study based on static and kinetic leaching tests

Heavy metal (HM) leaching from tungsten mine tailings is a serious environmental risk. In this study, we assess the HM pollution level of tungsten tailings, determine the HM leaching patterns and mechanisms, and estimate the HM fluxes from a tailings reservoir. The results showed that the comprehensive pollution index (CRSi) values that decreased in order of the HM pollution levels in the tailings were cadmium (Cd) > tungsten (W) > lead (Pb) > copper (Cu) = zinc (Zn) > arsenic (As) > manganese (Mn). This result indicated that Cd, W, and Pb were priority pollutants in tailings. The Res fraction of all HMs was greater than 50%. Pb and Cd had similar species fractions with high Exc fractions, and tungsten had a considerable proportion of the Wat fraction. The general acid neutralizing capacity (GANC) test divides the leaching process of HMs into two stages, and each of stage is affected by different mechanisms. A neutral environment promoted tungsten leaching in the column leching test, while an acidic environment promoted Cd and Pb leaching. In addition, the pH effect was more obvious in the early stage. The kinetic fitting results showed that the second-order dynamic model well simulated the leaching of W, Pb, and Cd in most cases. Based on column kinetic leaching test results and tailings parameters, the annual W, Pb, and Cd fluxes were estimated to be 6.35 × 108, 1.3288 × 109, and 1.012 × 108 mg/year, respectively. The above results can guide the environmental management of tungsten tailing reservoirs, such as selecting suitable repair materials and estimating repair service times.

Dynamic Bayesian hierarchical peak over threshold modeling for real-time crash-risk estimation from conflict extremes

Using traffic conflict-based extreme value theory (EVT) models to quantify real-time crash-risk of road facilities is a promising direction for developing proactive traffic safety management strategies. Existing EVT real-time crash-risk analysis studies have only focused on using block maxima models. This study proposes a dynamic Bayesian hierarchical peak over threshold modeling approach to estimate real-time crash-risk based on traffic conflicts. The proposed approach combines quantile regression, dynamic updating approach, Bayesian hierarchical structure, and the peak over threshold method to generate time-varying generalized Pareto distributions to derive real-time crash-risk measures (i.e., crash probability and return level). The derived real-time crash-risk measures are applied to estimate cycle-level crash-risk at three signalized intersections in Surrey, British Columbia. Five approaches are used to dynamically update the model parameters, including time trend model, generalized autoregressive conditional heteroskedasticity process approach, as well as the first-order, second-order, and third-order dynamic linear models. For comparison, static models are also developed. All the developed models are compared in terms of statistical fit and predictive performance. Based on the best fitted dynamic model, cycle-level crash probability and return level are calculated to measure signalized intersection safety at cycle level. The results show that dynamic models considerably outperform static models in terms of statistical fit and predictive performance. Further, the third-order dynamic model has the best performance, which is probably due to that the model incorporates two linear trends to respectively describe the variation of the coefficients as well as its change to better account for the variation in the effect of time-varying covariates. However, it should be noted that the third-order dynamic model development needs more computation time than other dynamic models, which may limit the application of the model.

Adaptive fault-tolerant fixed-time cruise control for virtually coupled train set

In the cruise control of the virtual coupled train set (VCTS), the control algorithm with high stability, high accuracy, and fast convergence speed is the basic requirement for the smooth and efficient operation of the VCTS. To this end, this paper studies the problem of fixed-time cruise control for VCTS. To begin with, by analyzing the dynamic evolution of the VCTS in an actual environment, a second-order VCTS train-following dynamic model is formulated with considering actuator faults, uncertain resistance, unknown disturbances, and control input saturation. Then, an improved barrier functions-based fixed-time sliding model control method is proposed to deal with the state constraints (i.e., safe distance and speed limit). To deal with parametric uncertainty, adaptive fault-tolerant control and core function technologies are integrated into the same framework. Furthermore, by using a function approximation method to handle the control input saturation, an adaptive fault-tolerant fixed-time cruise controller is designed which not only guarantees the fixed-time stability of the VCTS but also copes with parametric uncertainty, state constraints, and input saturation. Finally, the effectiveness of the proposed method is validated in simulation analysis.

A Second-Order Dynamic Friction Model Compared to Commercial Stick–Slip Models

Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick–slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why dynamic friction models were developed in recent decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best-known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too-simple approximation. The recently published second-order dynamic friction model describes the dynamics of a fictitious bristle more accurately. It is based on a regularized friction force characteristic, which is continuous and smooth but can maintain long-term stick due to an appropriate shift in the regularization. Its performance is compared here to stick–slip friction models, developed and launched not long ago by commercial multibody software packages. The results obtained by a virtual friction test-bench and by a more practical festoon cable system are very promising. Thus, the second-order dynamic friction model may serve not only as an alternative to the LuGre model but also to commercial stick–slip models.

