State-space Technique Research Articles

Free vibration analysis of fiber-reinforced composite multilayer cylindrical shells under hydrostatic pressure

With the development and application of composite materials in deepwater submersibles, the influence of high external pressure from deepwater environments on the vibration characteristics of composite pressure-resistant cylindrical shells cannot be ignored. In this paper, the free vibration characteristics of prestressed composite multilayer shells are methodically examined by establishing partial differential equations based on the three-dimensional elasticity theory. To solve these equations, the state-space technique and double Fourier series expansion are employed to transform them into state-space ordinary differential equations. These equations are utilized to analyze vibration problems of simply supported composite multilayer cylindrical shells with arbitrary layered angles. The initial stress equilibrium equation is solved to determine the prestress induced by the hydrostatic pressure. This overcomes the limitation of membrane stress and considers non-uniform distributions of radial and interlaminar prestresses. The proposed theoretical model and solution strategies are validated by comparing with theoretical and experimental results from the existing literature and the finite element method. Additionally, the present investigation reveals that the natural frequencies of thick shells can be calculated more accurately using the prestress derived by the proposed approach, especially subjected to noticeable hydrostatic pressure. Finally, the performed investigations indicate that the circumferential prestressing has a more pronounced effect on the shell's natural frequencies than axial prestressing.

Development of model predictive controller in avoidance design of Unmanned Aerial Vehicle (UAV)

This research was accomplished by employing already developed mathematical model of a 6DoF UAV in free space through the motion of the 6DoF aircraft (unmanned aerial vehicle) determined by coordinate systems which allow an aircraft’s position and orientation in space to be kept tracked. The discrete method of the model developed for simulation in Simulink was realized with a suitable transfer function. Then, an artificial neural network model predictive adaptive controller that can handle the nonlinearities associated with the UAV was developed based on state space technique and the model predictive controller (MPC) utilizes a neural network model to envisage future plant (aircraft) responses to potential control signals. The developed model predictive controller network was successfully trained offline using Feed-forward Back-propagation algorithm with speed and position as inputs since the underlying objective of this work is to improve the speed and position in order to advance the safety collision distance of the UAV because these parameters are mostly considered in the avoidance maneuver performance. Also, the results reveal that the speed of the generated UAV is approximately the input speed of 75MS–1 during the time the UAV is affecting maneuvering. Significance of the result is that the proposed algorithm is capable of generating collision-free trajectory for different waypoint cases.

Simulation of motions of a 6DoF unmanned aerial vehicle from the mathematical model in free space

This work prepares a smooth playing ground to modeling and simulation of a Collision Avoidance for Cooperative UAVs with Rolling Optimization Algorithm (ROA) Based on Predictive State Space (PSS) technique using Matlab, Simulink and Aerospace toolboxes of MathsWork. The methodological approach adopted is Computer Aided Software Engineering and to have handle collisions and maneuvers in a mathematical way, normal simulation of the trajectory of both the UAV and obstacles is defined by geometric approach. The goal of the work is to develop a mathematical model of a six degree of freedom (6DoF) of unmanned aerial vehicle (UAV) in free space for further modeling and simulation of a collision avoidance for cooperative UAVs with the required specifications. The motion (modeling of mathematical parameters like velocity, position, body rotational rate and Euler angles) of the 6DoF aircraft was determined by coordinate systems which allow the aircraft’s position and orientation in spaceto be kept tracked. The discrete form of the developed model for simulation was achieved using appropriate transfer functions. The development of the mathematical model will enable the development of an artificial NN model predictive controller (MPC) that can handle the nonlinearities associated with the UAV based on PSS technique.

