Order Dynamic Model Research Articles

Hybrid trajectory tracking control of wheeled mobile robots using predictive kinematic control and dynamic robust control

AbstractTrajectory tracking control of wheeled mobile robots (WMRs) is still a remarkable problem for many applications. In the present paper, a hybrid control is presented based on dynamic and kinematic equations of motion for wheeled mobile robots in the presence of the sum of the external disturbances and parametric uncertainty. The designed control for the WMR utilizes control and guidance to reach the reference path. In many studies, a control strategy is normally employed for WMR. However, in this study, hybrid control was used for the mentioned purpose. Akin to other studies, the kinematic control scheme here was based on the predictive control, and the dynamic control scheme was designed based on the robust control. Therefore, in this article, having introduced the kinematic model, a nonlinear predictive control was proved and designed. In the next step, a finite‐time integral type terminal sliding mode control (FITSMC) was designed based on the nonlinear dynamic model in order to automatically adjust the control gain and eliminate online disturbances and destructive chattering phenomena completely. In particular, a finite‐time disturbance observer was designed to estimate the external disturbances. The proof of the new proposed control scheme was presented using Lyapunov stability theory and numerical results. The mentioned integrated scheme, including predictive control (outer loop) and nonlinear adaptive control (inner loop), ensures the convergence and optimal tracking performance of all signals, as a result of which the tracking errors can arbitrarily converge to the origin in a finite time. In the final step, the simulation results were presented to show the effectiveness of the proposed scheme using MATLAB software, and the introduced control design was compared with a similar controller quantitatively and qualitatively.

Model Predictive Control and Service Life Monitoring for Molten Salt Solar Power Towers

A two-component system for control and monitoring of solar power towers with molten salt receivers is proposed. The control component consists of a model predictive control application (MPC) with a flexible objective function and on-line tunable weights, which runs on a Industrial PC and uses a reduced order dynamic model of the receiver’s thermal and flow dynamics. The second component consists of a service-life monitoring unit, which estimates the service-life consumption of the absorber tubes depending on the current mode of operation based on thermal stresses and creep fatigue in the high temperature regime. The calculation of stresses is done based on a detailed finite element study, in which a digital twin of the receiver was developed. By parallelising the model solver, the estimation of service-life consumption became capable of real-time operation. The system has been implemented at a test facility in Jülich, Germany, and awaits field experiments. In this paper, the modeling and architecture are presented along simulation results, which were validated on a hardware-in-the-loop test bench. The MPC showed good disturbance rejection while respecting process variable constraints during the simulation studies.

Shrinkage Estimation and Forecasting in Dynamic Regression Models Under Structural Instability

Abstract This paper introduces a Stein-like shrinkage method for estimating slope coefficients and forecasting in first order dynamic regression models under structural breaks. The model allows for unit root and non-stationary regressors. The proposed shrinkage estimator is a weighted average of a restricted estimator that ignores the break in the slope coefficients, and an unrestricted estimator that uses the observations within each regime. The restricted estimator is the most efficient estimator but inconsistent when there is a break. However, the unrestricted estimator is consistent but not efficient. Therefore, the proposed shrinkage estimator balances the trade-off between the bias and variance efficiency of the restricted estimator. The averaging weight is proportional to the weighted distance of the restricted estimator, and the unrestricted estimator. We derive the analytical large-sample approximation of the bias, mean squared error, and risk for the shrinkage estimator, the unrestricted estimator, and the restricted estimator. We show that the risk of the shrinkage estimator is lower than the risk of the unrestricted estimator under any break size and break points. Moreover, we extend the results for the model with a unit root and non-stationary regressors. We evaluate the finite sample performance of our proposed method via extensive simulation study, and empirically in forecasting output growth.

