State Space Matrix Research Articles

Directional control law functional analysis and design for civil aircraft simulator

Abstract Functional analyses of directional flight control law for a typical civil aircraft are conducted, including directional maneuver, rudder limiter, coordinated turn, Yaw Damper, Thrust Asymmetrical Compensation, Gust Alleviation, manual rudder trim, etc. Through inputs of doublet, step input, and sweeping frequency, open loop control characteristics are analyzed based on a linearized state-space matrix. Simulink block architecture of a closed-loop directional control law is constructed, aiming to fulfill flight control functions, including pedal-to-rudder control, Yaw Damper, coordinated turn, and gain-tuned rudder limiter. Simulations for the previously designed closed-loop directional control law are performed to verify the characteristics of directional handling qualities in the aspect of the Yaw Damper, directional static and dynamic stability, maneuverability, and sweeping frequency.

A new integrated modelling and control of ternary pumped storage hydro power generation for small signal stability studies

Pumped storage hydro power generation (PSHPG), a reliable renewable energy source with an energy storage feature, can impart efficient damping torque to power system oscillations to improve small signal stability with appropriate modelling and additional compensation through the governor. But ternary PSHPG (T-PSHPG) has the unique feature of hydraulic short circuit (HSC) mode, where both pumping and generating modes operate simultaneously. This study presents a novel fourth-order modified Heffron Phillips (MHP) model of T-PSHPG in coordination with a multi-band Power system stabilizer (MB-PSS) employing 2-way penstock, where primary penstock circulates water from the upper reservoir to the lower reservoir through the turbine and secondary penstock divides primary penstock, thereby creating short-circuit path through the pump. Also, this model includes additional reactive power droop control to maintain the voltage profile. A new state space matrix has been developed for coordinating T-PSHPG in HSC mode with MB-PSS. The control parameters of the proposed coordinated model are set by a new multi-objective differential evolution-improved particle swam optimization (DE-IPSO) algorithm. With variable load, random solar and wind source penetrations, it has been found that the proposed model can provide adequate damping actions. The sensitivity of the proposed model has been observed by varying critical model parameters by ±50 %. For all conditions, the settling time of speed variation is within 2.672 s to 5.951 s and the minimum damping ratio lies within 0.105 to 0.455. The minimum damping ratio is 0.32 and the settling time is found to be 3.1 s for system response subject to sudden solar power variation, which has been observed by shifting system eigenvalues toward the left half of the complex plane. Time and frequency domain parameters with sensitivity analysis predict system oscillations being damped effectively with consistency for the proposed modelling and control strategy. The results are verified in real-time with OPAL-RT real-time digital simulator. It has been justified by the present study that appropriate modelling of T-PSHPG along with coordinated control action provided by MB-PSS can handle critical power system oscillations efficiently and effective damping torque can be imparted in HSC mode.

Reliability analysis of a three-phase interleaved step-up DC-DC converter for electric vehicle

Increasing the amount of direct current (DC) loads in applications such as airplanes, spacecraft, electric vehicles (EV), and other similar applications DC-DC converters are commonly used. Hence, a three-phase interleaved step-up DC-DC converter (ISC) has been designed, and implemented, which is more appropriate for high-power applications. The modes of operation are explained in detail, and voltage gain calculations are performed. The state space matrix is derived from the voltage equation and the bode diagram is plotted using MATLAB code to investigate the stability study, which makes for a thorough frequency response analysis for the proposed converter. The military handbook (MIL-HDBK-217F) data have been used to perform the calculations to determine each and every component's reliability. The proposed ISC design is implemented into a hardware prototype that produces peak-to-peak output voltage of 139 V, rated voltage of 120 V and the testing outcomes are presented in great depth.