Consensus-based distributed formation control for coordinated battle system of manned/unmanned aerial vehicles

In this paper, a consensus-based distributed formation control method is proposed for improving the coordinated battle efficiency of coordinated battle system for manned/unmanned aerial vehicles (MAV/UAVs). The method proposed is designed based on consensus protocol, which contains three parts. First, the distributed structure with limited centralized strategy for MAV/UAVs cooperative system is designed. Second, a second-order dynamic model is built up to describe the distributed formation system, which is further simplified using feedback linearization method. Third, the information exchange topology of MAV/UAV-coordinated battle system is established on the basis of graph theory and leader–follower mechanism. Finally, the effectiveness of the proposed formation strategy for MAV/UAVs cooperative system is proved asymptotic convergence by constructing a reasonable Lyapunov function which guarantees the accurate formation maintenance. Simulation results are presented to demonstrate the effectiveness of the proposed method. And comparative simulation results reveal that the method proposed in this paper is superior to traditional algorithms in the aspects of accuracy and stability.

LuGre or not LuGre

The LuGre model is widely used in the analysis and control of systems with friction. Recently, it has even been made available in the commercial multibody dynamics simulation software system Adams. However, the LuGre model exhibits well-known drawbacks like too low and force rate-dependent break-away forces, drift problems during sticking periods, and significant differences in non-stationary situations between the pre-defined friction law and the one produced by the LuGre model. In the present literature, these problems are supposed to come from the model dynamics or its nonlinear nature. However, most of these drawbacks are not simple side effects of a dynamic friction model but are caused in the LuGre approach, as shown here, by a too simple and inconsistent model of the bristle dynamics. Standard examples and a more practical application demonstrate that the LuGre model is not a “what you see is what you get” approach. A dynamic friction model with accurate bristle dynamics and consistent friction force is set up here. It provides insight into the physical basis of the LuGre model dynamics. However, it results in a nonlinear and implicit differential equation, whose solution will not be easy because of the ambiguity of the friction characteristics. The standard workaround, a static model based on simple regularized characteristics, produces reliable and generally satisfactory results but definitely cannot maintain a stick. The paper presents a second-order dynamic friction model, which may serve as an alternative. It can maintain a stick and produces realistic and reliable results.

Removal of the Pigment Congo Red from Synthetic Wastewater with a Novel and Inexpensive Adsorbent Generated from Powdered Foeniculum Vulgare Seeds

In this research, powdered Foeniculum vulgare seed (FVSP) was treated separately with H2C2O4, ZnCl2, and a mixture of ZnCl2-CuS. The characteristics of the treated and untreated FVSP samples, as well as their abilities to eliminate Congo red (CR) from solutions, were investigated. The influences of the empirical circumstances on CR adsorption by the ideal adsorbent were studied. The thermodynamic, isothermal, and dynamic constants of this adsorption were also inspected. The ideal adsorbent was found to be the FVSP sample treated with a ZnCl2-CuS mixture, which eliminated 96.80% of the CR dye. The empirical outcomes proved that this adsorption was significantly affected by the empirical circumstances, and the second-order dynamic model as well as the Langmuir isotherm model fit the empirical data better than the first-order model and the Freundlich model. The values of Ea (15.3 kJ/mol) and ∆Ho (32.767 kJ/mol ≤ ∆Ho ≤ 35.495 kJ/mol) evidence that CR anions were endothermally adsorbed on Zn/Cu-FVSP via the ionic exchange mechanism. The superior Qmax values (434.78, 625.00, 833.33 mg/g), along with the cheapness and stability of the adsorbent used in this work, are evidence to confirm that this adsorbent will receive special interest in the field of contaminated water purification.

Existence and uniqueness of the solution to a second-order nonlinear dynamical system model with an unbounded variable and a discontinuous input

We consider an initial value problem for a second-order nonlinear dynamical system that allows discontinuous inputs. In this problem, one state variable is restricted in a closed and bounded interval while the other state variable is unlimited. The existence and uniqueness of the solution to this problem is studied in a time interval determined by two adjacent instants at which the input may be discontinuous. Some results are obtained on the maximal interval of existence of the unique solution in this time interval. The results are then extended to the entire time domain. A robot example is given to verify our results.