A second order dynamical system method for solving a maximally comonotone inclusion problem

In this paper a second order dynamical system model is proposed for computing a zero of a maximally comonotone operator in a Hilbert space. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed dynamical system. A proper tuning of the parameters can allow us to establish fast convergence properties of the trajectories generated by the dynamical system. The weak convergence of the trajectory to a zero of the maximally comonotone operator is also proved. Furthermore, a discrete version of the dynamical system is considered and convergence properties matching to that of the dynamical system are established under a same framework. Finally, the validity of the proposed dynamical system and its discrete version is demonstrated by two numerical examples.

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease.

Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator

Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam–Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power–Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.

Flexibility extension in hydropower for the provision of frequency control services within the European energy transition

This paper presents a comprehensive assessment of the large-scale deployment of hydropower on the provision of frequency regulation services, when equipped with the extended flexibility solutions being developed and/or tested within the scope of the XFLEX HYDRO project. The current analysis is performed on the Iberian Peninsula (IP) power grid considering its interconnection to the Continental Europe (CE) system, since this power system zone is expected to have the most severe frequency transient behaviour in future scenarios with increased shares of variable renewable energies. For this purpose, prospective scenarios with increased shares of time variable renewable generation were identified and analysed. To assess the impacts of the hydropower flexibility solutions on frequency dynamics after a major active power loss, extensive time domain simulations were performed of the power system, including reliable reduced order dynamic models for the hydropower flexibility solutions under evaluation. This research assesses the effects of synchronous and synthetic inertia, and of the Frequency Containment Reserve (FCR) and Fast Frequency Response (FFR) services as specified in European grid codes. The main findings highlight the potential of hydropower inertia and of adopting a variable speed technology for enhancing frequency stability, while contribute to better understand the role of hydropower plants in future power systems.

Two-Step Adaptive Control for Planar Type Docking of Autonomous Underwater Vehicle

Planar type docking enables a convenient underwater energy supply for irregularly shaped autonomous underwater vehicles (AUVs), but the corresponding control method is still challenging. Conventional control methods for torpedo-shaped AUVs are not suitable for planar type docking due to the significant differences in system structures and motion characteristics. This paper proposes a two-step adaptive control method to solve the planar type docking problem. The method makes a seamless combination of horizontal dynamic positioning and visual servo docking considering ocean current disturbance. The current disturbance is estimated and canceled in the pre-docking step using a current observer, and the positioning error is further compensated for by the vertical visual servo technique in the docking step. Reduced order dynamic models are distinctively established for different docking steps according to the motion characteristics, based on which the dynamic controllers are designed considering the model parameter uncertainties. Simulation is conducted with an initial distance of 10 m in the horizontal direction and 3 m in depth. Stable and accurate dynamic positioning under up to 0.4 m/s of current disturbances with different directions is validated. A 0.5 m lateral positioning error is successfully compensated for by the visual servo docking step. The proposed control method provides a valuable reference for similar types of docking application.

Parallel simulations for fast‐moving landslides: Space‐time mesh adaptation and sharp tracking of the wetting front

AbstractWe propose a highly scalable solver for a two‐dimensional depth‐integrated fluid dynamic model in order to simulate flow‐like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two‐step second‐order Taylor–Galerkin scheme, enriched by a suitable flux correction in order to avoid spurious oscillations, in particular near discontinuities and close to the wetting‐drying interface. A mesh adaptation procedure based on a gradient‐recovery a posteriori error estimator allows us to efficiently deal with a discretization of the domain customized to the phenomenon under investigation. Moreover, we resort to an adaptive scheme also in time to prevent filtering out the landslide dynamics, and to an interface tracking algorithm to avoid an excessive refinement in noninterfacial regions while preserving details along the wetting‐drying front. Finally, after verifying the performance of the proposed numerical method on idealized settings, we carry out a scalability analysis of the code both on idealized and real scenarios, to check the efficiency of the overall implementation.