Grid-Following Inverter-Based Resource: Numerical State–Space Modeling

In the pursuit of a sustainable electric power system, the integration of renewable energy sources and distributed energy resources is gradually replacing traditional power generation. These new resources are integrated into the grid via inverters, which, despite their efficient performance, present dynamic challenges to the power grid when implemented on a large scale. To maintain grid stability and ensure effective regulation during abnormal operations, various modeling techniques are necessary; while the dynamics of inverter-based resources (IBRs) are traditionally modeled by transfer functions, this paper sheds light on differential-algebraic equations (DAEs) modeling and numerical integration methods. The inherent limitations of transfer function modeling stem from its restricted applicability, as it is exclusively suitable for linear and time-invariant systems. In contrast, the nonlinear DAEs of the IBR system can be converted into a state–space form, which offers a versatile framework for modeling, evaluating, and designing a diverse array of systems. In addition to being compatible with time-varying systems and multiple-input multiple-output systems, the state–space technique may incorporate saturation and dead zone characteristics into the dynamic model. Our research focuses on IBR modeling in a grid-following scheme, which is current-controlled and synchronized to the grid by a phase-locked loop (PLL). The presented state–space model consists of the inverter, grid, control, and designed PLL. Beyond the discussion of its application to IBRs, the presented method holds the potential to solve a wide range of DAEs. The proposed model is compared with a benchmarked system.

Spatiotemporal evolution for early warning of ecological carrying capacity during the urbanization process in the Dongting Lake area, China

Early warning of ecological carrying capacity (ECC) is essential for the urbanization process. It provides information on the deterioration of the urban ecological environment and potential hazards and promotes sustainable development. However, research on early warning of ECC in the urbanization process has been limited and mainly focused on a single aspect of ECC, a comprehensive early warning system based on the three perspectives of ecological elasticity (EE), resource carrying (RC), and environmental carrying (EC) is still lacking. Additionally, previous studies did not effectively predict the future evolution trends of ECC and failed to reveal the spatiotemporal evolution characteristics. To address these shortcomings, in this study, we propose a comprehensive early warning indicator of ECC incorporating EE, RC, and EC. The state space technique and back-propagation (BP) neural network model were applied to analyze the spatiotemporal evolution of the warning state in the Dongting Lake area. The results showed that the ECC index decreased from 0.5383 to 0.5364 in 2001–2020, and the risk status was in the range of medium risk. This result was consistent with an analysis of the three subsystems, which indicated that urbanization exceeded the ECC. The early warning index of ECC is predicted to be 0.6257 in 2025. The risk status is predicted to be low risk. From 2001 to 2020, the risk status of counties were significantly different. Most counties in the central area had a low-risk status, and peripheral counties had a medium-risk status. The counties with the most serious risk status were mostly distributed along the edge of the area, in places with higher urbanization rates. Neither the spatial pattern nor the risk status is predicted to change substantially before 2025. Therefore, some targeted measures should be taken to improve the ECC and mitigate the risk.

Financial cycles in Europe: dynamics, synchronicity and implications for business cycles and macroeconomic imbalances

Using dynamic factor models and state-space techniques we quantify financial cycles for twenty European countries over the period 1960Q1–2015Q4 capturing imbalances across credit, housing, bond and equity markets. The paper documents the existence of slow-moving and persistent financial cycles, as well as cross-country synchronicity patterns in Europe. Spillover analysis points at the significant role the global financial cycle and the regional European financial cycle play in shaping national financial market dynamics. Quarterly Bayesian panel VAR estimations suggest that financial cycles influence business cycles and public debt dynamics, with stronger shock transmission observed in the euro area and systemic European economies.

Output trajectory controllability of a discrete-time sir epidemic model

Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease outputyd= (ydi)i∈{0,...,N}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach.