A self-organization reconstruction method of ESN reservoir structure based on reinforcement learning

The dynamic reservoir of the randomly generated Echo State Network (ESN) contains numerous redundant neurons, resulting in collinearity in the high-dimensional state space matrix. This collinearity impacts the prediction performance of the network. In order to address this issue, this paper introduces a self-organizing ESN structure optimization model that is based on reinforcement learning, called SR-ESN. The SR-ESN model employs pruning methods to reconstruct the reservoir using contribution and decision mechanisms. To mitigate potential instability caused by high coupling among neurons in a single reservoir, the concept of ensemble learning is applied to create multiple initial reservoir pools, thereby enhancing screening diversity. Simultaneously, the model utilizes reinforcement learning's decision mechanism to identify effective neurons. Neurons with low contribution are pruned, while those with high contribution are retained for self-organizing reconstruction. This optimization of the network structure enhances its prediction performance. Based on both artificial and real datasets, the proposed SR-ESN model demonstrates superior prediction performance with minimal structural complexity compared to other prediction models.

Modified state space method for long-term behavior of viscoelastic laminated angle-ply plate

This work proposes a modified state space method (SSM) to develop the analytical solution for viscoelastic laminated angle-ply plates subjected to long-term loading situations. Within the analytical model, the plate’s stresses and displacements are governed by orthotropic elasticity theory combined with Boltzmann superposition. The convolution within the governing equation is resolved through the application of Laplace transform. The modified SSM is proposed to provide a general solution for each lamina by extracting the complex variable of the Laplace transform from the state space equation. This modification addresses a limitation of the traditional SSM where the exponential function of the state space matrix is computationally infeasible to calculate. The analytical solution of the laminated angle-ply plate is ultimately derived using the transfer matrix method followed by the inverse Laplace transform. Through comparative analysis, it is observed that the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. In addition, the work explores the bending creep and recovery behaviors of viscoelastic laminated angle-ply plate under various parameters.

Stability Region of Grid-Forming Wind Turbine with Variable Parameters Using Bialternate Sum Matrix Approach

Although the stability regions of wind turbines in the islanding mode have been widely researched, small-signal modeling of grid-forming wind turbines (GFWTs) in the islanding mode has yet to be explored. In addition, the state-space matrix of the wind turbine system has yet to be fully represented. Therefore, this paper proposes a small-signal modeling of GFWT and a method for identifying the stabilization region of a system with variable parameters. First, small-signal modeling of a GFWT based on virtual synchronous generator control is developed. Second, the bialternate sum matrix approach is used to determine the system stabilization region. The system matrix with multiple variable parameters is first decomposed into the sum of several matrices in this paper. Furthermore, the rotor-side generator control is simplified. It can reduce the dimensionality of the system matrix model. Finally, the simulation shows that the proposed method for determining the stabilization region of the variable system is accurate.

Detection and localization of fault in DC microgrid using discrete Teager energy and generalized least square method

PurposeThis paper aims to introduce a new fault protection scheme for microgrid DC networks with ring buses.Design/methodology/approachIt is well recognized that the protection scheme in a DC ring bus microgrid becomes very complicated due to the bidirectional power flow. To provide reliable protection, the differential current signal is decomposed into several basic modes using adaptive variational mode decomposition (VMD). In this method, the mode number and the penalty factor are chosen optimally by using arithmetic optimization algorithm, yielding satisfactory decomposition results than the conventional VMD. Weighted Kurtosis index is used as the measurement index to select the sensitive mode, which is used to evaluate the discrete Teager energy (DTE) that indicates the occurrence of DC faults. For localizing cable faults, the current signals from the two ends are used on a sample-to-sample basis to formulate the state space matrix, which is solved by using generalized least squares approach. The proposed protection method is validated in MATLAB/SIMULINK by considering various test cases.FindingsDTE is used to detect pole-pole and pole-ground fault and other disturbances such as high-impedance faults and series arc faults with a reduced detection time (10 ms) compared to some existing techniques.Originality/valueVerification of this method is performed considering various test cases in MATLAB/SIMULINK platform yielding fast detection timings and accurate fault location.