Predicting solutions of the stochastic fractional order dynamical system using machine learning

The solution of fractional-order systems has been a complex problem for our research. Traditional methods like the predictor-corrector method and other solution steps are complicated and cumbersome to derive, which makes it more difficult for our solution efficiency. The development of machine learning and nonlinear dynamics has provided us with new ideas to solve some complex problems. Therefore, this study considers how to improve the accuracy and efficiency of the solution based on traditional methods. Finally, we propose an efficient and accurate nonlinear auto-regressive neural network for the fractional order dynamic system prediction model (FODS-NAR). First, we demonstrate by example that the FODS-NAR algorithm can predict the solution of a stochastic fractional order system. Second, we compare the FODS-NAR algorithm with the famous and good reservoir computing (RC) algorithms. We find that FODS-NAR gives more accurate predictions than the traditional RC algorithm with the same system parameters, and the residuals of the FODS-NAR algorithm are closer to 0. Consequently, we conclude that the FODS-NAR algorithm is a method with higher accuracy and prediction results closer to the state of fractional-order stochastic systems. In addition, we analyze the effects of the number of neurons and the order of delays in the FODS-NAR algorithm on the prediction results and derive a range of their optimal values.

Transient Dynamics and Propagation of Voltage and Frequency Fluctuations in Transmission Grids

The energy transition towards increased electric power production from renewable energy (RE) resources creates new challenges to ensure the stability of power grids. In conventional power grids voltage fluctuations can be controlled locally. Here, it is explored whether this may be changed by the energy transition. It is well established that the increase of RE resources in power grids increases the amplitude of frequency deviations and the velocity with which these deviations spread throughout the power grid. However, its effect on voltage dynamics and propagation has not been systematically studied. Here, a systematic study is carried out of the transients of voltage amplitude, phase and frequency deviations due to local contingencies in dependence on system inertia, heterogeneity and topology. The 3rd order dynamic power grid model is studied numerically and analytically and compared with real grid simulations for the Nigerian (330 kV) power grid and other grid models, using DigSILENT PowerFactory software. A quantitative analysis of the parametric dependence of the velocity with which a disturbance propagates throughout the grid and of the period of oscillations of the frequency and voltage transients is provided. Beating patterns are found in the transients and are identified as footprints of the location of the fault bus, as caused by multiple reflections of propagating disturbances from the grid boundary. These may result in interarea oscillations. It is confirmed that voltage deviations remain local for realistic ranges of parameters, but that it can propagate by literally surfing on the frequency deviation wave. However, it is found that this no longer holds true when the electrical power in the grid approaches its critical value beyond which no stationary solution exists. Furthermore, time dependent second moments of the geodesic distance weighted with frequency deviations <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\delta \omega }(t)$ </tex-math></inline-formula> and voltage deviations <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\delta V}(t)$ </tex-math></inline-formula> , respectively are evaluated, confirming a ballistic disturbance propagation in homogeneous model grids. However, in real grid simulations, a linear time dependence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S(t)$ </tex-math></inline-formula> is observed, indicating a diffusive propagation due to multiple scattering from the inhomogeneities in these power grids.

AquaClimber: a limbed swimming and climbing robot based on reduced order models

Many legged robots have taken insight from animals to run, jump, and climb. Very few, however, have extended the flexibility of limbs to the task of swimming. In this paper, we address the study of multi-modal limbed locomotion by extending our lateral plane reduced order dynamic model of climbing to swimming. Following this, we develop a robot, AquaClimber, which utilizes the model’s locomotive style, similar to human freestyle swimming, to propel itself through fluid and to climb vertical walls, as well as transition between the two. A comparison of simulation and model results indicate that the simulation can predict how hand design, arm compliance, and driving frequency affect swimming speed and behavior. Using this reduced order model, we have successfully developed the first limbed aquatic-scansorial multi-modal robot.