Flutter analysis of honeycomb sandwich trapezoidal wings reinforced with GPLs

Flutter analysis of honeycomb sandwich trapezoidal wings subjected to supersonic airflow is investigated. It is assumed that the sandwich trapezoidal wing is made of an orthotropic honeycomb core surrounded by two face sheets which are reinforced with graphene platelets (GPLs). Applying the Hamilton’s principle, the governing equations of motion based on the first-order shear deformation theory (FSDT) are derived in the Cartesian coordinates. Using a mapping, these equations are converted from Cartesian coordinates to trapezoidal coordinates. Then, the transformed partial differential equations are discretized using generalized differential quadrature (GDQ) method and solved by the state space technique. The influences of various parameters such as the geometry of trapezoidal wings and hexagonal cells, GPLs distribution patterns and the weight fraction of GPLs on the stability region are investigated in detail. It is concluded that the internal geometrical parameters of the hexagonal core have no significant effects on the stability region of the wing. Furthermore, adding a slight percent of GPLs into polymer matrix of face sheets has an enormous effect on the stability region. So that, by adding just 0.5%, 1% and 1.2% GPLs weight fraction, the critical flutter aerodynamic pressure increases approximately 169%, 339% and 407%, respectively. It is also shown that the critical flutter aerodynamic pressure of a trapezoidal wing is more than that of the rectangular and skew wings having the same weight. The obtained numerical results of this research can be used as a suitable tool in analysis and design of wings of aeronautic vehicles at supersonic speeds.

Wrinkling of Elastic Cylinders With Material Properties Varying in Radial Direction

Although the instability of graded elastic cylinders has been analyzed by many researchers, most of them focused on the core-shell cylinders and film-substrate structures with inhomogeneous Young’s modulus. For a radially graded elastic cylinder subjected to the axial compression, the variation of Poisson’s ratio may result in the radial and circumferential stresses and thereby affects the critical condition of instability. By assuming linear elasticity with nonlinear kinematics, the governing equation for the incremental stress field is developed for instability analysis of the cylinder with radially graded material properties (Young’s modulus and Poisson’s ratio). Considering the arbitrariness of material properties, the state space technique is implemented and a semi-analytical solution is acquired. The obtained solution is validated by the finite element results. Numerical examples show that the critical condition of instability for graded elastic cylinders is related to whether Poisson’s ratio is assumed to be constant.

Linear Quadratic Regulator-Based PI Control of a Non-Ideal Quadratic Boost PFC Converter for Low-Power Wind Energy Conversion Systems Supplying Uninterruptible DC Power

DC–DC converters are efficient in providing a regulated power with power factor control in switch-mode power supplies and also in electric vehicle charging stations. The aim of this research work is to design an efficient DC–DC quadratic boost power factor correction converter for Wind Energy Conversion Systems (WECS) to provide uninterruptible DC power in case of one or two modules loss for low-power applications. The state-space model of the converter is derived using a state-space averaging technique through small signal modeling by considering the non-linearities. The reduced-order model is obtained using Routh-Pade's approximation method to reduce the complexity involved in the design of the controller parameters for the outer and inner loops. The outer voltage is regulated using an Internal Mode Control (IMC)-based proportional integral (PI) controller to overcome the effect of right-half plane zero (RHP) and three-phase currents are shaped by using three PI controllers. The three inner PI controllers for each phase are tuned using three methodologies like Zieglar Nichols, Skogestad and Linear Quadratic Regulator (LQR)-based PI control. The transient and steady-state performances of the closed-loop system are analyzed for variations in the load and set point using extensive computer-based simulation studies. The results reveal that the LQR-based PI controller show considerably better performance in terms of less settling time, overshoot, power factor and %THD, including parasitic parameters of the components.

Three-Dimensional Transient Analysis of FGM Rectangular Sandwich Plate Subjected to Thermal Loading Using State Space Differential Quadrature Method

In this paper, transient response of functionally graded materials (FGM) rectangular sandwich plates subjected to thermal loading based on three-dimensional theory of elasticity is carried out. The facing layers are made of metal and ceramics whereas core layer is FGM with exponential function distribution. For the case of simply supported boundary conditions, obtained state space differential equations are solved analytically by using Fourier series expansions along the in-plane coordinates and Laplace transformation. For other edges, boundary condition semi-analytical method is used by applying differential quadrature method (DQM) along the in-plane direction and state space technique across the transverse coordinate. After carrying out the convergence of the present method, accuracy of this study is validated by comparing the numerical results with those reported in the literature. Finally, influences of the boundary conditions, length-to-thickness ratios, length-to-width ratios, time constant and the FGM graded index on elastic behavior of sandwich plate are examined.

