Second-order Dynamics Research Articles

Optimal closed-loop control for different generation scenarios

This article studies the stability of the model posed by the second-order dynamics of the synchronous machine connected to an infinite busbar. A semi-defined programming problem is formulated to obtain a closed-loop controller that stabilizes the state variables. Given that initially the matrix that determines the behavior of the dynamics of said system presents asymptotically unstable eigenvalues, they are redirected in such a way that when faced with variations in electrical power at different instants of time, the behavior is asymptotically stable. Based on the above, we will determine if it is necessary to add semi-defined type constraints to complete a semi-defined problem that will be seen as a convex optimization problem, thus guaranteeing a global optimum within the feasible region; and showing how the stability of the variation of the state variables can be achieved for two generation scenarios.

A stochastic SPOD-Galerkin model for broadband turbulent flows

The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number $M=0.9$ and Reynolds number of $Re_D\approx 10^6$.

Sasakian Structure Associated with a Second-Order ODE and Hamiltonian Dynamical Systems

We define a contact metric structure on the manifold corresponding to a second order ordinary differential equation $d^2y/dx^2=f(x,y,y')$ and show that the contact metric structure is Sasakian if and only if the 1-form $\frac{1}{2}(dp-fdx)$ defines a Poisson structure. We consider a Hamiltonian dynamical system defined by this Poisson structure and show that the Hamiltonian vector field, which is a multiple of the Reeb vector field, admits a compatible bi-Hamiltonian structure for which $f$ can be regarded as a Hamiltonian function. As a particular case, we give a compatible bi-Hamiltonian structure of the Reeb vector field such that the structure equations correspond to the Maurer-Cartan equations of an invariant coframe on the Heisenberg group and the independent variable plays the role of a Hamiltonian function. We also show that the first Chern class of the normal bundle of an integral curve of a multiple of the Reeb vector field vanishes iff $f_x+ff_p = \Psi (x)$ for some $\Psi$.

An unconditionally stable time integration method with controllable dissipation for second-order nonlinear dynamics

An unconditionally stable time integration method with controllable dissipation for second-order nonlinear dynamics

Accelerated Diffusion-Based Sampling by the Non-Reversible Dynamics with Skew-Symmetric Matrices

Langevin dynamics (LD) has been extensively studied theoretically and practically as a basic sampling technique. Recently, the incorporation of non-reversible dynamics into LD is attracting attention because it accelerates the mixing speed of LD. Popular choices for non-reversible dynamics include underdamped Langevin dynamics (ULD), which uses second-order dynamics and perturbations with skew-symmetric matrices. Although ULD has been widely used in practice, the application of skew acceleration is limited although it is expected to show superior performance theoretically. Current work lacks a theoretical understanding of issues that are important to practitioners, including the selection criteria for skew-symmetric matrices, quantitative evaluations of acceleration, and the large memory cost of storing skew matrices. In this study, we theoretically and numerically clarify these problems by analyzing acceleration focusing on how the skew-symmetric matrix perturbs the Hessian matrix of potential functions. We also present a practical algorithm that accelerates the standard LD and ULD, which uses novel memory-efficient skew-symmetric matrices under parallel-chain Monte Carlo settings.

Optimal consensus control for unknown second-order multi-agent systems: Using model-free reinforcement learning method

In this paper, the optimal consensus control problem with second-order dynamics consisting of leader and follower agents is discussed. For optimal consensus problem, the optimal control policies rely on algebraic Riccati equations (AREs) equation, which are difficult to solve. Furthermore, both the follower agents’ and the leader agent’s dynamics are assumed to be completely unknown. As the consensus problem based on feedback control, the second-order discrete-time multi-agent systems (DT-MASs) model with directed topology is formulated to the optimal tracking control problem via online deep reinforcement learning method. Based on graph theory, matrix analysis, Lyapunov stability, deep learning and optimal control, the optimality of value function and the stability of the consensus error systems for the unknown second-order systems are guaranteed for each agent. The results show that the designed policy iteration algorithm not only stabilizes the distributed dynamic systems, but also makes all agents’ position and velocity states reach consensus, respectively. Finally, the correctness of our theoretical results is illustrated under two numerical simulations based on the designing model-free actor-critic networks.

