Nonlinear Dynamic Mathematical Model Research Articles

Variable structure based control strategy for treatment of HCV infection

Hepatitis C is such a harmful disease which can lead to serious health problems and it is caused by the Hepatitis C Virus (HCV) which causes liver inflammation and sometimes liver cancer. In this work, the control treatment strategy for HCV infection has been proposed. The advanced nonlinear dynamical mathematical model of HCV that has two control inputs and three state variables such as virions, infected hepatocytes and uninfected hepatocytes are considered for controller design in this research work. Moreover, four nonlinear controllers such as the Fractional Order Terminal Sliding Mode Controller (FOTSMC), Integral Terminal Sliding Mode Controller (ITSMC), Double Integral Sliding Mode Controller (DISMC) and Integral Sliding Mode Controller (ISMC) have been proposed in this work for HCV infection control inside the human body. In order to control the amount of uninfected hepatocytes to its required maximum safe limit, controllers are designed for antiviral therapy in which the amount of virions and infected hepatocytes are tracked to zero. One control input is ribavirin which blocks virions production and the other is pegylated interferon (peg-IFN-α) that acts as reducing infected hepatocytes. By doing so, uninfected hepatocytes increase and achieve the required maximum safe limit. To prove the stability of the whole system, Lyapunov stability analysis is used in this work. Simulation results and comparative analysis are carried out by using MATLAB/Simulink. It can be depicted from the given results that the virions and infected hepatocytes are reduced to their required levels completely using FOTSMC and the Sustained Virologic Response (SVR) rate is also enhanced in it. It reduces the treatment period as compared to previous strategies introduced in the literature and also system behaves very nicely even in the presence of un-modeled disturbances.

A General Approach for the Modelling of Negative Feedback Physiological Control Systems.

Mathematical models can improve the understanding of physiological systems behaviour, which is a fundamental topic in the bioengineering field. Having a reliable model enables researchers to carry out in silico experiments, which require less time and resources compared to their in vivo and in vitro counterparts. This work's objective is to capture the characteristics that a nonlinear dynamical mathematical model should exhibit, in order to describe physiological control systems at different scales. The similarities among various negative feedback physiological systems have been investigated and a unique general framework to describe them has been proposed. Within such a framework, both the existence and stability of equilibrium points are investigated. The model here introduced is based on a closed-loop topology, on which the homeostatic process is based. Finally, to validate the model, three paradigmatic examples of physiological control systems are illustrated and discussed: the ultrasensitivity mechanism for achieving homeostasis in biomolecular circuits, the blood glucose regulation, and the neuromuscular reflex arc (also referred to as muscle stretch reflex). The results show that, by a suitable choice of the modelling functions, the dynamic evolution of the systems under study can be described through the proposed general nonlinear model. Furthermore, the analysis of the equilibrium points and dynamics of the above-mentioned systems are consistent with the literature.

Modeling outcome trajectories in patients with acquired brain injury using a non-linear dynamic evolution approach

This study describes a dynamic non-linear mathematical approach for modeling the course of disease in acquired brain injury (ABI) patients. Data from a multicentric study were used to evaluate the reliability of the Michaelis–Menten (MM) model applied to well-known clinical variables that assess the outcome of ABI patients. The sample consisted of 156 ABI patients admitted to eight neurorehabilitation subacute units and evaluated at baseline (T0), 4 months after the event (T1) and at discharge (T2). The MM model was used to characterize the trend of the first Principal Component Analysis (PCA) dimension (represented by the variables: feeding modality, RLAS, ERBI-A, Tracheostomy, CRS-r and ERBI-B) in order to predict the most plausible outcome, in terms of positive or negative Glasgow outcome score (GOS) at discharge. Exploring the evolution of the PCA dimension 1 over time, after day 86 the MM model better differentiated between the time course for individuals with a positive and negative GOS (accuracy: 85%; sensitivity: 90.6%; specificity: 62.5%). The non-linear dynamic mathematical model can be used to provide more comprehensive trajectories of the clinical evolution of ABI patients during the rehabilitation period. Our model can be used to address patients for interventions designed for a specific outcome trajectory.

