Phase Trajectories Research Articles

Standardizing Life Cycle Organization: A Synergetic Quality Management Approach

Standardization is essential for innovation (on the impacts on design, manufacturing, and operation processes) and its dissemination, both within a country and internationally. A phenomenological information model has been developed for the system of standards, which will be used as an information base for integrated quality management systems, environmental safety, and energy saving depending on the type of products, requirements of technical regulations, and conformity assessment procedures. Phase portraits of the life cycle system of complex products were constructed, and a general expression for the Lyapunov exponents characterizing the overall behavior of the dynamic system in phase space was obtained. The presence of particular areas to which, regardless of the initial conditions, all phase trajectories rapidly evolve has been established. The critical conditions for the control parameters were found. A diagram was constructed that determines the stability of the system states of the life cycle of complex products. It was found that the processes of the life cycle of complex products are carried out in two stages: in the first, there is a rapid evolution of components and parameters of technical and software tools, as well as energetic elements of functional subsystems, which is reflected in a specific attractive section of phase portraits, in the second, further slow development along it.

Generating functions of the Cauchy operator of a hamiltonian system

The article is related to the mathematical apparatus for describing the phase trajectories of a hamiltonian system. An approach related to the construction of generating functions for the Cauchy operator is proposed. It is shown that one-parameter families of generating functions satisfy the Hamilton—Jacobi equation or its modifications. Using the example of small oscillations of a mathematical pendulum, it is shown that the description of the Cauchy operator for sufficiently long periods of time requires the use of generating functions of various types. With the help of generating functions, a variational principle similar to the principle of least action is formulated. The efficiency of using generating functions in the development of conservative methods of numerical integration is also noted.

Estimates of the phase trajectories of controlled systems with multi-valued impulses

Estimates of the phase trajectories of controlled systems with multi-valued impulses

Решение линейно-квадратичных задач в дискретно-непрерывном формате с внешними воздействиями

Two linear-quadratic problems are considered on the set of piecewise-constant controls. The first problem contains a discrete perturbation on the right side of the controlled system and uncertain parameters in a quadratic functional with sign-indefinite matrices. Its solution is obtained by the guaranteed result rule and is implemented in the form of a finite-dimensional minimax problem. There are obtained conditions for the parameters that convert the objective function to a convex-concave structure and give the possibility of an effective solving of the problem. These are linear inequalities containing extreme eigenvalues of symmetric matrices. The second problem is related to the functional in the discrete variant, which is defined as the deviation of the phase trajectory from consecutive time realizations of the external influence. It gives the opportunity of the step by step searching of the extremmum at each node point of the time interval. Local problems can be effectively solved in a finite number of iterations.

МОДЕЛИРОВАНИЕ УГЛОВОГО ДВИЖЕНИЯ КОСМИЧЕСКОГО АППАРАТА ПЕРЕМЕННОГО СОСТАВА С УЧЁТОМ ДЕСТАБИЛИЗИРУЮЩИХ СВОЙСТВ РЕАКТИВНОЙ СТРУИ

The work presents simulation of dynamics of a spacecraft~(SC) with variable mass. A generalized method for analyzing the phase trajectory curvature is used, being refined for the case in which the moments of forces applied to the SC depend on the angular velocity. Special cases are considered along with analyzing a spacecraft with dynamic asymmetry. Using the method, the presence of complex evolutions of angular motion is shown, in which the jet stream of the engine creates Coriolis effects (Magnus effect), destabilizing the precession cone and leading to an increase in the nutation angle.