A second-order dynamic and static ship path planning model based on reinforcement learning and heuristic search algorithms

Ship path planning plays an important role in the intelligent decision-making system which can provide important navigation information for ship and coordinate with other ships via wireless networks. However, existing methods still suffer from slow path planning and low security problems. In this paper, we propose a second-order ship path planning model, which consists of two main steps, i.e., first-order static global path planning and second-order dynamic local path planning. Specifically, we first create a raster map using ArcGIS. Second, the global path planning is performed on the raster map based on the Dyna-Sarsa(lambda) model, which integrates the eligibility trace and the Dyna framework on the Sarsa algorithm. Particularly, the eligibility trace has a short-term memory for the trajectory, which can improve the convergence speed of the model. Meanwhile, the Dyna framework obtains simulation experience through simulation training, which can further improve the convergence speed of the model. Then, the improved ship trajectory prediction model based on stacked bidirectional gated recurrent unit is used to identify the risk of ship collision and switch the path planning from the first order to the second order. Finally, the second-order dynamic local path planning is presented based on the FCC-A* algorithm, where the cost function of the traditional path planning A* algorithm is rewritten using the fuzzy collision cost membership function (fuzzy collision cost, FCC) to reduce the collision risk of ships. The proposed model is evaluated on the Baltic Sea geographic information and ship trajectory datasets. The experimental results show that the eligibility trace and the Dyna learning framework in the proposed model can effectively improve the planning efficiency of the ship’s global path planning, and the collision risk membership function can effectively reduce the number of collisions in A* local path planning and thus improve the navigation safety of encountering ships.

Adaptive optimal trajectory tracking control of AUVs based on reinforcement learning

In this paper, an adaptive model-free optimal reinforcement learning (RL) neural network (NN) control scheme based on filter error is proposed for the trajectory tracking control problem of an autonomous underwater vehicle (AUV) with input saturation. Generally, the optimal control is realized by solving the Hamilton–Jacobi–Bellman (HJB) equation. However, due to its inherent nonlinearity and complexity, the HJB equation of AUV dynamics is challenging to solve. To deal with this problem, an RL strategy based on an actor–critic framework is proposed to approximate the solution of the HJB equation, where actor and critic NNs are used to perform control behavior and evaluate control performance, respectively. In addition, for the AUV system with the second-order strict-feedback dynamic model, the optimal controller design method based on filtering errors is proposed for the first time to simplify the controller design and accelerate the response speed of the system. Then, to solve the model-dependent problem, an extended state observer (ESO) is designed to estimate the unknown nonlinear dynamics, and an adaptive law is designed to estimate the unknown model parameters. To deal with the input saturation, an auxiliary variable system is utilized in the control law. The strict Lyapunov analysis guarantees that all signals of the system are semi-global uniformly ultimately bounded (SGUUB). Finally, the superiority of the proposed method is verified by comparative experiments.

Multicluster Consensus for Large-Scale Heterogenous Manned/Unmanned Aerial Team With Random Link Failure via Pinning Control

This brief investigates the multi-cluster consensus for heterogenous manned/unmanned aerial system with random link failure via pinning control method. Each cluster is composed of first-order and second-order dynamic models. A distributed control protocol is proposed to construct the weakly connected topology with restricted communication load in large-scale heterogenous aerial team. Based on the graph theory, matrix analysis and Lyapunov theorem, sufficient consensus conditions are derived. Numerical examples validate the theoretic results.

Discrete-time formation control of multiple heterogeneous underwater gliders

The formation control of underwater gliders has been widely concerned due to its practical potential in various applications of ocean observation. This paper investigates the problems of formation control of multiple heterogeneous gliders based on consensus algorithm with discrete information. A nonlinear second-order dynamic model is obtained for the complex nonlinear underactuated gliders. By combining the consensus of speed control in forward direction and path following in lateral direction, formation control protocol with unavailable velocity information and asynchronous communication is proposed for multiple gliders. The glider formation control system (GFCS) is designed to drive a fleet of gliders following a set of explicitly specified trajectories. Two cases of simulation with six heterogeneous gliders and six homogeneous gliders respectively are performed to demonstrate the methodology and verify the effectiveness and reliability of the formation control protocol for discrete-time multi-glider system, which is proved to be applicable to formation scaling and transformation of multiple gliders.

Real-time implementation of a super twisting control algorithm for an upper limb wearable robot

This paper proposes a robust nonlinear controller for an active orthosis. The system is composed of the upper limb orthosis worn by the arm, which can be represented by a nonlinear second-order dynamical model. A robust control strategy is developed to guarantee an accurate and precise movement that encounter important issues such as unknown disturbance torque, inertial and viscous and the parameter uncertainties. A novel control strategy is proposed based on the Super Twisting Algorithm (STW). The stability analysis is performed based on the Lyapunov theory. For further dissemination of the proposed method, a wearable robot arm was built and the exoskeleton building process includes the following parts: mechanical design, mechanical components, electronic circuit design, robot assembly, programming of closed-loop control algorithms in the microprocessor. Hardware-in-the-loop is being implemented by a DAQ-Advantech, PCI-1716 AE, and PC to test the super twisting control algorithm. An experimental prototype, including the arm wearable exoskeleton, is designed and implemented. Experimental results indicate the proposed controller is able to reach high tracking accuracy.