Mitigation strategies for airborne disease transmission in orchestras using computational fluid dynamics.

The COVID-19 pandemic forced performing arts groups to cancel shows and entire seasons due to safety concerns for the audience and performers. It is unclear to what extent aerosols generated by wind instruments contribute to exposure because their fate is dependent on the airflow onstage. We use transient, second-order accurate computational fluid dynamics (CFD) simulations and quantitative microbial risk assessment to estimate aerosol concentrations and the associated risk and assess strategies to mitigate exposure in two distinct concert venues. Mitigation strategies involved rearranging musicians and altering the airflow by changing HVAC settings, opening doors, and introducing flow-directing geometries. Our results indicate that the proposed mitigation strategies can reduce aerosol concentrations in the breathing zone by a factor of 100, corresponding to a similar decrease in the probability of infection.

Three-dimensional terminal angle constraint finite-time dual-layer guidance law with autopilot dynamics

Considering the problem of intercepting a target at desired terminal angles in the three-dimensional (3D) space, this paper proposes a finite-time dual-layer guidance law with consideration of the second-order autopilot dynamics. The proposed guidance law owns a cascaded structure, which is divided into an outer system and an inner system. To achieve the finite-time convergence, the outer and inner controllers are developed based on the nonsingular terminal sliding mode control. With the aid of the command filter, which can compute the first and the second derivatives of the virtual signal simultaneously, the design procedure of the fourth-order guidance system is simplified into two steps. Moreover, extended state observers are used to estimate the unknown target maneuver and the acceleration derivative of the missile, which facilitates the real implementation. Simulation results verify the performance of the proposed guidance law.

Distributed Algorithm Design for Resource Allocation Problems of Second-Order Multiagent Systems Over Weight-Balanced Digraphs

This paper studies two distributed resource allocation problems of second-order systems over weight-balanced communication networks. In the first problem, the decisions of agents are coupled by network resource constraints, and in the second problem, the decisions of agents are constrained by local constraints and network resource constraints. Compared with many existing resource allocation problems, the formulation involves the dynamics of agents. The second-order dynamics of agents induce the difficult in algorithm design and analysis, since the decisions of agents could not be directly decided by their control inputs. In order to optimally allocate the network resource, two distributed algorithms are designed via state feedback and gradient descent for the two problems, respectively. Besides, the convergence of the two algorithms are analyzed. By the two algorithms, the second-order agents converge to the optimal allocation of the two problems, respectively. Finally, two examples about economic dispatch problems verify the two algorithms.

Nonlinear stochastic modelling with Langevin regression.

Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker–Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.

Distributed Average Tracking Problem Under Directed Networks: A Distributed Estimator-Based Design

This article considers the distributed average tracking (DAT) problem that a group of agents aims to track the average of local reference signals. The communication network is strongly connected but not required to be weight balanced. A framework of distributed estimator-based algorithm design without any initialization requirement is presented. For agents with nominal first-order (FO) dynamics, a class of distributed estimators is proposed to estimate the average of local reference signals within fixed time, with which each agent finally achieves the DAT within fixed time. For agents with second-order dynamics subject to modeling uncertainty, unmodeled dynamics, as well as external disturbances, a class of distributed estimator is proposed to estimate the average of local reference signals within fixed time, and then a local disturbance-observer-based control protocol is proposed for each agent to achieve DAT asymptotically. Different from most of the existing DAT results under general directed networks that DAT error can only be made globally ultimately bounded, the exact DAT can be achieved within fixed time or asymptotically here. Further, the idea of distributed estimator is applied to solve a class of distributed optimization problems within finite time. Finally, two simulation examples are given to show the effectiveness of the theoretical results.