Transient modes of high-speed rotor whit electric drive

The paper presents the results of the study of the transient modes of a high-speed rotor with formally six degree of freedom, driven by an electric motor-generator during transition trough the resonance. Based on the Newton-Euler equation, the differential equations of motion are derived, and the frequency spectrum of the considered electro-mechanical system is determined. The following cases are considered: - transition trough resonance with unlimited (ideal energy source) and limited excitation by the motor; unstable frequency zones; phase trajectories and the influence of the electro-magnetic constant of the motor on the stability. The analysis of the stationary and nonstationary processes was carried out using the asymptotic method of Bogoliybov-Mitropolski. The stability of vibrations are determined by numerical solution of the equations in variations of the equilibrium states. These transitions are of great importance for the recently widespread so-called uninterruptible power sources (UP), as well as the kinetic energy recovery system (KERS ) used as additional propulsion energy .

A Metallurgical Dynamics-Based Method for Production State Characterization and End-Point Time Prediction of Basic Oxygen Furnace Steelmaking

Basic Oxygen Furnace (BOF) steelmaking is an important way for steel production. Correctly recognizing different blowing periods and abnormal refining states is significant to ensure normal production process, while accurately predicting the end-point time helps to increase the first-time qualification rate of molten steel. Since the decarburization products CO and CO2 are the main compositions of off-gas, information of off-gas is explored for BOF steelmaking control. However, the problem is that most of the existing research directly gave the proportions of CO and CO2 as model input but barely considered the variation information of off-gas to describe the production state. At the same time, the off-gas information can be expected to recognize the last blowing period and predict the end-point time earlier than the existing methods that are based on sub-lance or furnace flame image, but little literature makes an attempt. Therefore, this work proposes a new method based on functional data analysis (FDA) and phase plane (PP), defined as FDA-PP, to describe and predict the BOF steelmaking process from the metallurgical dynamics viewpoint. This method extracts the total proportion of CO and CO2 and its first-order derivative as dynamics features of steelmaking process via FDA, which indicate the reaction velocity and acceleration of decarburization reaction, and describes the evolution of dynamics features via PP. Then, the FDA-PP method extracts the features of phase trajectories for production state recognition and end-point time prediction. Experiments on a real production dataset demonstrate that the FDA-PP method has higher production state recognition accuracy than the classical phase space, SVM, and BP methods, which is 87.78% for blowing periods of normal batches, 90.94% for splashing anomaly, and 81.29% for drying anomaly, respectively. At the same time, the FDA-PP method decreases the mean relative prediction error (MRE) of the end-point time prediction for abnormal batches by about 10% compared with the SVM and BP methods.

Integrated Direct Yaw Control and Antislip Regulation Mixed Control of Distributed Drive Electric Vehicle Using Cosimulation Methodology

The improvement of handling and stability performance of Distributed Drive Electric Vehicle (DDEV) is analyzed, visualized, and designed by proposing and deploying the mixed control strategies in this paper including Direct Yaw Control (DYC), Antislip Regulation (ASR) and a novel Dual-mode Switching Control (DMSC). First, by drawing the phase trajectory stability domain, the vehicle stability limit boundary can be determined, which provides the basis for the lateral stability constraint of the vehicle. Then, the practicability and real time visualization of driving efficiency and timeliness of DDEV is achieved to reduce the margin of error for the desired torque value by employing the DYC strategy which uses a fuzzy PID algorithm. Furthermore, the ASR strategy which adopts the optimal slip rate algorithm to determine the requirement of desired torque value based on the different road conditions is used to reduce slip phenomenon effectively and to maintain handling control of DDEV. In response to different scenes especially conflict and coexistence between DYC and ASR, the DMSC strategy is applied to find a more suitable slip rate range by using the root mean square error method (REME). Finally, the cosimulation platform of ADAMS/Car and MATLAB/Simulink is built to simulate the mixed control strategies by integrating DYC, ASR, and DMSC. The simulation results show that the DMSC can effectively prevent DDEV from entering the dangerous limit driving state when turning and driving. The strategy has a more significant control effect needed to meet the requirements of the driving safety of the vehicle and handling stability. The DMSC is adopted and downloaded into the electronic control unit of our student type formula vehicle called Flash V6 which was designed and developed by a team of students, the ZUST ATTACKER Team.