Neural-Network-Based Immune Optimization Regulation Using Adaptive Dynamic Programming

This article investigates optimal regulation scheme between tumor and immune cells based on the adaptive dynamic programming (ADP) approach. The therapeutic goal is to inhibit the growth of tumor cells to allowable injury degree and maximize the number of immune cells in the meantime. The reliable controller is derived through the ADP approach to make the number of cells achieve the specific ideal states. First, the main objective is to weaken the negative effect caused by chemotherapy and immunotherapy, which means that the minimal dose of chemotherapeutic and immunotherapeutic drugs can be operational in the treatment process. Second, according to the nonlinear dynamical mathematical model of tumor cells, chemotherapy and immunotherapeutic drugs can act as powerful regulatory measures, which is a closed-loop control behavior. Finally, states of the system and critic weight errors are proved to be ultimately uniformly bounded with the appropriate optimization control strategy and the simulation results are shown to demonstrate the effectiveness of the cybernetics methodology.

Design and performance of directional rectification control system in an aircraft with a novel type of wheel-ski landing gear

AbstractFor a hypersonic-speed aircraft with a flat fuselage structure that has narrow space for a traditional wheel-type landing gear retraction, a novel type of wheel-ski landing gear is designed, which is different from traditional landing gears in force distribution and actuation methods. In order to capture the direction control performance of an aircraft with the wheel-ski landing gear, the aircraft ground taxiing nonlinear dynamic mathematical model is built based on a certain type of aircraft data. The experiment of the wheel-ski landing gear actuator and the differential brake control system is carried out to verify that the electric wheel-ski actuator model with the pressure sensor is in good agreement with the test results, indicating the model validity and the speediness of the differential brake response. Then a new fuzzy combined direction rectifying control law is designed based on the optimisation method and the fuzzy control theory. Comparing with the PD wheel-ski differential brake control, the direction rectifying efficiencies increase higher than 140% during the whole taxiing process. In addition, the combined control law can also decrease the overshoots of the yaw angle responses effectively. Finally, the stability and robustness of the designed combined direction control law are verified under various working conditions.

Adaptive nonlinear control scheme for containment of COVID-19 spread

An early understanding of effective policy and transmission dynamics can help us prevent further outbreaks of the COVID-19. This article proposes a nonlinear adaptive control strategy based on effective policy to contain this epidemic. A mathematical model of nonlinear dynamics of the COVID-19 transmission in India is considered. The model also takes uncertainty into account. The control input calculated by the proposed controller prescribes the contact rate of the disease so that the number of infectious population converges to a desired zero value. The controller utilizes a Lyapunov theorem-based adaption law to be able to deal with modeling uncertainties, instability, and divergence. The controller performance on the nonlinear and uncertain model of the COVID-19 transmission has been investigated through a simulation study.

NSGA-II algorithm-based LQG controller design for nuclear reactor power control

The design of reactor power control system is closely related to the safety and economy of nuclear power plants. To improve its power control performance, this study takes a pressurized water reactor as the research object. The nonlinear dynamic mathematical model and its state space model were first derived; Then the Linear Quadratic Gaussian (LQG) optimal control method was adopted to design the reactor power controller; Furthermore, the multi-objective optimization of the linear quadratic regulator (LQR) weighting coefficient is carried out based on the elitist nondominated sorting genetic algorithm version II (NSGA-II). The results show that the LQG controller optimized based on NSGA-II method not only has fast response, high control accuracy and good stability, but also has good robustness and can obtain superior reactor power control performance.

STUDY OF THE NATURE OF OVERVOLTAGES IN THE ELECTRICAL NETWORK ARISING FROM VOLTAGE TRANSFORMERS

A non-linear dynamic mathematical model of voltage transformer has been considered and overvoltages arising on the elements of voltage transformer equivalent circuit during transient processes have been investigated. The influence of voltage transformer secondary circuit capacitance on overvoltage multiplicity in the primary circuits and the duration of transients has been determined. The advantages of approximation of nonlinearity of voltage transformers by hyperbolic sine are used. Mathematical expressions determining the nature of changes in the forced and free components of the transient process in an electrical network with a voltage transformer have been obtained. It is shown that with the increase of the electric network capacitance the duration of the transition process damping increases and the frequency of the forced oscillations and the level of overvoltage decrease. It is proved that even small, in comparison with the primary nominal sinusoidal voltage, aperiodic components of the voltage transient process can lead to significant overvoltages during voltage transformer outages. It has been substantiated that both the secondary resistance and the switching torque influence the overvoltage multiplicity arising in the primary winding of voltage transformers. It is shown that the closed secondary winding worsens the disconnection process of non-linear inductance of voltage transformers. The values to which overvoltages increase in this case are determined. According to the results of calculations it is determined that with open secondary winding of voltage transformers the duration of transient process significantly increases. It has been found that the decrease of frequency of forced oscillations, which occurs in this case, is accompanied by an increase of currents in the primary winding of the voltage transformer, which is dangerous in terms of thermal stability of the winding insulation. It is shown, that closing the secondary winding of voltage transformers leads to significant reduction of transient damping time. It is suggested that this algorithm can be used to provide a rapid breakdown (suppression) of ferroresonant processes. The effectiveness of such a measure of stopping of ferroresonance processes as short-term shunting of secondary winding of voltage transformers has been investigated. The correlation of parameters of electric networks (capacity of busbar sections, nonlinearity of characteristics of voltage transformers, disconnection torque, etc.) at which ferroresonance process may occur and consideration of which may allow, in terms of prevention of ferroresonance processes, to identify substations (electric networks) that require more detailed research has been determined. The results of analytical studies were tested in the electric networks of JSC "Kharkivoblenergo" and used in the electricity distribution system for the selection of specific voltage transformers for certain configurations of electrical networks.