Linear-based gain-determining method for adaptive backstepping controller

This paper presents a linear-based gain-determining method for nonlinear adaptive backstepping controllers. Usually, the gains for nonlinear controllers are tuned by the trial and error method. This method becomes more difficult as the number of gains increases. A user-friendly method is proposed in this work to deal with the problem. Firstly, a linear auxiliary system is formed by separating the linear parts from the nonlinear system. Then, linear state-space techniques are used to determine the gains for state-feedback by the linear auxiliary system. After that, by converting the state-feedback gains to backstepping gains, the gains of the nonlinear backstepping controller can be determined. The proficiency of the gain-determining method is proved by simulations with two linear techniques.

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

Port-Controlled Hamiltonian Based Controller for Three-Level Ćuk PFC Converter for Battery Charging Application

This paper reveals energy shaping passivity-based control methodology for a three-level (TL) Ćuk PFC converter. The proposed control methodology is based on the dynamic model of the system along with the idea of energy shaping and damping injection. First, a dynamic model of the TL Ćuk PFC converter is developed using the port-controlled Hamiltonian formulation and the state-space averaging technique. Then, the PCH control technique is implemented in the system and the stability analysis is carried out. In order to eliminate the steady state error, a PI controller is integrated with the PCH-PBC control scheme. Further, the performances of aforesaid system are investigated for battery charging application with the help of MATLAB/Simulink. To validate the simulation study, a prototype model of TL Ćuk PFC converter with proposed controller is built using OP-5142 real-time simulator and test results are recorded. Furthermore, the power quality features of TL Ćuk PFC converter are assessed through monitoring of input current THD under different operating conditions. To assess the system performance in terms of efficiency, input p.f., input current THD, and controller parameters, the proposed controller is compared with benchmark PI controller under dynamic variations at the input voltage and the load.

Hopfield Neural Network-Based Average Current Mode Control of Synchronous SEPIC Converter

ABSTRACT Average Current Mode (ACM) controlled synchronous DC–DC converters are increasingly required for computer power supplies and electric vehicle battery chargers. In this study, Generalized Hopfield Neural Network (GHNN) tuned PI controllers has been proposed for ACM control of synchronous single ended primary inductance converter (SEPIC). The dynamic converter model, required for designing the controllers, is derived using the state-space averaging technique considering all the converter non-idealities. In addition, modified Hankel matrix method is applied to reduce the derived converter model to its first-order equivalent to minimize the design complexity. Using the reduced-order model, the control loop errors are formulated as objective functions in terms of their PI controller parameters. These objective functions are then solved using GHNN to obtain the optimal PI controller parameters. The transient and steady-state performance of the converter with the proposed controller is studied and compared with controllers tuned using Zeigler Nicholas (ZN) method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Reduced-Order Linear Quadratic Regulator (ROLQR) control scheme for variations in the input voltage, reference voltage and load using MATLAB/ Simulink R2015b software tool. Results revealed that the proposed GHNN based controller has fast dynamic performance with less settling time, % overshoot, and steady-state error than existing control methods. A 100W converter prototype is also constructed and tested using TMS320C2000TM microcontroller to verify the effectiveness of the GHNN control algorithm.

On the three-dimensional dynamics of microtubule by considering initially stress

To design anticancer drug Taxol working more efficiently, looking at details of microtubules' dynamic behavior has become more important for researchers worldwide. According to this issue, dynamic stability analysis of microtubule-associated proteins (MAPs) using the state-space technique based on three-dimension elasticity theory is presented. Besides, the MAPs structure is under various body pressure. The state-space technique is applied along the radial direction, and the differential quadrature method (DQM) along the axial direction in the case of another end supports. The novelty of the current study considers the various boundary conditions for MAPs structure and body pressure, which is implemented on the proposed model using the theory of Three-dimension (3D) elasticity. The validity of applied solutions is examined by comparing results with those of available literature, experimental data, and molecular dynamic (MD) simulation outcomes. A thorough parametric investigation is conducted on the effect of initial stress, boundary conditions, and geometry of the shell (such as mid-radius to thickness and length to mid-radius ratios) on the dynamic stability of the MAPs structures under initial stress.

