Search Results (47)

This paper analyzes the stability of trajectory tracking in fixed-wing UAV swarms subject to time-delayed feedback control. A delay-dependent stability criterion is established using a combination of Routh–Hurwitz analysis and a transcendental characteristic equation method. The study identifies a critical delay threshold beyond which the tracking objective becomes unstable. The influence of delayed feedback on the system dynamics is analyzed, showing how time delays affect the swarm’s ability to maintain formation. Numerical simulations confirm the theoretical predictions and illustrate the loss of stability as the delay increases. The findings underline the importance of accounting for delays when evaluating control performance in UAV swarm coordination. Full article

In this paper, a unique method for controlling the effects of nonlinear vibrational responses in a cantilever beam system under harmonic excitation is presented. The Nonlinear Integral Negative Derivative Feedback (NINDF) controller is used for this purpose in this study. With this method, the cantilever beam is represented by a three-DOF nonlinear system, and the NINDF controller is represented by a first-order and second-order filter. The authors derive analytical solutions for the autonomous system with the controller by utilising perturbation analysis on the linearised system model. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The stability of the system is assessed using the Routh–Hurwitz criterion. Moreover, symmetry is present in the frequency–response curves (FRCs) for a variety of parameter values. The results show that, when compared to other controllers, the effectiveness of vibration suppression is directly correlated with the product of the NINDF control signal. The amplitude response of the system is demonstrated, and the analytical solutions are validated through numerical simulations using the fourth-order Runge–Kutta method. The accuracy and reliability of the suggested approach are demonstrated via the significant correlation between the analytical and numerical results. Full article

In the continuous drilling process of oil wells, to achieve the efficient screening of drilling fluids by the vibrating screen while ensuring the safety of the screening operation, an anti-resonance system driven by two exciters with triple-frequency (denoted as 3:1 frequency ratio) is proposed. Initially, differential motion equations are formulated utilizing Lagrange’s equation, followed by the definition of vibration isolation coefficients adopting ratios. Triple-frequency synchronization and stability criterion between two eccentric blocks are subsequently elucidated via the asymptotic method and Routh–Hurwitz criterion. Concurrently, the effects of structural parameters on vibration isolation capacity, steady-state trajectory, and the triple-frequency synchronization phase are investigated through numerical computation. Ultimately, the reliability of the theoretical study is corroborated by simulation analysis. Results indicate that under the allowable system parameters for the practical project, the amplitude of the vibration body can exceed three times that of the isolation body; the two solutions of the stable phase difference (SPD) are different by π, one of which is stable and the other is unstable, and the stability of phase difference is determined by the sign of the stability coefficient. This work is useful for developing new vibrating screens and other multi-frequency vibration machines. Full article

Many studies aim to suppress vibrations in vibrating dynamic systems, such as bridges, highways, and aircraft. In this study, we scrutinize the primary resonance of a cantilever beam excited by an external force via a proportional fractional-order derivative controller (PFD). The average method is used to obtain the approximate solution of the vibrating system. The stability of the control system is illustrated using the Routh–Hurwitz criterion. We investigate the performance of some chosen parameters of the studied system to generate response curves. The performance of the linear fractional feedback control is studied at different values of the fractional order. Full article