Guidance and control for autonomous emergency landing of the rotorcraft using the incremental backstepping controller in 3-dimensional terrain environments

This paper treats the approach to safe emergency landing for an autonomous rotorcraft in 3-dimensional terrain environments. The autorotation flight that the rotorcraft flies without the power supply is dangerous and needs the high-skilled control ability of the pilot. Ordinary, this flight is divided into three phases: Entry, Steady-Descent, and Flare phase. The emergency landing trajectory is generated by imitating each phase. The Trajectory optimization method using the high-fidelity math model is applied to the entry and flare phase to consider the complex dynamics of the rotorcraft. To generate a steady-descent phase trajectory without obstacle collisions, one of the path planning methods, the improved Rapidly-exploring Random Tree algorithm is used. The Incremental Backstepping controller is adopted as the trajectory tracking controller. Simulation is conducted in the One Engine Inoperative condition. Through the simulation, it is shown that the method proposed in this paper guarantees the safe landing of the rotorcraft in an emergency like engine failure.

Oblique Quasi-kink Modes in Solar Coronal Slabs Embedded in an Asymmetric Magnetic Environment: Resonant Damping, Phase and Group Diagrams

There has been considerable interest in magnetoacoustic waves in static, straight, field-aligned, 1D equilibria where the exteriors of a magnetic slab are different between the two sides. We focus on trapped, transverse fundamental, oblique quasi-kink modes in pressureless setups, where the density varies continuously from a uniform interior (with density ρ i) to a uniform exterior on either side (with density ρ L or ρ R), assuming ρ L ≤ ρ R ≤ ρ i. The continuous structuring and oblique propagation make our study new, relative to pertinent studies, and lead to wave damping via the Alfvén resonance. We compute resonantly damped quasi-kink modes as resistive eigenmodes, and isolate the effects of system asymmetry by varying ρ i/ρ R from the “Fully Symmetric” (ρ i/ρ R = ρ i/ρ L) to the “Fully Asymmetric” limit (ρ i/ρ R = 1). We find that the damping rates possess a nonmonotonic ρ i/ρ R-dependence as a result of the difference between the two Alfvén continua, and resonant absorption occurs only in one continuum when ρ i/ρ R is below some threshold. We also find that the system asymmetry results in two qualitatively different regimes for the phase and group diagrams. The phase and group trajectories lie essentially on the same side (different sides) relative to the equilibrium magnetic field when the configuration is not far from a “Fully Asymmetric” (“Fully Symmetric”) one. Our numerical results are understood by making analytical progress in the thin-boundary limit, and discussed for imaging observations of axial standing modes and impulsively excited wavetrains.

Phase portrait‐based stability region estimation for grid‐connected VSC with PLL

Here, the stability region of grid-connected VSC with phase locked loop (PLL) is estimated. First, the conservative stability region is derived via the classical Lyapunov method. Then an energy function is constructed as the general stable condition for the VSC system. Based on the constructed energy function, two estimation methods of the system stability region by approximation of phase trajectory are proposed. The stability regions by the proposed methods are less conservative than that by the classical Lyapunov method. A stability evaluation function for the initial states of the VSC system is further proposed based on the estimated stability region. Time-domain simulations verify the correctness of the proposed methods and the effectiveness of the stability evaluation function.

Stable and unstable curves in vehicle three-dimensional state space

In the field of vehicle system dynamics, revealing the dynamic characteristics of nonlinear vehicle models with high degrees of freedom is a key point in current research. In the classic 2-DOF (degrees of freedom) model, the dynamics is analysed and represented in two-dimensional state space. However, it is necessary to reveal the three-dimensional state characteristics of the system when analysing high-DOF vehicle models. The concept of equilibrium points in two-dimensional space will be extended to curves in three-dimensional space, including stable curves and unstable curves, which can qualitatively reveal the evolvement characteristics of the system under different control parameters. In addition, because the dissipation of energy method can quantitatively reveal the global dynamic characteristics of the vehicle, this paper combines the (un)stable curves in the three-dimensional space with dissipation of energy to better analyse the global dynamics characteristics and mutually verify the correctness of conclusions. In this paper, first, the connection between (un)stable curves and region boundary is established. Second, the theoretical analysis of relationship between dissipation of energy and phase trajectories convergence characteristics is perfected. Third, the static and dynamic characteristics of vehicle system are analysed. Therefore, this paper proposed the concept of stable and unstable curves to intuitively reveal the global dynamics characteristics and system evolvement characteristics in three-dimensional state space.