Optimal trajectory tracking control of unmanned aerial vehicle using ANFIS-IPSO system

Accurate and precise trajectory tracking is crucial for unmanned aerial vehicle (UAVs) to operate in disturbed environments. This paper presents a novel tracking hybrid controller for a quadrotor UAV that combines the robust adaptive neuro-fuzzy inference system (ANFIS) controller and Improved Particle Swarm Optimization algorithm (IPSO) model based on functional inertia weight. The controller is implemented in a three degrees of freedom (3 DOF) quadrotor symbolized with its non-linear dynamical mathematical model. To achieve Cartesian position trajectory tracking capability, the construction of the controller can be divided into two stages: a regular ANFIS controller to guarantee fast convergence rapidity and IPSO aims to facilitate convergence to the ANFIS’s optimal parameters to accurately reproduce a desired reference trajectory. Simulation results are given to confirm the advantages of the proposed intelligent control, compared with ANFIS and PID control methods.

Dynamic model of high speed following traffic flow

For the physical phenomenon of high-speed car following in the road traffic flow, all the vehicles with small spacing do not run at low speed. The speeds of the vehicles are significantly higher than those they normally should be when they are in this vehicles’s density. There are more than 7% of high-speed following vehicles in the measured data. At present, the traditional traffic flow model cannot simulate the phenomenon of high-speed car following, so a new nonlinear dynamic mathematical model is needed to describe and analyze the physical phenomenon. In order to study the physical phenomenon of high-speed car following in road traffic, a traffic flow dynamics model for simulating the phenomena is proposed, which combines with the prospect theory and takes into account some factors such as driver’s decision-making behavior and randomization. It is called HCCA (high-speed car following celluar automat) model. In the model, the prospect theory is used to analyze the driver’s lane changing behavior under the uncertain conditions. Combined with the characteristics of the radical driver, the dynamic prediction speed is considered for the front car followed by the radical driver, and the HCCA dynamics rules of high-speed following traffic flow mechanics are defined. By the computer numerical simulation, the evolution mechanism and the characteristics of high-speed car-following flow are studied. The results show that compared with the symmetric two-lane cellular automata (STCA) dynamic model, the HCCA dynamic model established in this paper can simulate abundant traffic physical phenomena, and reproduce complex traffic phenomena such as free flow, synchronous flow and wide-range motion congestion. Finally, the phenomenon of high-speed car following is simulated and the results of high-speed car following rate over 7% with small spacing are in good agreement with the measured results. It overcomes the shortage that traditional STCA model cannot simulate the synchronous flow. It is found that the larger the proportion of radical drivers, the larger the high-speed car following rate and traffic flow with small spacing are under the same road density. The high-speed car following traffic flow mechanics model proposed in this paper has a certain reference significance and practical value for analyzing the physical phenomenon of high-speed car following and enriching the traffic flow theory.

ВИКОРИСТАННЯ МОДЕЛІ НЕЛІНІЙНОЇ ДИНАМІКИ ДЛЯ АНАЛІЗУ ВПЛИВУ СИСТЕМИ УПРАВЛІННЯ ЗНАННЯМИ НА РЕАЛІЗАЦІЮ ВИСОКОТЕХНОЛОГІЧНИХ ПРОЕКТІВ

