First-order System Research Articles

Automatic control of constant temperature and humidity in building air conditioning systems based on frequency domain analysis

How to solve their automatic control of constant temperature and humidity gradually becomes a research hotspot as the continuous upgrading of air conditioning systems. This study aims to optimize the traditional proportional-integral-differential controller for improvement to solve the time-delay instability phenomenon in temperature and humidity control. The objective of this study is to optimize existing proportional-integral-differential controllers to improve the time-delay instability problem that is common in temperature and humidity control. Firstly, it treats the controlled object as a first-order and second-order system with time-delay characteristics. Next, the Smith predictor controller is generalized equivalent to ensure that the equivalent system does not contain time-delay. Finally, an analysis of the first-order and second-order closed-loop control system is conducted by combining Smith predictive controller and proportional-integral-differential controller. The system achieves the goal of automatic control of constant temperature and humidity by adjusting the control parameters. The experiment showcased that the temperature control time of the proposed control scheme under first-order and second-order time-delays was 16 s and 3 s, respectively. Meanwhile, the humidity control time was 14 s and 13 s, respectively. In practical applications, the proposed control scheme achieved good control effects in all four seasons. This indicates that the controller designed in this study possesses good control performance. It also can achieve the goal of constant temperature and humidity control. This can provide technical support for the automation control of air conditioning systems.

Nonautonomous spectral submanifolds for model reduction of nonlinear mechanical systems under parametric resonance.

We use the recent theory of spectral submanifolds (SSMs) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization of SSMs and their reduced dynamics. We provide these results for both general first-order and second-order mechanical systems under periodic and quasiperiodic excitation using a multi-index based approach, thereby optimizing memory requirements and the computational procedure. We further provide theoretical results that simplify the SSM parametrization for general second-order dynamical systems. More practically, we show how the reduced dynamics on the SSM can be used to extract the resonance tongues and the forced response around the principal resonances in parametrically excited systems. In the case of two-dimensional SSMs, we formulate explicit expressions for computing the steady-state response as the zero-level set of a two-dimensional function for systems that are subject to external as well as parametric excitation. This allows us to parallelize the computation of the forced response over the range of excitation frequencies. We demonstrate our results on several examples of varying complexity, including finite-element-type examples of mechanical systems. Furthermore, we provide an open-source implementation of all these results in the software package SSMTool.

System identification based on characteristic curves: a mathematical connection between power series and Fourier analysis for first-order nonlinear systems

System identification based on characteristic curves: a mathematical connection between power series and Fourier analysis for first-order nonlinear systems

Nanosecond-level second-order characteristics in dynamic calibration of thin film thermocouples by short-pulse laser

In this study, we explore the dynamic response of thin-film thermocouples (TFTCs) to transient temperature changes, emphasizing their nanosecond response capabilities. Traditionally, TFTCs are modeled as first-order systems. By employing magnetron sputtering, we have prepared NiCr/NiSi TFTCs with a novel integrated lead method. A 7.6 ns short-pulse laser served as the heat source, capturing the TFTCs’ transient response with a high-speed collector at 200 M/s. Unexpectedly, the TFTCs’ response curves exhibited oscillations at high acquisition rates. Through frequency response analysis, we have established a pulse response model for the TFTCs that is highly consistent with experimental results. For the first time, we confirmed the TFTCs’ second-order dynamic characteristics. Furthermore, our findings that various substrate materials and lead methods impact the damping characteristics of TFTCs led us to conduct pulsed laser damage experiments. These experiments revealed a correlation between damping properties and the extent of damage.

Observers for hyperbolic systems with multiple delays in the nonlocal boundary condition and its application to secure image encryption

In this article, we propose a step-by-step observer design for a first-order linear hyperbolic system with multiple delays in the nonlocal boundary condition. In the proposed approach inspired by the backstepping methodology, the observer gains are obtained following seven successive steps. Next, we present the application of this observer design in the context of image encryption. We consider a system where a local nonlinear term causing a chaotic vibration is added to the nonlocal boundary condition with time lags. A synchronization system for this chaotic system can be constructed using the same observer design method. The chaotic states generated by both systems can be used to encrypt and decrypt image data. The time lags, and weight functions included in the nonlocal boundary condition play the role of common encryption keys. By considering a system that includes arbitrarily many delays, this approach allows for a significant increase in the number of common encryption keys compared to conventional methods, resulting in greatly improved communication security.

Fourth-Order Accurate Compact Scheme for First-Order Maxwell’s Equations

We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell’s equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-order elliptic equations. We develop compatible boundary conditions for these elliptic equations while maintaining a compact stencil. The proposed scheme is compared computationally with a non-compact scheme and with a convolutional dispersion relation preserving (DRP) scheme.