Hydrophobic adsorbent prepared from spent methanol-to-propylene catalyst for directional adsorption of high COD oily wastewater

Spent methanol-to-propylene (MTP) catalysts have a large specific surface area and high porosity but are usually disposed of in landfills directly, and recycling has rarely been reported. In this study, the spent MTP catalyst was moderately dealuminized with organic acids and etched with alkali solvent to increase its specific surface area, further silanized by octyl triethoxy silane (OTS). A novel superhydrophobic adsorbent covered with –Si(CH2)7CH3 groups was obtained. The characterization of XRD, SEM, FTIR and XPS shows that the adsorbent maintains a typical ZSM-5 zeolite structure, and the –Si(CH2)7CH3 group is successfully grafted into the sample, not only on the surface but also in some pore space. Taking high chemical oxygen demand (COD) wastewater as the object, the influence of contract time, pH and temperature on COD removal was investigated. The removal process could be better depicted by the Langmuir isotherm model and the pseudo second-order dynamic model. Furthermore, the results of the thermodynamic study (∆G is − 79.35 kJ/mol, ∆S is 423.68 J/mol K, and ∆H is 46.91 kJ/mol) show that the adsorption was a spontaneous and endothermic process. These findings indicate that the modified spent MTP catalyst has potential application for the removal of COD from wastewater.

Distributed output feedback consensus tracking control of multiple nonholonomic mobile robots with only position information of leader

In this paper, distributed output feedback consensus tracking control of multiple nonholonomic mobile robots with limited information of leader is studied. Different from the existing results, the considered consensus problem has the following features: (i) each robot is described by a second-order dynamic model with parametric uncertainty and external disturbances, (ii) the global information of the directed graphs is not required, (iii) only the position of the leader is available for a subset of robots and thus its velocity information is no longer needed. To solve such a problem, an adaptive output feedback control scheme which involves estimator, observer and controller design is proposed. A fully distributed estimator is constructed to estimate the position of the leader for each robot. Based on the estimated information, an adaptive observer-based output feedback controller is designed to realize consensus tracking. It is shown that the boundedness of all the signals in the resulting closed-loop system is guaranteed, and the consensus tracking error of the system converges to an adjustable neighborhood of zero by appropriately choosing design parameters. Simulation results are provided to verify the effectiveness of the proposed scheme.

A Bayesian Dynamical Approach for Human Action Recognition.

We introduce a generative Bayesian switching dynamical model for action recognition in 3D skeletal data. Our model encodes highly correlated skeletal data into a few sets of low-dimensional switching temporal processes and from there decodes to the motion data and their associated action labels. We parameterize these temporal processes with regard to a switching deep autoregressive prior to accommodate both multimodal and higher-order nonlinear inter-dependencies. This results in a dynamical deep generative latent model that parses meaningful intrinsic states in skeletal dynamics and enables action recognition. These sequences of states provide visual and quantitative interpretations about motion primitives that gave rise to each action class, which have not been explored previously. In contrast to previous works, which often overlook temporal dynamics, our method explicitly model temporal transitions and is generative. Our experiments on two large-scale 3D skeletal datasets substantiate the superior performance of our model in comparison with the state-of-the-art methods. Specifically, our method achieved 6.3% higher action classification accuracy (by incorporating a dynamical generative framework), and 3.5% better predictive error (by employing a nonlinear second-order dynamical transition model) when compared with the best-performing competitors.

Development of a second-order dynamic model for quantifying impact of thermal mass on indoor thermal environment

Indoor thermal environment can be significantly influenced by thermal mass, which is not considered quantitatively in building thermal design due to the lack of a simple and accurate calculation model. For this reason, a temperature elastic coefficient (TEC) is proposed to characterize the dynamic heat transfer between inner surfaces of external walls (ISEW) and indoor air, and an effective thermal capacity (ETC) is used to characterize thermal mass. A second-order dynamic model is thus developed to efficiently evaluate the impact of thermal mass on indoor thermal environment by employing the TEC and ETC. The results show that both the TEC and the ETC are affected by the insulation position, wall thermal resistance, air change rate and window-wall ratio (WWR), but independent of the outdoor air temperature, indoor heat source intensity and solar radiation. Furthermore, the combination of the second-order dynamic model and the database models of ETC and the TEC are determined by using multiple nonlinear regression analysis, and can help policy makers and building thermal designers to estimate the impact of thermal mass on the indoor thermal environment quickly and accurately.