The article determines that at the present stage of the project management development in information-oriented society, the decision-making process on the efficiency of the knowledge management system assessment is complicated, due to the lack of approaches that determine the impact of the system on the project implementation. The article presents the main results of the analysis of the current state of the problem of modeling the knowledge management system of high-tech projects, which helped to establish that one of the factors of the introduction of an effective system of knowledge preservation is the ability to assess the impact of the system on the project environment.In order to solve the problem, the mathematical model of nonlinear dynamics for the analysis of the influence of knowledge management system on the project based on the Bulirsch–Stoer method was proposed, it is possible to evaluate the influence of elements of the knowledge management system on the projected stages of the project implementation and to calculate the duration of the project taking into account their influence. The mathematical model of nonlinear dynamics for the analysis of the influence of the knowledge management system on the Bulirsch–Stoer method is given to evaluate the influence of elements of the knowledge management system on the projected implementation stages and to calculate the duration of the project, taking into account their impact. Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (ODEs) with high accuracy and comparatively little computational effort. The step-by-step tracking of the knowledge management system impact on the project development will allow the project manager to predict both its successful completion and the risks of deviation from the scheduled time due to the loss of critical knowledge, which largely stems from the successful implementation of the project.Further research will be aimed at developing a model that allows us to assess the profitability of the system in the design environment, based on the results of the proposed mathematical model.

Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses

Abstract Different kinematic mathematical models of nonlinear dynamics of a contact interaction of two microbeams are derived and studied. Dynamics of one of the microbeams is governed by kinematic hypotheses of the first, second, and third approximation orders. The second beam is excited through a contact interaction with the first beam and is described by the kinematic hypothesis of the second-order approximation in both geometric linear and nonlinear frameworks. The derived nonlinear partial differential equations (PDEs) are transformed to the counterpart system of nonlinear ordinary differential equations (ODEs) by the finite difference method. Nonlinear contact interaction dynamics of the microbeam structure is analyzed with the help of time series (signals), Fourier spectra, and wavelet spectra based on various mother wavelets, Morlet wavelet spectra employed to study synchronization phenomena, Poincaré maps, phase portraits, and the Lyapunov exponents estimated with the Wolf, Kantz, and Rosenstein algorithms. We have illustrated that neglecting the shear function (Euler–Bernoulli model) yields erroneous numerical results. We have shown that the geometric nonlinearity cannot be neglected in the analysis even for small two-layer microbeam deflection. In addition, we have detected that the contact between two microbeams takes place in the vicinity of x ≈ 0.2 x \approx 0.2 and x ≈ 0.8 x \approx 0.8 instead of the beams central points.

Information Diffusion Nonlinear Dynamics Modeling and Evolution Analysis in Online Social Network Based on Emergency Events

A nonlinear dynamic emergency public event information diffusion system and mathematical model for public events are proposed based on the propagation dynamics. First, public emergency information communication is analyzed and designed, the opinion evolution is divided into and the viewpoint of value, influence, interest, conformity, intimacy five factors of information diffusion for public emergencies; second, the dynamic diffusion network is designed; information propagation mathematical public emergencies the final model is constructed; the proposed model and social reality and the true statistics of empirical experiments are simulated and analyzed. The experimental results show that the model and the real emergency public event propagation process are consistent, the development trend can predict public events, and the proposed mathematical model is reasonable and effective.

Nonlinear Regenerative Dynamics Analysis of the Multicutter Turning Process

This work presents nonlinear dynamics modeling results for an investigation of continuous cut stability in multicutter turning. The dynamics modeling of the multicutter turning process is carried out through the complete mathematical model of nonlinear dynamics. The dynamic stability of the system is estimated through the possibility of self-oscillations generation (Poincare - Andronov - Hopf bifurcation) of the cutters with lobes of the stability diagram. This paper analyzes the relationship of the axial offset and the cutter angular position for compensation of the system parameters. As a result, the analysis of the influence of the technological system parameters on the chip thickness, their cross-sectional shape and the stability of the system is carried out.

Modelling, simulations and operational performance of a stand-alone hybrid wind/PV energy system supplying induction motor for pumping applications

This paper presents a stand-alone Wind/PV hybrid power system supplying a three phase induction motor for pumping applications. The nonlinear dynamical mathematical model for the system components is presented and used for numerical simulations. The system comprises a fixed speed wind turbine driving a self-excited induction generator (SEIG) terminated by capacitor bank, and a photovoltaic (PV) array integrated via DC-DC converter, inverter and LC filter. The two sources feed (IM) driving a centrifugal pump. The duty ratio of the converter is controlled to maintain constant voltage at common coupling point. System performance is tested by changing the load torque coupled to the motor at certain solar irradiance levels and with fixing load torque with successive step changes of the solar irradiance levels. It is concluded that the system has the ability to run at wide range of solar intensity levels and motor loading conditions. Numerical simulations are executed using MATLAB software.