A fractional-order multiple-model type-2 fuzzy control for interconnected power systems incorporating renewable energies and demand response

Frequency regulation in Multi-region Interconnected Power Systems (MIPS), incorporating wind turbine systems, energy storage units, and demand response, is a challenging control problem. The problem involves maintaining grid stability, integrating variable renewable energy sources, enhancing grid resilience, optimizing energy storage and demand response capabilities, and ensuring regulatory compliance. Effective frequency regulation is a key problem for reliable and sustainable power system operation. In this paper, complex and uncertain dynamics in various components of a MIPS are modeled using multiple first-order dynamic fractional-order Type-2 Fuzzy Logic Systems (T2-FLSs). The models are evaluated, and the best possible dynamic model is chosen. With the best possible model, an optimal controller is designed. The stability and optimality analysis are presented through a Linear Matrix Inequality (LMI) approach. The adaptive laws of T2-FLSs are derived such that some LMI-based conditions are satisfied. The designed controller does not depend on the dynamics of MIPS. The uncertainties of time-varying load, wind energy, and solar power are modeled using T2-FLSs. The suggested LMI technique presents adaptation laws for T2-FLSs to ensure stability in the presage of natural disturbances and errors. The designed scheme is validated by applying to a practical 39-bus IEEE test system that includes the wind farms, demand response, and energy storage systems. The simulation results under various conditions verify the usefulness of the suggested controller. The comparisons with conventional controllers demonstrate that the suggested approach is more effective under uncertainties and natural perturbations.

Precise integration boundary element method for solving nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity

The precise integration boundary element method (PIBEM) is used to solve nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity in this article. At first, a boundary-domain integral equation can be obtained by using the fundamental solution for steady linear heat conduction problems. Secondly, the domain integrals are converted into boundary integrals by using the radial integration method to get a pure boundary integral equation, which can retain the advantage of dimension reduction of the boundary element method. Then, after discretization, a first-order nonlinear differential equation system in time is obtained, and the precise integration method with predictor-corrector technique is used to solve the system of nonlinear equations. In the end, several numerical examples are presented to verify the accuracy and stability of the presented method. The results obtained by the presented method are less affected by the time step size and satisfactory results can be obtained even for a large time step size.

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This article addresses the bifurcation characteristics and vibration reduction of a 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2$$\\end{document}-DOF dynamical system simulating the nonlinear oscillation of an asymmetric rotor model subjected to simultaneous multiparametric and external excitations. To suppress the system's vibrations, two 1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/2$$\\end{document}-DOF active dampers are attached to the system in linear and cubic nonlinear forms via a magnetic coupling actuator. The closed-loop system model is derived as two differential equations with multi-control terms, including cubic, quantic, and septic, coupled nonlinearly to two first-order systems. Applying perturbation theory, the system model is solved, and the autonomous system describing the closed-loop slow-flow dynamics is obtained. Through numerical algorithms, the motion bifurcation is analyzed using various tools such as 2D and 3D bifurcation diagrams, two-parameter stability charts, basins of attraction, orbit plots, and time response profiles. The analytical investigations confirm that the uncontrolled model behaves like a hardening Duffing oscillator with multistability characteristics, displaying simultaneous mono-stable, bi-stable, tri-stable, or quadri-stable periodic oscillations depending on both the asymmetric nonlinearities and angular velocity. Subsequently, the influence of different control parameters is analyzed to determine the threshold between mono and multi-stability conditions. Finally, optimal control parameters are designed to eliminate multistability characteristics and achieve minimum and safe vibration levels.

Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain

We present a gradient-based calibration algorithm to identify the system matrices of a linear port-Hamiltonian system from given input–output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal control with ordinary differential equations and define a constrained optimization problem. The input-to-state stability is discussed which is the key step towards the existence of optimal controls. Further, we derive the first-order optimality system taking into account the port-Hamiltonian structure. Indeed, the proposed method preserves the skew symmetry and positive (semi)-definiteness of the system matrices throughout the optimization iterations. Numerical results with perturbed and unperturbed synthetic data, as well as an example from the PHS benchmark collection [17] demonstrate the feasibility of the approach.