In the development trend of intelligent and high-performance construction machinery, the dual-spool electro-hydraulic valve, as a new-generation core control element, directly affects the operation accuracy and energy-efficiency level of construction machinery. The standard linear extended state observer (LESO) produces relatively serious peaks as the system order increases, which leads to the degradation of the observer’s performance and affects the controller’s accuracy. To solve this problem, this paper innovatively proposes an output feedback control strategy for a cascaded structure observer for the dual-spool electro-hydraulic valve. This paper designs an output feedback controller based on the cascaded structure observer. The uniform exponential stability (USE) criterion ensures that the tracking error of the observer for the system state is bounded. The expected load pressure is constructed based on the expected trajectory to replace the actual load pressure, avoiding the influence of the nonlinear coupling between the load pressure and the input signal on the control system. Finally, a stable output feedback controller is obtained based on the backstepping control method and Hurwitz polynomial stability analysis. This study first applies the cascaded structure observer to the field of dual-spool electro-hydraulic valve control, providing a new theoretical framework and technical path for the high-precision control of the hydraulic system of construction machinery. Theoretical analysis shows that compared with the standard LESO, the cascaded structure observer can significantly reduce the online computational burden and effectively suppress the peak phenomenon, providing stronger estimation ability. Finally, a large number of simulation examples verify the effectiveness and superiority of the output feedback controller based on the cascaded structure observer. In all four test scenarios, the average tracking error of C1 (the output feedback controller designed based on the cascaded structure linear extended state observer) is about 5.1%, the average tracking error of C2 (the output feedback controller designed based on the standard structure linear extended state observer) is about 7.8%, and the average tracking error of C3 (the high-gain PID controller) is about 19.2%. The average control accuracy of the designed C1 controller is improved by 2.7% and 14.1% compared with C2 and C3, respectively. In terms of the estimation of external disturbances, the average error of C1 is 14% and the average error of C2 is 29.6%. The estimation accuracy of the former is improved by 15.6% compared with the latter. Full article

Aiming to solve the difficult problem of the miniaturization of servo valves, this paper designs a subminiature two-dimensional (2D) electro-hydraulic servo valve, which realizes the integration of the pilot stage and the power stage and significantly improves the work-to-weight ratio. Meanwhile, a high-power-density brushless DC motor (BLDC) is adopted as the electro-mechanical converter to further reduce the volume and mass. Firstly, the structure and working principle of the two-dimensional (2D) servo valve are described, and the mathematical model of the electro-mechanical converter is established. Aiming at the special working condition of the electro-mechanical converter with high-frequency oscillation at a small turning angle, this paper designs a position–current double closed-loop PID control algorithm based on the framework of the vector control algorithm (FOC). At the same time, the current feedforward compensation technique is included to cope with the high-frequency nonlinear disturbance problem of the electro-mechanical converter. The stability conditions of the electro-mechanical converter and the main valve were established based on the Routh–Hurwitz criterion, and the effects of the control algorithm of the electro-mechanical converter and the main parameters of the main valve on the stability of the system were analyzed. The dynamic and static characteristics of the 2D valve were simulated and analyzed by establishing a joint simulation model in Matlab/Simulink and AMESim. The prototype was fabricated, and the experimental bench was built; the size of the experimental prototype was 31.7 mm × 29.3 mm × 31 mm, and its mass was 73 g. Under a system pressure of 7 MPa, the flow rate of this valve was 5 L/min; the hysteresis loop of the spool-displacement input–output curve was 4.8%, and the linearity was 2.54%, which indicated that it had the ability of high-precision control and that it was suitable for the precision fluid system. The step response time was 7.5 ms, with no overshoot; the frequency response amplitude bandwidth was about 90 Hz (−3 dB); the phase bandwidth was about 95 Hz (−90°); and the dynamic characterization experiment showed that it had a fast response characteristic, which can satisfy the demand of high-frequency and high-dynamic working conditions. Full article

To explore the nonlinear dynamics of a piezoelectric energy harvesting device, we consider the simultaneous parametric and external excitations. Based on Bernoulli–Euler beam theory, a new dynamic model is proposed taking into account the curvature of the beam, geometric and electro-mechanical coupling nonlinearities, and damping nonlinearity, with inextensible deformation. The system is discretized by using the Galerkin–Bubnov procedure and then is investigated by the optimal auxiliary functions method. Explicit analytical expressions of the approximate solutions are presented for a complex problem near the primary resonance. The main novelty of our approach relies on the presence of different auxiliary functions, the involvement of a few convergence-control parameters, the construction of the initial and first iteration, and much freedom in selecting the procedure for obtaining the optimal values of the convergence-control parameters. Our procedure proves to be very efficient, simple, easy to implement, and very accurate to solve a complicated nonlinear dynamical system. To study the stability of equilibrium points, the Routh–Hurwitz criterion is adopted. The Hopf and saddle node bifurcations are studied. Global stability is analyzed by the Lyapunov function, La Salle’s invariance principle, and Pontryagin’s principle with respect to the control variables. Full article