Modified state space method for bending creep and recovery behaviors of viscoelastic orthotropic laminated plate

A modified state space method (SSM) is proposed first to solve the analytical solution of viscoelastic orthotropic laminated (VOL) plate under time-varying load. This modification extends the applicability of traditional SSM from elastic materials to viscoelastic materials by resolving a limitation of the traditional SSM, where computing the exponential function of the state space matrix is infeasible. In the analytical model, the long-term stresses and displacements are established based on the orthotropic elasticity theory combined with the Boltzmann superposition. The convolution within the governing equation is resolved through Laplace transform. By using the proposed modified SSM, the general solution for each viscoelastic lamina is derived out, by separating the complex variable of Laplace transform out from the state space matrix. The analytical solution is ultimately derived using series expansion, transfer matrix method and inverse Laplace transform. The proposed model can provide long-term creep stress distribution in the VOL plate by creep deflection data from experiment. The comparison with existing results indicates the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. At last, the bending creep and recovery behaviors of the VOL plate are investigated in detail.

On the algorithmization of construction of the transition intensity matrix in systems with a large number of same elements

In this article, using the example of a multi-channel exponential queueing system with reordering of requests, we study the problem of computer construction of the state space and coefficient matrix of a system of equilibrium equations. As a result, general principles for solving problems of this type are formulated.

Simulation of a Building with Hourly and Daily Varying Ventilation Flow: An Application of the Simulink S-Function

This paper presents an application of the Simulink stvmgain S-function for the thermal modelling of a building zone based on the resistance–capacitance scheme of EN ISO 13790. That model in the form of the state-space matrix with time-varying elements was used in simulations of a building with hourly and, suggested in that standard, daily averaged ventilation airflow in five European cities. The following two ventilation schedules were used: occupancy-based; and wind-dependent. Comparative simulations were conducted in EnergyPlus. In general, the results obtained for the annual heating and cooling demand were better for hourly than daily averaged ventilation with an error below 10%. However, in several cases of cooling, the error was above 30%. When considering hourly indoor air temperatures, the proposed method provided very good results with MAE of up to 0.52 °C and 0.46 °C, RMSE < 0.69 °C and 0.62 °C, and CV(RMSE) < 3.09% and 2.75% for the daily averaged and hourly ventilation flow, respectively. For wind-driven ventilation, the temperatures were as follows: MAE < 0.49 °C and 0.48 °C; RMSE < 0.69 °C and 0.68 °C; and CV(RMSE) < 3.01% and 2.97%.

Fault-Tolerant Self-Tuning Control for Three-Phase Three-Level T-Type Rectifier

This paper proposes a sensorless self-tuning control algorithm for a three-phase T-type rectifier. The proposed sensorless algorithm consists of three layers including an observer, which estimates grid voltages or currents based on the Kalman filter algorithm (KFA), an online estimator, which estimates the state-space matrix parameters, and a linear quadratic tracker (LQT), which is the main controller in this study. On the other hand, the performance of the LQT depends on the gains that need to be adjusted according to the system parameters, which is a challenge. To overcome this problem, a self-tuning method based on recursive least square algorithm (RLSA) is also proposed to tune the gains of LQT online. An experimental prototype is established, and the results, including the steady-state and dynamic performances, are carried out and presented to validate the effectiveness of the proposed controller.