Dynamic response of a wind turbine wake subjected to surge and heave step motions under different inflow conditions

The development of floating offshore wind turbines poses new challenges since the floating platform introduces complex dynamics in the wind turbine wake. These wake dynamics are intricately tied to the advection velocity, referring to the velocity of the downstream propagation of the air flow, and used in the context of wind farm modelling. The present article investigates the far-wake dynamic response of a wind turbine model subjected to heave (up-down translation) and surge (fore-aft translation) step motions under two distinct inflow conditions. Wind tunnel experiments were conducted with hot-wires in a realistic turbulent inflow and a low shear and no ground effect inflow, achieved by varying the hub height of the wind turbine model in the atmospheric boundary layer developed in the test section. The results show that the dynamic response of the wake under the low shear and no ground effect inflow conditions aligns with a second-order system with the presence of undershoots and overshoots. In contrast, under realistic conditions, it appears like a first-order system with undershoots and overshoots less evident in most cases. Despite these variations the determined advection velocity remains roughly the same and consistent with the literature for both heave and surge step motions, regardless of the inflow conditions.

New Adaptive Super-Twisting Extended-State Observer-Based Sliding Mode Scheme with Application to FOWT Pitch Control

This paper details the transformation of the velocity or position-tracking problem of a class of uncertain systems using finite time stability control for first-order uncertain systems. A new composite extended-state observer sliding mode (ESOSM) scheme is proposed, which includes an adaptive super-twisting-like ESO and an adaptive super-twisting controller. The adaptive super-twisting controller is implemented through a barrier function-based second-order sliding mode algorithm. To further reduce control chattering and improve control performance, the adaptive super-twisting-like ESO, which employs high-order terms in the super-twisting algorithm to accelerate convergence, is designed to observe the lumped uncertainty in real time. The advantages of the proposed scheme are verified by a numerical example and application with regard to floating offshore wind turbine (FOWT) pitch control. Compared with proportional integral (PI) and adaptive super-twisting sliding mode (ASTSM) schemes, better results are obtained in velocity tracking and fatigue load suppression. For the FOWT pitch control application, the platform roll, pitch, and yaw are decreased by 3%, 2%, and 4%, respectively, compared to the PI scheme at an average turbulent wind speed of 17 m/s and turbulence intensity of 17.27%.

Theoretico-experimental analysis of bistability in the oscillatory response of a TaOx ReRAM to pulse train stimuli

Fading memory is the capability of a physical system to approach a unique asymptotic behaviour, irrespective of the initial conditions, when stimulated by an input from a certain class. Standard stimuli from the AC periodic class typically induce fading memory effects in non-volatile memristors, as uncovered for the first time back in 2016. Very recently, a deep investigation of resistance switching phenomena in a TaOx resistive random access memory cell revealed the capability of the nano-device to exhibit one of two possible oscillatory behaviours, depending upon the initial condition, when subject to a particular periodic excitation. This interesting finding was, however, left unexplained. Bistability is the simplest form of local fading memory. In a system, endowed with local fading memory under a given stimulus, the initial condition does not affect the long-term behaviour of the state as long as it is drawn from the basin of attraction of either of the distinct coexisting state-space attractors (two limit cycles for the periodically forced memristor acting as a bistable oscillator). Here, the history of the system, encoded in the initial condition, is, thus, erasable only locally through ad hoc stimulation. Motivated by the discovery of local history erase effects in our resistive random access memory cell, this study applies a powerful system-theoretic tool, enabling the analysis of the response of first-order systems to square pulse train-based periodic stimuli, known as the time-average state dynamic route, to an accurate physics-based mathematical model, earlier fitted to the nano-device, to determine a strategy for specifying the parameters of an excitation signal, consisting of the sequence of two square pulses of opposite polarity per period so as to induce various forms of monostability or multistability in the non-volatile memristor. In particular, as an absolute novelty in the literature, experimental measurements validate the theoretical prediction on the capability of the device to operate as one of two distinct oscillators, depending upon the initial condition, under a specific pulse train excitation signal. The coexistence of multiple oscillatory operating modes in the periodically forced resistive random access memory cell, an example par excellence of their unique non-linear dynamics, may inspire the development and circuit implementation of novel sensing and mem-computing paradigms.

Pinning Group Consensus of Multi-agent Systems Under DoS Attacks

In this paper, group consensus is investigated for a class of nonlinear multi-agent systems suffered from the DoS attacks. Firstly, a first-order nonlinear multi-agent system is constructed, which is divided into M subsystems and each subsystem has an unique leader. Then a protocol is proposed and a Lyapunov function candidate is chosen. By means of the stability theory, a sufficient criterion, which involves the duration of DoS attacks, coupling strength and control gain, is obtained for achieving group consensus in first-order system. That is, the nodes in each subsystem can track the leader of that group. Furthermore, the result is extended to nonlinear second-order multi-agent systems and the controller is also improved to obtain sufficient conditions for group consensus. Additionally, the lower bounds of the coupling strength and average interval of DoS attacks can be determined from the obtained sufficient conditions. Finally, several numerical simulations are presented to explain the effectiveness of the proposed controllers and the derived theoretical results.