Modelling, simulations and operational performance of a stand-alone hybrid wind/PV energy system supplying induction motor for pumping applications

This paper presents a stand-alone Wind/PV hybrid power system supplying a three phase induction motor for pumping applications. The nonlinear dynamical mathematical model for the system components is presented and used for numerical simulations. The system comprises a fixed speed wind turbine driving a self-excited induction generator (SEIG) terminated by capacitor bank, and a photovoltaic (PV) array integrated via DC-DC converter, inverter and LC filter. The two sources feed (IM) driving a centrifugal pump. The duty ratio of the converter is controlled to maintain constant voltage at common coupling point. System performance is tested by changing the load torque coupled to the motor at certain solar irradiance levels and with fixing load torque with successive step changes of the solar irradiance levels. It is concluded that the system has the ability to run at wide range of solar intensity levels and motor loading conditions. Numerical simulations are executed using MATLAB software.

Efficiency of application of direct-drive circuit for improvement of starting characteristics of gas turbine engine

The effectiveness of measures to improve the starting characteristics of gas turbine engines (GTE) is considered. To improve the reliability of the GTE launch, it is proposed to use the so-called gearless GTE scheme, created for a “more electric aircraft”, which uses an integrated high-speed starter generator and electric drive units for fuel, oil and other life support of gas turbine engines. With the help of a nonlinear dynamic mathematical startup model, the effect of the magnitude of the given moment of inertia of the rotor on the starting characteristics of the gas turbine engine is evaluated. Change it in the direction of reduction was carried out by replacing the gearbox with attachments to one unit a high-speed starter-generator, installed coaxially with the rotor. Determination of the value of the given moment of inertia of the rotor, aggregates, bearings was carried out using the developed 3-DCAD-models. In the mathematical model of start-up, the thermal state of the oil system, the mechanical power losses for rotating aggregates, bearings, gears are taken into account. The quantitative dependence of the starting characteristics on the moment of inertia of the GTE rotor and other factors is established. For comparison of the basic APU and APU of the direct-drive circuit simulation of the start in the most stressful operating conditions P H = 101,3 kPa at low negative temperatures t H = -40 °C and under normal conditions P H = 101,3 kPa and t H = +15 °C, for “cold” and “hot” state of the engine before starting was made. The tendencies of the moment of inertia of the rotors of the executed and newly created GTE are analyzed. It is shown that the gearless APU in comparison with the basic APU due to the reduction of the moment of inertia by 9,68 % and the reduction of the oil pumped volume in the oil system has a significant improvement in the launch characteristics under ground launch conditions ( P H = 101,3 kPa).

The p53–Mdm2 regulation relationship under different radiation doses based on the continuous–discrete extended Kalman filter algorithm

The tumour suppressor gene p53 plays a key role in cell response to DNA damage, and the p53–Mdm2 regulation relationship is crucial for the expression of p53. In this paper, based on gene expression time-series data of human leukaemia cells after exposure to ionising radiation, with ionising radiation as input, a nonlinear continuous time-delay dynamic stochastic mathematical model of a p53–Mdm2 network is established using a continuous–discrete extended Kalman filter algorithm. The accuracy of the established model is then validated. Numerical simulation is used to simulate the dynamic regulation in p53–Mdm2 networks for low, medium, and high ionising radiation doses. The results show that the proposed algorithm is convergent and that the error rate of the model is only 1.19%. In addition, the model can simulate accurately the response of the p53–Mdm2 network to different doses of ionising radiation. The methods proposed in this paper can supply the foundation for research on the dynamics of the p53–Mdm2 gene regulation relationship and play a guiding role in research on the p53–Mdm2 response process after DNA damage under different doses of ionising radiation.

Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC

The use of a unified power flow controller (UPFC) to control the bifurcations of a subsynchronous resonance (SSR) in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS) where a voltage source converter (VSC) is used based on gate-turn-off (GTO) thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS). The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC) where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.

Modelling of a Vector-current Controlled UPFC and Comprehensive Comparison with the Power-angle Control Strategy

This paper establishes the non-linear dynamic mathematical model of the vector-current controlled unified power flow controller (UPFC) and the linearized model of the UPFC is derived in detail afterwards for the analysis of dynamic performance stability. Then, the paper carries out deep investigations on the comparison and analysis for the above two control strategies applied to the UPFC in the aspects of dynamic interaction and auxiliary damping effect. The relative gain array (RGA) method is used to assess the dynamic interactions among the multiple control functions of the UPFC, and damping torque analysis (DTA) method is used to compare the damping performance of the UPFC auxiliary damping controller. The results of quantitative comparison by RGA and DTA analysis show that the vector-current controlled UPFC exhibits better decoupling characteristic among multiple control loops, while the power-angle controlled UPFC exhibits better auxiliary damping performance. Conclusions are further validated by the non-linear simulation results via a two-area four-machine system.