Synchronization transitions in a discrete memristor-coupled bi-neuron model

When synaptic connection is created to couple two neurons, the electromagnetic induction current is unavoidably induced, which can be imitated by a flux-controlled memristor. To construct a discrete model of coupled neurons, a discrete memristor is used to couple two Rulkov maps bidirectionally and a discrete synapse is obtained. This discrete bi-neuron model composed of two map neurons has infinitely many fixed points. The synchronization behaviors are detected by calculating normalized synchronization error, and the memristive effects and dynamical behaviors are investigated by using bifurcation diagrams and phase trajectories. The results show that the discrete bi-neuron model can generate complete and lag synchronization behaviors, and the transitions of spiking-bursting firings and synchronizations are strongly affected by the coupling strength and initial state of the coupled channel embedded with memristor. In particular, the synchronization transitions via memristor coupling demonstrate the coexistence of multiple firing patterns of the discrete bi-neuron model and manifest the realization of synchronous control of coupled neurons. All these meaningful phenomena are verified by digital hardware experiments.

A Non-Flat Terrain Biped Gait Planner Based on DIRCON.

Various constraints exist in bipedal movement. Due to the natural ability of effectively handling constraints, trajectory optimization has become one of the mainstream methods in biped gait planning, especially when constraints become much more complex on non-flat terrain. In this paper, we propose a multi-modal biped gait planner based on DIRCON, which can generate different gaits for multiple, non-flat terrains. Firstly, a virtual knot is designed to model the state transitions when the swing foot contacts terrain and is inserted as the first knot of the target trajectory of the current support phase. Thus, a complete gait or multi-modal gaits sequence can be generated at one time. Then, slacked complementary constraints, which can avoid undesired trajectories, are elaborated to describe the coupling relationships between terrain information and bipedal motion for trajectory optimization based gait planning. The concrete form of the gait planner is also delivered. Finally, we verify the performance of the planner, as well as the structural design of our newly designed biped robot in CoppeliaSim through flat terrain walking, stairs terrain walking and quincuncial piles walking. The three experiments show that the gaits planned by the proposed planner can enable the robot to walk stably over non-flat terrains, even through simple PD control.

Exploring Physical Activity During the Discharge Transition Phase in People With Acquired Brain Injury—An Observational Study

ObjectiveTo explore physical activity trajectories during the discharge transition phase after in-hospital rehabilitation after acquired brain injury (ABI). DesignA cross-sectional observational study. SettingTransition from an in-hospital rehabilitation center to community-based living. ParticipantsIndependently walking patients with ABI (n=10) who were ready for discharge. InterventionsNot applicable. Main Outcome MeasuresTwo weeks of physically active time continuously monitored with an accelerometer and classified by a machine learning algorithm summed as daily average and total active time for each participant and classified into standing, walking, running, bike riding, stair climbing, ambulation, and sedentary time. Physical activity trajectories showing the total daily active time for all participants were inspected before and after discharge, and the average active time per participant was plotted against self-reported scores of potentially explanatory factors. ResultsAverage total physically active time was 5:49 hours (range 4:26-7:13 hours). Average daily physically active time for participants appeared to be related to functional independence measure sub scores, fatigue, and pre-morbid physical activity level. Individual physical activity trajectories showed a decreased walking activity after discharge, which increased again after 1-2 days. ConclusionsDaily total physically active time among participants was higher than expected. Factors expectedly related to physical activity trajectories in the discharge transition phase were explored and showed some relation to functional scores.