A novel predefined performance barrier function based adaptive sliding mode control method for RLV under mismatched disturbance

PurposeThis paper aims to present a novel adaptive sliding mode control (ASMC) method based on the predefined performance barrier function for reusable launch vehicle under attitude constraints and mismatched disturbances.Design/methodology/approachA novel ASMC based on barrier function is adopted to deal with matched and mismatched disturbances. The upper bounds of the disturbances are not required to be known in advance. Meanwhile, a predefined performance function (PPF) with prescribed convergence time is used to adjust the boundary of the barrier function. The transient performance, including the overshoot, convergence rate and settling time, as well as the steady-state performance of the attitude tracking error are retained in the predetermined region under the barrier function and PPF. The stability of the proposed control method is analyzed via Lyapunov method.FindingsIn contrast to conventional adaptive back-stepping methods, the proposed method is comparatively simple and effective which does not need to disassemble the control system into multiple first-order systems. The proposed barrier function based on PPF can adjust not only the switching gain in an adaptive way but also the convergence time and steady-state error. And the efficiency of the proposed method is illustrated by conducting numerical simulations.Originality/valueA novel barrier function based ASMC method is proposed to fit in the amplitude of the mismatched and matched disturbances. The transient and steady-state performance of attitude tracking error can be selected as prior control parameters.

Performance and compensation method of first-order liquid crystal beam-steering system under continuous wave laser irradiation

The effects of laser irradiation thermal deposition on the performance degradation of liquid crystal (LC) devices in high-power laser systems are extremely vital. In this study, the first-order beam-steering system (FBS) was developed using a passive liquid crystal polarization grating (LCPG) and liquid crystal adjustable wave-plate (LCAW). The LCPG was prepared by holographic exposure technology, and the LCAW was prepared using the standard LC cell preparation process. We investigated the influences of diffraction efficiency of FBS under a 1070-nm continuous-wave (CW) laser irradiation. The energy is concentrated in the −1st order at first. When the half-wave retardation was reached, all the energy is concentrated in the +1st order (∼97 %), and the beam is deflected. Once the phase retardation decreases below the half-wave retardation, the energy gradually reconcentrates in the −1st order. When the LCAW fails, the diffraction the energy is refocused to the −1st order by the LCPG. The results indicated that both thermal deposition and driving voltage reduce the phase retardation of the LCAW, generating a variation of energy between in ±1st orders. By reducing the driving voltage, this half-wave retardation can be recovered under a certain half-wave voltage and laser power density, and the diffraction efficiency of the +1st order can be compensated to ∼97 %. If the reduced phase retardation is not less than half-wave, the FBS can still be modulated in high-power continuous lasers. Our research provides a reference for the development of beam-steering technology based on LC materials in high-power laser systems.

Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems

We provide a rigorous justication of nonlinear geometric optics expansions for reflecting pulses in space dimensions n>1. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The justification applies to N×N systems with N interacting pulses which depend on phases that may be nonlinear. The coherence assumption made in a number of earlier works is dropped. We consider problems in which incoming pulses are generated from pulse boundary data as well as problems in which a single outgoing pulse reflects off a possibly curved boundary to produce a number of incoming pulses. Although we focus here on boundary problems, it is clear that similar results hold by similar methods for the Cauchy problem for N×N systems in free space.

Dissipativity Analysis of Memristive Inertial Competitive Neural Networks with Mixed Delays

Without altering the inertial system into the two first-order differential systems, this paper primarily works over the global exponential dissipativity (GED) of memristive inertial competitive neural networks (MICNNs) with mixed delays. For this purpose, a novel differential inequality is primarily established around the discussed system. Then, by applying the founded inequality and constructing some novel Lyapunov functionals, the GED criteria in the algebraic form and the linear matrix inequality (LMI) form are given, respectively. Furthermore, the estimation of the global exponential attractive set (GEAS) is furnished. Finally, a specific illustrative example is analyzed to check the correctness and feasibility of the obtained findings.

Fixed-time cluster optimization of multi-agent systems on directed detail-balanced networks

This paper investigates the fixed-time cluster optimization problem of first-order multi-agent systems (MASs) under directed detail-balanced networks, in which the optimization objective is a linear combination of local objective functions. Two piecewise distributed control protocols are proposed to solve the optimization problem with time-invariant and time-varying objective functions, respectively. Under the two proposed piecewise control protocols, the fixed-time cluster optimization problem can be solved on the basis of maintaining the cluster consensus unchanged. Furthermore, the initial states of all the agents need not be restricted to the minimum of their local cost functions. Finally, we provide two examples to illustrate the effectiveness of the proposed control protocols.

Finite-time bearing-only formation of first-order multi-agent systems under pinning control

Finite-time bearing-only formation of first-order multi-agent systems under pinning control