In distributed energy grid-connected systems, fast and accurate grid synchronization technology is crucial for system stability. This article proposes an improved phase-locked loop (FECSOGI-PLL) based on frequency error compensation. By introducing an unbiased adaptive frequency compensation mechanism, the SOGI resonant frequency is adjusted in real time to accurately track the input signal. A linear time invariant (LTI) model of the FECSOGI-PLL was established in the article, and its wider stability domain was clarified based on the Routh–Hurwitz criterion. The strong robustness of its fast response under non-ideal conditions, such as frequency jumps and amplitude drops, was verified through simulation and experiments. The core innovation of this study lies in the first implementation of unbiased adaptive regulation of the SOGI resonant frequency through the frequency error compensation mechanism, as well as the system design method based on the extended stability domain, providing theoretical support and engineering practice reference for high robustness power grid synchronization technology. Full article

This paper presents a mathematical model to examine the transmission and stability dynamics of the SEIR model for COVID-19. To assess disease progression, the model incorporates a time delay for the time delay and survival rates. Then, we use the Routh–Hurwitz criterion, the LaSalle stability principle, and Hopf bifurcation analysis to look at disease-free and endemic equilibrium points. We investigate global stability using the Lyapunov function and simulate the model behavior with real COVID-19 data from Indonesia. The results confirm the impact of time delay on disease transmission, mitigation strategies, and population recovery rates, demonstrating that rapid interventions can significantly impact the course of the epidemic. The results indicate that a balance between transmission reduction and vaccination efforts is crucial for achieving long-term stability and controlling disease outbreaks. Finally, we estimate the degree of disease control and look at the rate of disease spread by simulating the genuine data. Full article

This study develops a modified SIR model (Susceptible–Infected–Recovered) to analyze the dynamics of the COVID-19 pandemic. In this model, infected individuals are categorized into the following two classes: $I_a$, representing asymptomatic individuals, and $I_s$, representing symptomatic individuals. Moreover, accounting for the psychological impacts of COVID-19, the incidence function is nonlinear and expressed as $Sg(I_a,I_s)={\displaystyle \frac{\beta S(I_a+I_s)}{1+\alpha (I_a+I_s)}}$. Additionally, the model is based on a symmetry hypothesis, according to which individuals within the same compartment share common characteristics, and an asymmetry hypothesis, which highlights the diversity of symptoms and the possibility that some individuals may remain asymptomatic after exposure. Subsequently, using the next-generation matrix method, we compute the threshold value ($R_0$), which estimates contagiousness. We establish local stability through the Routh–Hurwitz criterion for both disease-free and endemic equilibria. Furthermore, we demonstrate global stability in these equilibria by employing the direct Lyapunov method and La-Salle’s invariance principle. The sensitivity index is calculated to assess the variation of $R_0$ with respect to the key parameters of the model. Finally, numerical simulations are conducted to illustrate and validate the analytical findings. Full article

COVID-19 is an enveloped virus with a single-stranded $RNA$ genome. The surface of the virus contains spike proteins, which enable the virus to attach to host cells and enter the interior of the cells. After entering the cell, the virus exploits the host cell’s mechanisms for replication and dissemination. Since the end of 2019, COVID-19 has spread rapidly around the world, leading to a large-scale epidemic. In response to the COVID-19 pandemic, the global scientific community quickly launched vaccine research and development. Vaccination is regarded as a crucial strategy for controlling viral transmission and mitigating severe cases. In this paper, we propose a novel mathematical model for COVID-19 infection incorporating vaccine-induced immunization failure. As a cornerstone of infectious disease prevention measures, vaccination stands as the most effective and efficient strategy for curtailing disease transmission. Nevertheless, even with vaccination, the occurrence of vaccine immunization failure is not uncommon. This necessitates a comprehensive understanding and consideration of vaccine effectiveness in epidemiological models and public health strategies. In this paper, the basic regeneration number is calculated by the next generation matrix method, and the local and global asymptotic stability of disease-free equilibrium point and endemic equilibrium point are proven by methods such as the Routh–Hurwitz criterion and Lyapunov functions. Additionally, we conduct fractional-order numerical simulations to verify that order $0.86$ provides the best fit with COVID-19 data. This study sheds light on the roles of immunization failure and fractional-order control. Full article