Impact of quarantine on fractional order dynamical model of Covid-19

In this paper, a Covid-19 dynamical transmission model of a coupled non-linear fractional differential equation in the Atangana-Baleanu Caputo sense is proposed. The basic dynamical transmission features of the proposed system are briefly discussed. The qualitative as well as quantitative results on the existence and uniqueness of the solutions are evaluated through the fixed point theorem. The Ulam-Hyers stability analysis of the suggested system is established. The two-step Adams-Bashforth-Moulton (ABM) numerical method is employed to find its numerical solution. The numerical simulation is performed to accesses the impact of various biological parameters on the dynamics of Covid-19 disease.

A low-order dynamical model for fire-vegetation-climate interactions

Climate conditions play a key role in determining the occurrence and severity of wildfires. Despite the impacts of wildfires on ecosystems, human livelihoods, and air quality, little is known conceptually about how natural or anthropogenic shifts in climate may influence the fire activity on a regional or global scale. Here, we introduce a new low order dynamical model that describes the nonlinear interactions between climate, vegetation (fire fuel) and fire probabilities. This 1-dimensional model describes the influence of precipitation and temperature on burned area and fuel availability. Estimating key parameters from observations, the model successfully reproduces the spatio-temporal variability of wildfire occurrences, particularly, in semi-arid regions in Africa, South America, and northern Australia. The fidelity of the model translates into a high degree of longer-term predictability of fire conditions in these vulnerable regions. Our new low-order modeling framework may provide guidance to forestry managers to assess fire risks under present and future climate conditions.

Reduced order dynamical models for complex dynamics in manufacturing and natural systems using machine learning

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources, respectively. Current dynamic models for full industrial process plants exist as highly accurate first-principle relationships. However, their integration is computationally intensive and provides no simplified understanding of the underlying mechanisms driving the overall dynamics. Similarly, for natural systems, most dynamical models are first principle based, with high data requirements and low state accuracy. Consequently, lower-order models that may sacrifice accuracy for simplicity and ease of training can prove useful. Yet, there have been few attempts at finding low-order models of chemical manufacturing processes and natural systems, with work focusing on modeling individual mechanisms. We seek to fill this research gap by using a machine learning (ML) approach, SINDy, validated on a soybean-diesel process plant and watershed system. This ML method combines sparse, grey-box modeling with additional nonlinear optimization to identify governing dynamics as ODEs. We find a linear ODE model for the process plant that gives an accurate relation between input and output and selected internal molar flow rates reflective of underlying linear stoichiometric mechanisms and an internal mass balance. For the natural system, we modify the SINDy approach to include the effect of past dynamics on training the model, which gives a nonlinear model for streamflow dynamics. This improves dynamical transitions, but falls short of accurate state estimation. We conclude that the proposed ML approach works well for non-chaotic systems with minimal hysteresis, but is limited when this condition is not met.

The Fornax3D project: intrinsic correlations between orbital properties and the stellar initial mass function

ABSTRACT Variations of the stellar initial mass function (IMF) in external galaxies have been inferred from a variety of independent probes. Yet the physical conditions causing these variations remain largely unknown. In this work, we explore new spatially resolved measurements of the IMF for three edge-on lenticular galaxies in the Fornax cluster. We utilize existing orbit-based dynamical models in order to fit the new IMF maps within an orbital framework. We find that, within each galaxy, the high-angular momentum disc-like stars exhibit an IMF which is rich in dwarf stars. The centrally concentrated pressure-supported orbits exhibit similarly dwarf-rich IMF. Conversely, orbits at large radius which have intermediate angular momentum exhibit IMF which are markedly less dwarf-rich relative to the other regions of the same galaxy. Assuming that the stars which reside, in the present-day, on dynamically hot orbits at large radii are dominated by accreted populations, we interpret these findings as a correlation between the dwarf-richness of a population of stars, and the mass of the host in which it formed. Specifically, deeper gravitational potentials would produce more dwarf-rich populations, resulting in the relative deficiency of dwarf stars which originated in the lower mass accreted satellites. The central and high-angular momentum populations are likely dominated by in situ stars, which were formed in the more massive host itself. There are also global differences between the three galaxies studied here, of up to ∼0.3 dex in the IMF parameter ξ. We find no local dynamical or chemical property which alone can fully account for the IMF variations.