From chiral kinetic theory to relativistic viscous spin hydrodynamics

In this work, we start with chiral kinetic theory and construct the spin hydrodynamic framework for a chiral spinor system. Using the 14-moment expansion formalism, we obtain the equations of motion of second-order dissipative relativistic fluid dynamics with non-trivial spin polarization density. In a chiral spinor system, the spin alignment effect could be treated in the same framework as the Chiral Vortical Effect (CVE). However, the quantum corrections due to fluid vorticity induce not only CVE terms in the vector/axial charge currents but also corrections to the stress tensor. In this framework, viscous corrections to the hadron spin polarization are self-consistently obtained, which will be important for the precise prediction of the polarization rate for the observed hadrons, e.g. $\Lambda$-hyperon.

Fixed-Time Cooperative Behavioral Control for Networked Autonomous Agents With Second-Order Nonlinear Dynamics.

In this article, we investigate the fixed-time behavioral control problem for a team of second-order nonlinear agents, aiming to achieve a desired formation with collision/obstacle avoidance. In the proposed approach, the two behaviors(tasks) for each agent are prioritized and integrated via the framework of the null-space-based behavioral projection, leading to a desired merged velocity that guarantees the fixed-time convergence of task errors. To track this desired velocity, we design a fixed-time sliding-mode controller for each agent with state-independent adaptive gains, which provides a fixed-time convergence of the tracking error. The control scheme is implemented in a distributed manner, where each agent only acquires information from its neighbors in the network. Moreover, we adopt an online learning algorithm to improve the robustness of the closed system with respect to uncertainties/disturbances. Finally, simulation results are provided to show the effectiveness of the proposed approach.

An improved Kirkwood–Bethe model for calculating near-field shockwave propagation of underwater explosions

To calculate the near-field shockwave propagation of underwater explosions for different explosives quickly and accurately, an improved calculation model, based on the Kirkwood–Bethe theory, is proposed. Based on the detonation theory and shock jump conditions, the model establishes initial equilibrium conditions and an initial shockwave-front state of the explosion bubble interface. By incorporating a second-order Mach-precision bubble dynamics equation, the model determines the physical parameters and enthalpy change functions at the initial expanding stage in real time. By solving the isentropic flow of the enthalpy change function G at varying delay times, a functional relation was established between the enthalpy change function and the pressure at arbitrary flow points and times. The model obtained the near-field shockwave-front peak-pressure spatial distributions of underwater explosions and the pressure decay time constants at arbitrary flow points. The results indicated that the proposed method can quickly and accurately determine the near-field shockwave propagation of underwater explosions for different explosives, with satisfactory agreement with experimental data. The proposed method relates the explosive detonation, explosion bubble expansion, and shockwave propagation, thus connecting the explosive parameters with the shockwave front state parameters.

Second-order Saddle Dynamics in Isomerization Reaction

The role of second-order saddle in the isomerization dynamics was investigated by considering the $$E-Z$$ isomerization of guanidine. The potential energy profile for the reaction was mapped using the ab initio wavefunction method. The isomerization path involved a torsional motion about the imine (C-N) bond in a clockwise or an anticlockwise fashion resulting in two degenerate transition states corresponding to a barrier of 23.67 kcal/mol. An alternative energetically favorable path ( $$\sim$$ 1 kcal/mol higher than the transition states) by an in-plane motion of the imine (N-H) bond via a second-order saddle point on the potential energy surface was also obtained. The dynamics of the isomerization was investigated by ab initio classical trajectory simulations. The trajectories reveal that isomerization happens via the transition states as well as the second-order saddle. The dynamics was found to be nonstatistical with trajectories exhibiting recrossing and the higher energy second-order saddle pathway preferred over the traditional transition state pathway. Wavelet based time-frequency analysis of internal coordinates indicate regular dynamics and existence of long-lived quasi-periodic trajectories in the phase space.

Posture Dynamic Modeling and Stability Analysis of a Magnetic Driven Dual-Spin Spherical Capsule Robot.