The COVID-19 pandemic has not only brought a virus to the public, but also spawned a large number of rumors. The Internet has made it very convenient for media websites to record and spread rumors, while the official government, as the subject of rumor control, can release rumor-refutation information to reduce the harm of rumors. Therefore, this study took into account information-carrying variables, such as media websites and official governments, and expanded the classic ISR rumor propagation model into a five-dimensional, two-level rumor propagation model that interacts between the main body layer and the information layer. Based on the constructed model, the mean field equation was obtained. Through mathematical analysis, the equilibrium point and the basic reproduction number of rumors were calculated. At the same time, stability analysis was conducted using the Routh Hurwitz stability criterion. Finally, a numerical simulation verified that when the basic regeneration number was less than 1, rumors disappeared in the system; when the basic regeneration number was greater than 1, rumors continued to exist in the system and rumors erupted. The executive power of the official government to dispel rumors, that is, the effectiveness of the government, played a decisive role in suppressing the spread of rumors. Full article

The choice of management strategy for companies operating in different sectors of the economy is of great importance for their sustainable development. In many cases, companies are in competition within the scope of the same activities, meaning that the profit of one company is at the expense of the other. The choice of strategies for each of the firms in this case can be optimized using game theory for a non-cooperative game case where the two players have antagonistic interests. The aim of this research is to develop a methodology which, in non-cooperative games, accounts for the benefits of different criteria for each of the strategies of the two participants. In this research a new integrated sequential interactive model for urban systems (SIMUS)–game theory technique for decision making in the case of non-cooperative games is proposed. The methodology includes three steps. The first step consists of a determination of the strategies of both players and the selection of criteria for their assessment. In the second step the SIMUS method for multi-criteria analysis is applied to identify the benefits of the strategies for both players according to the criteria. The model formation in game theory is drawn up in the third step. The payoff matrix of the game is formed based on the benefits obtained from the SIMUS method. The strategies of both players are solved by dual linear programming. Finally, to verify the results of the new approach we apply four criteria to make a decision—Laplace’s criterion, the minimax and maximin criteria, Savage’s criterion and Hurwitz’s criterion. The new integrated SIMUS–game theory approach is applied to a real example in the transport sector. The Bulgarian transport network is investigated regarding route and transport type selection for a carriage of containers between a starting point, Sofia, and a destination, Varna, in the case of competition between railway and road operators. Two strategies for a railway operator and three strategies for a road operator are examined. The benefits of the strategies for both operators are determined using the SIMUS method, based on seven criteria representing environmental, technological, infrastructural, economic, security and safety factors. The optimal strategies for both operators are determined using the game model and dual linear programming. It is discovered that the railway operator will apply their first strategy and that the road operator will also apply their first strategy. Both players will obtain a profit if they implement their optimal strategies. The new integrated SIMUS–game theory approach can be used in different areas of research, when the strategies for both players in non-cooperatives games need to be established. Full article

The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model’s solutions, calculating the basic reproduction number (${\mathcal{R}}_0$) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin’s maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings. Full article

This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the system as a three-degree-of-freedom nonlinear system representing the beam flutter, coupled with a first-order and a second-order filter representing the NIPPF controller. By applying perturbation analysis to the linearized system model, the authors obtain analytical solutions for the autonomous system with the controller. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The Routh–Hurwitz criterion is utilized to evaluate the system’s stability. Furthermore, the frequency–response curves (FRCs) exhibit symmetry across a range of parameter values. The findings highlight that the effectiveness of vibration suppression is directly related to the product of the NIPPF control signal after comparing with different controllers. Numerical simulations, conducted using the fourth-order Runge–Kutta method, validate the analytical solutions and demonstrate the system’s amplitude response. The strong correlation between the analytical and numerical results highlights the accuracy and dependability of the proposed method. Full article