Multichannel deconvolution of vibrational signals: A state-space inverse filtering approach.

Deconvolution of noisy measurements, especially when they are multichannel, has always been a challenging problem. The processing techniques developed range from simple Fourier methods to more sophisticated model-based parametric methodologies based on the underlying acoustics of the problem at hand. Methods relying on multichannel mean-squared error processors (Wiener filters) have evolved over long periods from the seminal efforts in seismic processing. However, when more is known about the acoustics, then model-based state-space techniques incorporating the underlying process physics can improve the processing significantly. The problems of interest are the vibrational response of tightly coupled acoustic test objects excited by an out-of-the-ordinary transient, potentially impairing their operational performance. Employing a multiple input/multiple output structural model of the test objects under investigation enables the development of an inverse filter by applying subspace identification techniques during initial calibration measurements. Feasibility applications based on a mass transport experiment and test object calibration test demonstrate the ability of the processor to extract the excitations successfully.

Data-driven Modelling of Thermal Solid Sorption Storage Systems

An approach fofsr data-driven modelling of open sorption storage systems using zeolite as storage material is presented. The overall dynamic simulation model has the inflow air stream mass flow and absolute humidity as inputs and computes the outflow air temperature. The model is sub-divided into several components, where dynamic state space and process model identification techniques are applied. A comparison of the proposed modelling technique with simulated data from a validated model based on first principles shows that a reasonable accuracy − for a model application in temperature control systems design − can be obtained. It was found that using the proposed strategy, only a limited number of experiments are required, thus saving experimental time. Moreover, the computational requirements for a simulation using the proposed model are greatly reduced compared to a simulation model where differential equations discretised in time and space must be solved.

Application of Improved Dynamic Substructure Finite Element Model-Based State-Space Techniques in Mistuned Blisks

Aeroengine is a complex mechanical equipment, and it works at high temperature, pressure, rotational-speed, and severe loads. One of the core problems is that the vibration and mistuning of bladed disk lead to failure and affect the safety and reliability of aeroengine. Previously, one sector taken as the research object is not suitable; the integrally mistuned bladed disk (blisk) is taken as the research object is very necessary; however, the computational efficiency of mistuned blisk is very low. Therefore, a reduced-order model approach, i.e., an improved dynamic substructure finite element model-based state-space technique (IDSFEM-SST), is proposed to investigate the mistuned blisk. Firstly, the reduced-order substructure finite element model is established by this method, and then, the modal frequencies and modal strain energy amplitudes are investigated. Secondly, the maximum displacement responses are analyzed. Finally, the computational efficiency and accuracy of mistuned blisk via IDSFEM-SST is compared with that of the classical dynamic substructure finite element model and the high-fidelity finite element model to verify the effectiveness of this approach. This study has significance to the dynamic research and engineering practices for complex mechanical structures.

Port‐controlled Hamiltonian‐based controller for an interleaved boost PFC converter

This study reveals the energy shaping port-controlled Hamiltonian passivity-based control (PCH-PBC) technique for an interleaved boost power factor correction (IBPFC) converter. First, the mathematical modelling of an IBPFC converter is developed under all possible operating modes. Then, the average state-space model of the system is established with the help of averaging state-space technique. Further, the PCH technique is applied for controller design and the stability analysis of the proposed system is carried out. A proportional-integral (PI) controller is integrated with the PCH-PBC controller to achieve minimum steady-state errors. Finally, a Simulink model of the proposed system is developed using the Simulink toolbox of MATLAB software and its performances are studied under several operating conditions and verified through experimentation. To assess the system performance in terms of efficiency and input current total harmonic distortion (THD), the comparative study is also carried out under different controllers. Based on the simulation outcomes, the proposed controller is compared with the benchmark PI controller, adaptive passivity-based controller in terms of different control parameters. The performances of the controller are also investigated against dynamic variations at the input voltage and the load. It is observed that the proposed PCH-PBC controller achieves robustness against the aforesaid variations.