In order to realize the intervention operation in the unstructured and ample environments such as stomach and colon, a dual-spin spherical capsule robot (DSCR) driven by pure magnetic torque generated by the universal rotating magnetic field (URMF) is proposed. The coupled magnetic torque, the viscoelastic friction torque, and the gravity torque were analyzed. Furthermore, the posture dynamic model describing the electric-magnetic-mechanical-liquid coupling dynamic behavior of the DSCR in the gastrointestinal (GI) tract was established. This model is a second-order periodic variable coefficient dynamics equation, which should be regarded as an extension of the Lagrange case for the dual-spin body system under the fixed-point motion, since the external torques were applied. Based on the Floquet–Lyapunov theory, the stability domain of the DSCR for the asymptotically stable motion and periodic motion were obtained by investigating the influence of the angular velocity of the URMF, the magnetic induction intensity, and the centroid deviation. Research results show that the DSCR can realize three kinds of motion, which are asymptotically stable motion, periodic motion, and chaotic motion, according to the distribution of the system characteristic multipliers. Moreover, the posture stability of the DSCR can be improved by increasing the angular velocity of the URMF and reducing the magnetic induction intensity.

Secure and privacy preserving consensus for second-order systems based on Paillier encryption

This paper aims at secure and privacy-preserving consensus algorithms of networked systems. Due to the technical challenges behind decentralized design of such algorithms, the existing results are mainly restricted to a network of systems with simplest first-order dynamics. Like many other control problems, breakthrough of the gap between first-order dynamics and higher-order ones demands for more advanced technical developments. In this paper, we explore a Paillier encryption based average consensus algorithm for a network of systems with second-order dynamics, with randomness added to network weights. The conditions for privacy-preserving, especially depending on consensus rate, are thoroughly studied with theoretical analysis and numerical verification.

Second-Order Dynamics with Hessian-Driven Damping for Linearly Constrained Convex Minimization

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 5 March 2020Accepted: 14 June 2021Published online: 18 October 2021Keywordsdissipative inertial dynamics, Hessian-driven damping, Lyapunov analysis, asymptotic properties, Bregman distance, convex minimizationAMS Subject Headings37N40, 46N10, 49M30, 65K05, 90C25Publication DataISSN (print): 0363-0129ISSN (online): 1095-7138Publisher: Society for Industrial and Applied MathematicsCODEN: sjcodc

MPPT Control Paradigms for PMSG-WECS: A Synergistic Control Strategy With Gain-Scheduled Sliding Mode Observer

The wind energy conversion system (WECS) frequently operates under highly stochastic and unpredictable wind speed. Thus, the maximum power (MP) extraction, in such unpredictable scenarios, becomes a very appealing control objective. This paper focuses on the extraction of MP from a variable-speed WECSs, which further drive a permanent magnet synchronous generator (PMSG). At the first stage, the dynamical model of the PMSG is converted into Bronwsky form, which is comprised of both visible and internal dynamics. The first-order internal dynamics are proved stable, i.e., the system is minimum phase. The control of the second-order visible dynamics, to track a varying profile of the wind speed, is the main consideration. This job is accomplished via Backstepping-based robust Sliding Mode Control (SMC) strategy. Since, a conventional SMC suffers from inherited chattering issue, thus, the discontinuous control component in SMC scheme is replaced with super-twisting and real-twisting control laws. In addition, the immeasurable states’ information are estimated via gain-scheduled sliding mode observer. The overall closed-loop stability is ensured by analysing the quasi-linear form, which supports the separation principle. The theoretical claims are authenticated via simulation results, which are performed in Matlab/Simulink environment. Besides, a comparative analysis is carried out with the standard literature results, which quite obviously outshines the investigated control approaches in terms of varying wind profile tracking and the corresponding control input.

On Attitude Tracking Control With Communication-Saving: An Integrated Quantized and Event-Based Scheme

A novel integrated quantized- and event-based control (IQEC) scheme for intra-spacecraft with communication-saving ability is proposed to address the attitude tracking control problem. The IQEC scheme reduces the control updating frequency and the data length per transmission based on the event-based control and quantized communication techniques, thus reducing the system communication occupation. By suitable control system configuration, the purpose of communication-saving is achieved, from sensors to the computing unit and from the computing unit to actuators. The proposed algorithm's effectiveness is verified via numerical simulation that uses a general actuator model with second-order dynamics.