LEGGED ROBOT LOCOMOTION IN RESISTIVE TERRAIN: A COMPARISON OF TWO METHODS

Every day new technology appears. In the field of legged robots, it is not otherwise. LIDAR vision, artificial intelligence, computing power and new drives help to improve the state of legged robots. One of the unsolved problems is still terrain navigation, such as locomotion in resistive terrain. To determine the correct locomotion, research must be carried out. In this paper, we compare two different situations, where a six-legged robot walks through variable resistive terrain with different gait in the first one and with different leg trajectories in the swing phase in the second one.

Terminal Adaptive Guidance for Autonomous Hypersonic Strike Weapons via Reinforcement Metalearning

An adaptive guidance system suitable for the terminal phase trajectory of a hypersonic strike weapon is optimized using reinforcement meta learning. The guidance system maps observations directly to commanded bank angle, angle of attack, and sideslip angle rates. Importantly, the observations are directly measurable from radar seeker outputs with minimal processing. The optimization framework implements a shaping reward that minimizes the line-of-sight rotation rate, with a terminal reward given if the agent satisfies path constraints and meets terminal accuracy and speed criteria. This paper shows that the guidance system can adapt to off-nominal flight conditions, including perturbation of aerodynamic coefficient parameters, actuator failure scenarios, sensor scale factor errors, and actuator lag, while satisfying heating rate, dynamic pressure, and load path constraints, as well as a minimum impact speed constraint. This paper demonstrates precision strike capability against a maneuvering ground target and the ability to divert to a new target, the latter being important to maximize strike effectiveness for a group of hypersonic strike weapons. Moreover, this paper demonstrates a threat evasion strategy against interceptors with limited midcourse correction capability, where the hypersonic strike weapon implements multiple diverts to alternate targets, with the last divert to the actual target.

Influence of noise on wear fault diagnosis based on recurrence plot

Recurrence plot (RP) and recurrence quantification analysis (RQA) have been widely applied in fault diagnosis of tribo-systems. The influence of noise on the RP, RQA quantifiers and RP-based wear fault diagnosis was studied by analyzing theoretical signals and vibration signals. With the decrease of signal-to-noise ratio (SNR), the vertical and diagonal structures of RP of noisy Lorenz and Rössler signals are discretized into isolated points, and RQA quantifiers decrease gradually. This effect is due to the interference of noise on the phase trajectory of original signals. Noise makes some phase points escape the hypersphere, which leads to the disappearance of recurrence relationship. Recurrence plot-convolutional neural network (RP-CNN) can diagnose wear forms with 99.2% accuracy by analyzing the denoised vibration signals, which is 2.2% higher than that without denoising. The results will help to improve the reliability and accuracy of recurrence analysis applied in fault diagnosis of tribo-systems.

Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms

A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes into account the influence of heredity and is described using derivative fractional orders. The article investigates the Selkov fractional dynamic model using the Adams–Bashforth–Moulton numerical method, constructs oscillograms and phase trajectories, and studies the equilibrium points. Based on the spectra of the maximum Lyapunov exponents, it is shown that in the fractional dynamic model there can be relaxation and damped oscillations.

Analysis of resonance and bifurcation in a fractional order nonlinear Duffing system

In this paper, resonance and bifurcation of a nonlinear damped fractional‐order Duffing system are studied. The amplitude and phase of the steady‐state response of system are obtained by means of the average method, the stability is analyzed, and then the amplitude‐frequency characteristic curves of the system with different parameters are drawn based on the implicit function equation of amplitude. Grunwald–Letnikov fractional derivative is used to discretize the system numerically, the response curve and phase trajectory of the system under different parameters are obtained; meanwhile, the dynamic behavior is analyzed. The bifurcation and saddle bifurcation behavior of the system is studied through numerical simulation with different parameters.