A Simplified Model of the HVDC Transmission System for Sub-Synchronous Oscillations

As the installed capacity of the power system is scaled up and the distance of transmission increases constantly, high-voltage direct current (HVDC) transmission technology has been widely applied across the power system. The HVDC system can lead to sub-synchronous oscillations (SSO) in the turbine and new energy generation systems. When the SSO caused by HVDC are studied through small signal analysis, it is usually necessary to establish the detailed state space model and electromagnetic transient model, which shows various disadvantages such as the high complexity of the model, the high order of the state space matrix, the complex calculation of eigenvalues, and the slow pace of simulation. In the present study, a simplified model intended for the HVDC transmission system is proposed, which can be used to simplify the calculation model and accelerate the simulation by omitting the high-frequency component and simultaneously keeping the sub-synchronous frequency component unchanged. The time domain simulation method is used to compare the dynamic response of the proposed simplified simulation model with that of the original detailed model, and the accuracy of the proposed model is demonstrated. The proposed simplified simulation model is applied to explore the SSO of wind-thermal power bundling in the HVDC transmission system. Additionally, the simulation results of SSO are compared by using the simplified model and the detailed model; the results of which demonstrate the effectiveness and rapidity of the simplified simulation model. The simplified model proposed can greatly improve the efficiency of SSO risk assessment. By selecting reasonable types and parameters of new energy units, SSO of the system can be avoided under risky operation mode, and the power grid operation mode can be monitored and adjusted to ensure the safe operation of the system. Finally, it can promote the sustainable development of the power system.

Finite dimensional approximations in operator algebras

A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an operator algebra is RFD if and only if every representation can be approximated by finite dimensional ones in the point weak operator topology. This is a non-self-adjoint version of a theorem of Exel and Loring for C⁎-algebras. Moreover, we construct an example of an operator algebra for which approximation in the point strong operator topology is not possible. As a consequence, the maximal C⁎-algebra generated by this operator algebra is not RFD. This answers questions of Clouâtre and Ramsey and of Clouâtre and Dor-On.

The Mental Illness-Health Matrix and the Mental State Space Matrix: Complementary meta-conceptual frameworks for evaluating psychological states.

It is increasingly appreciated that mental health may not just involve a relative absence of mental illness, but the active presence of positive psychological desiderata. However, research attention on mental illness and health has tended to remain siloed and disconnected-proceeding along parallel tracks-with their potential relationship underexplored and undertheorized. As such, we sought to develop theoretical models to help us better understand the interaction of these two domains of experience. Through extensive engagement with relevant literature, we created two complementary meta-conceptual frameworks to represent and evaluate states of mental illness and health. The Mental Illness-Health Matrix allows different forms of mental illness and health to be situated and assessed within a common framework. The Mental State Space Matrix further enables these various forms to be conceptualized and appraised in terms of numerous common parameters (e.g., valence and arousal). It is hoped that these frameworks will stimulate and support further research on the inter-relational dynamics of illness and health. Indeed, the matrices themselves are provisional works-in-progress, with their articulation here intended as a foundation for their further development as understanding of these topics evolves and improves.

Acoustic insulation characteristics improvement of a thick CNT-reinforced doubly-curved shell by using GPLRC and MEE composite layers

Noise reduction in structures and human living environments is one of the most important issues in engineering that is always given special attention. Sound insulation has always been improved using different methods, one of which is to use the properties of materials. Herewith, the aim of this paper is to take advantage of graphene-platelet reinforced composites and magneto-electro-elastic (MEE) material properties for sound attenuation. The present paper deals with the analysis of sound transmission loss (STL) through a three-layer sandwich doubly-curved shell where an MEE sheet is integrated with two nanocomposite sheets. In addition, these two nanocomposite sheets are reinforced by functionally graded (FG) distributions of CNT and graphene platelet (GPL)-reinforced composites, respectively. Firstly, the three-dimensional elasticity theory is employed to derive the governing equations of motion. Then, the vibroacoustic analysis for the resultant equations is completed according to the state space and transfer matrix method. Comparing the obtained results with the available literature discloses that the offered procedure has a high precision for structural acoustic problems. In the next step, in addition to inspecting two kinds of MEE composites, the effective parameters, such as layup configuration, FG distribution, volume fraction, weight fraction, radii of curvature, electromagnetic boundary conditions, and interphase thickness, are assessed on the STL. This assessment shows that the parameters involved in this paper are highly interdependent. Accordingly, the analysis of these parameters is done simultaneously with the aid of three- and four-dimensional plots in order that the optimal value for each parameter can be realized. As seen clearly in the outcomes, the electromagnetic boundary conditions parameters, compared to the other parameters, can much more alter the STL trend, so that a slight change in electric potential results in great change in the STL.