Gender differences in the perception of inflation

Using data from Italy (1994–2018), we investigate gender differences in consumers’ inflation perceptions over time. We introduce a dynamic model in order to detect the changes in the shape of the probability distributions of judgments across time and to compare the behavior of the two groups of respondents. The model components describe the deep conviction of respondents about past inflation and the uncertainty generated by the intrinsic fuzziness surrounding the evaluation process. The results suggest that women tend to perceive a higher level of inflation than men, but this propensity has changed over the years. The Euro changeover and other economic events produced an increase in the heterogeneity of men’s responses and decreased the gap between the feelings of men and women about inflation. When the perceived inflation closely tracked the true rate, the gender difference was more pronounced because of the smaller heterogeneity and the higher asymmetry in the distribution of women’s judgments.

Control Based on Feedback Linearization of a Mobile Manipulator Robot for Trajectory Tracking

The use of robotic systems has now become almost necessary in various fields. Of which, the realization of any hard or dangerous place requiring an implication of manipulation and locomotion, is necessarily entrusted to a mobile manipulator. In this work, we present a control approach that ensures the stability of the system, based on the linearization of feedback. We have determined the kinematic and dynamic models in order to apply the control with a high degree of accuracy. The approach is validated by simulation tests.

Equivalent Modelling of Hybrid RES Plant for Power System Transient Stability Studies

The paper proposes methodology for development of dynamic equivalent model of hybrid renewable energy source (HRES) plant suitable for reliable assessment of the overall transient stability of the realistic, large power systems. Transient stability index is used for system stability assessment, and consequently for the evaluation of the model performance. The historical plant production data and transmission network short-circuit fault statistics, together with probabilistically modelled uncertainties associated with system operation, are used to generate a set of realistic dynamic responses of the plant over the period of one year. The use of clustering algorithms enabled unsupervised grouping&#x002F;clustering of responses and development of the low order equivalent models in the form of a transfer function with voltage as an input and real and reactive power as outputs. The methodology is illustrated on a number of case studies using two HRES plant configurations. It is demonstrated that a very few low order dynamic models can be used to model the HRES plant during the year for sufficiently accurate transient stability assessment of the power system. The possibility of deriving these equivalent models based on forecasted HRES plant composition makes them attractive for practical application in power system dynamic security studies.

Autonomous navigation for Mars probes using only satellite-to-satellite tracking measurements by singularity-avoiding orbit elements

AbstractThis paper proposes a novel autonomous navigation method for Mars-orbiting probes. Satellite-to-satellite tracking (SST) between two probes is generally deemed to involve autonomous measurements with no dependence on any external observation sites on the Earth. For the conventional two-body dynamic model, it is well known that the orbit states cannot be estimated by merely using such SST measurements. Considering the effects of third-body gravitation perturbation and the weak Mars tesseral harmonics perturbation, autonomous navigation with SST measurements alone becomes weakly observable and may be achieved by some nonlinear filtering techniques. Two significant improvements are made to mitigate the nonlinearity brought by the dynamic models. First, singularity-avoiding orbit elements are selected to represent the dynamic models in order to reduce the intensity of the nonlinearity which cannot be overcome by the traditional position–velocity state expression. Second, the unscented Kalman filter method is effectively utilised to avoid the linearised errors calculated by its extended Kalman filter counterpart which may exceed the tesseral harmonics perturbation. A constellation, consisting of one low-orbit probe and one high-orbit probe, is designed to realise the autonomous orbit determination of both participating Mars probes. A reliable navigation solution is successfully obtained by Monte Carlo simulation runs. It shows that the errors of the semimajor axes of the two Mars probes are less than 10 m and the position errors are less than 1 km.