Analysis and Application of Matrix-Form Neural Networks for Fast Matrix-Variable Convex Optimization.

Matrix-variable optimization is a generalization of vector-variable optimization and has been found to have many important applications. To reduce computation time and storage requirement, this article presents two matrix-form recurrent neural networks (RNNs), one continuous-time model and another discrete-time model, for solving matrix-variable optimization problems with linear constraints. The two proposed matrix-form RNNs have low complexity and are suitable for parallel implementation in terms of matrix state space. The proposed continuous-time matrix-form RNN can significantly generalize existing continuous-time vector-form RNN. The proposed discrete-time matrix-form RNN can be effectively used in blind image restoration, where the storage requirement and computational cost are largely reduced. Theoretically, the two proposed matrix-form RNNs are guaranteed to be globally convergent to the optimal solution under mild conditions. Computed results show that the proposed matrix-form RNN-based algorithm is superior to related vector-form RNN and matrix-form RNN-based algorithms, in terms of computation time.

Longitudinal flight dynamics modeling and a flight stability analysis of a monocopter

A monocopter, which is a biology-inspired aircraft based on the samara, has been proved to have passive flight stability. However, due to the asymmetry of its configurations and the constant rotation during flight, its flight dynamics equation is complex. In this paper, the longitudinal stability of a monocopter is systematically analyzed. The longitudinal motion of the monocopter is used as the main research object in this paper. By transforming the body axis coordinate frame to the semi-body axis coordinate frame, its longitudinal dynamics equation is greatly simplified. Then, a fourth-order state space matrix of the longitudinal motion of the monocopter is established, and its longitudinal stability is analyzed at different pitch angles of the wing. Furthermore, the fourth-order state space matrix is simplified into a third-order matrix, and the Rouse criterion is used to analyze the stability of the simplified state space. A set of sufficient conditions is obtained as the criterion for longitudinal stability. Based on this criterion, it is found that the product of inertia Iyzb is a very important factor affecting the stability. Then, the inertial parameters of the aircraft are modified, which greatly expands the range of the pitch angle that maintains longitudinal stability. Finally, the six-degree-of-freedom nonlinear flight dynamic simulation is performed to verify the rationality of the longitudinal stability criterion.

Improved method for analysing the dynamic response of gear transmission systems

PurposeThe purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.Design/methodology/approachAn improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.FindingsThe calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.Originality/valueThe proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.

Matrix-Form Neural Networks for Complex-Variable Basis Pursuit Problem With Application to Sparse Signal Reconstruction.

In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time.

Mathematical Modeling and Stability Analysis of Tiltrotor Aircraft

The key problem in the development process of a tiltrotor is its mathematical modeling. Regarding that, this paper proposes a dividing modeling method which divides a tiltrotor into five parts (rotor, wing, fuselage, horizontal tail, and vertical fin) and to develop aerodynamic models for each of them. In that way, force and moment generated by each part are obtained. Then by blade element theory, we develop the rotor’s dynamic model and rotor flapping angle expression; by mature lifting line theory, the build dynamic models of the wings, fuselage, horizontal tail and vertical fin and the rotors’ dynamic interference on wings, as well as nacelle tilt’s variation against center of gravity and moment of inertia, are taken into account. In MATLAB/Simulink simulation environment, a non-linear tiltrotor simulation model is built, Trim command is applied to trim the tiltrotor, and the XV-15 tiltrotor is taken as an example to validate rationality of the model developed. In the end, the non-linear simulation model is linearized to obtain a state-space matrix, and thus the stability analysis of the tiltrotor is performed.