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Copyright of Journal of Engineering (17264073) is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A new model for the non-linear propeller-pendulum system is derived in this study. The model takes into consideration the effects of external disturbances and the properties of the pendulum elements. Two systems with PID controllers are simulated. In the first system, Simulink is used to implement the system and tune the PID parameters. In the second system, a MATLAB script is used to simulate the system and tune the PID parameters. The scrip uses the Runge-Kutta method for solving the system’s equation and uses particle swarm optimization (PSO) to tune the parameters. Further, both systems were investigated under two disturbance conditions. The performance of these systems is evaluated based on comparing the settling time, the peak overshoot, and the integral of the absolute errors (IAE). The results show that when there is no disturbance, both systems are capable of tracking the desired signal successfully. However, the results also show that the application of disturbances causes the first system to lose its smooth response. In contrast, the second system demonstrates a robust response and effective countermeasures to disturbance effects. The results of unit step disturbance are as follows: the settling time, peak overshoot, and IAE of the first system are 13.16s, 11.6%, and 1.706, respectively. Further, the settling time, peak overshoot, and IAE of the second system are 2.388s, 6.6%, and 0.299, respectively. It can be concluded that Simulink is not recommended to be used for tuning the PID controller in the presence of disturbances.

In the proposed approach, a 3D response of the guy line treated as a small-sag cable is considered. The strong dynamic wind action leads to the base motion excitation of the guy line. Longitudinal cable displacements are coupled with lateral ones. Hamilton's principle and Galerkin method are used to obtain the set of differential equations of motion. The cable excitation is assumed as a narrow-band stochastic process modelled as a response of an auxiliary linear filter to a Gaussian white noise process. The equivalent linearization technique is applied to obtain approximate analytical results verified against the numerical Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

This paper presents a comparison of three different non-linear time series modelling approaches: NARMAX (Non-linear Autoregressive Moving Average with Exogenous Inputs), Beta-t-EGARCH (Beta t Exponential Generalized Autoregressive Conditional Heteroscedasticity), and Radial Basis Function Neural Networks (RBFNN) applied to weekly stock market index data. We will explain three types of models and compare their compositions and structures. Then, we will show which model gives better predictions. To study series data, the comparison involved analysing the structure of the model and its errors in various time series models and summarising their findings. We divide the data into two parts: training data to structure the time series and testing. The training data tests the model's predictions. Then, we can analyse the model with the errors and the best deterrence predictions. After selecting the NARMAX and Beta-t-EGARCH models, we test them with specific criteria. The best choice is finding the model with the lowest average errors. For this study, we analysed the weekly average closing of the Aramco 2222 index from 15 December 2019 to 16 July 2023 and made 187 observations.

In this study, we have employed the highly significant hyperbolic tangent (tanh) method to conduct an in-depth analysis of nonlinear coupled KdV systems of partial differential equations. In comparison to existing sophisticated approaches, this proposed method yields more comprehensive exact solutions for traveling waves without requiring excessive additional effort. We have successfully applied this method to two examples drawn from the literature of nonlinear partial differential equation systems. [ABSTRACT FROM AUTHOR]

In this work we have applied a very important the hyperbolic tangent (tanh) method in the analytical study of nonlinear coupled KdV systems of partial differential equations. Compared to existing sophisticated approaches, this proposed method gives more general exact traveling wave solutions without much extra effort. Two applications from the literature of non linear PDE systems have been solved by the method. [ABSTRACT FROM AUTHOR]

A continuously stirred tank reactor (CSTR) is largely used in water treatment and in chemical and biological processes. It is characterized by a complex non‐linear behaviour. Operating large reactors in industry can be expensive, so a common trick used to reduce costs is to operate multiple CSTRs in series. Consequently, the CSTR is usually exposed to faults and noises. This paper addresses the design of a robust observer for estimation and fault diagnosis strategy on two CSTRs in series. The considered system is affected simultaneously by time‐varying actuator and sensor faults with measurement noises. The Takagi‐Sugeno multimodel approach is proposed to transform the non‐linear model into an interpolation of several linear sub‐models with non‐measurable premise variables. The purpose of this brief is to provide the state and the fault estimation for the considered system using a proportional multiple integral (PMI) unknown input observer. The exponential stability conditions are studied with the Lyapunov theory and L2 optimization and formulated in terms of linear matrix inequalities. In addition, a comparative study with a PMI observer is conducted. Finally, the proposed observer is used for time‐varying fault detection and isolation. [ABSTRACT FROM AUTHOR]

A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ∞ approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.

Abstract The problems of inconsistent data sampling frequency, outliers, and coloured noise often exist in system identification, resulting in unsatisfactory identification results. In this study, a novel identification method of input non‐uniform sampling Wiener model with a coloured heavy‐tailed noise is proposed. The lifted Wiener model with coloured noise and outlier value disturbed is constructed. Under the expectation‐maximisation (EM) algorithm framework, the student's t‐distribution is introduced to model the contaminated output data. The variance scale is regarded as a unique latent variable, and the iterative parameter estimation formula of the non‐uniform sampling Wiener model is derived. The idea of the auxiliary model is applied to acquire the unmeasured middle variable and handle the coloured noise variable in the non‐uniformly sampled Wiener model. The Differential Evolution algorithm is used to calculate the intractable part of the Q‐function. The convergence analysis of the proposed algorithm is given. Two numerical examples and one water tank simulation are employed to indicate the effectiveness of the proposed method.

Accurate trajectory tracking is a paramount objective when a mobile robot must perform complicated tasks. In high-speed movements, time delays appear when reaching the desired position and orientation, as well as overshoots in the changes of orientation, which prevent the execution of some tasks. One of the aspects that most influences the tracking performance is the control system of the actuators of the robot wheels. It usually implements PID controllers that, in the case of low-cost robots, do not yield a good tracking performance owing to friction nonlinearity, hardware time delay and saturation. We propose to overcome these problems by designing an advanced process control system composed of a PID controller plus a prefilter combined with a Smith predictor, an anti-windup scheme and a Coulomb friction compensator. The contribution of this article is the motor control scheme and the method to tune the parameters of the controllers. It has been implemented in a well-known low-cost small mobile robot and experiments have been carried out that demonstrate the improvement achieved in the performance by using this control system. [ABSTRACT FROM AUTHOR]

Future broadband satellite communication (SatCom) systems require a high throughput of data transmission, which calls for operation at higher frequency bands. Adaptive coding and modulation (ACM) technology has been considered as a means to obtain improved performance further at these frequencies. However, the ACM protocols in current DVB-S2 and DVB-S2(X) standards do not take the effects that arise from the non-linear link with memory into account, which is generated by the cascade of a high-power amplifier (HPA) and digital root raised cosine (RRC) filters. This paper first reveals the non-linear characteristics of the SatCom link, and transfers this into an equivalent full-linear link with an additive noise source thanks to the pre-distortion algorithm. Using this equivalent modeling, an approach of selecting/adapting the optimum coding, modulation scheme and associated system configurations for a given channel fading level is proposed. Both simulations and experimental test-bed performance are presented to validate the proposed method.

This paper shows a proposal for a control scheme for the trajectory tracking problem in a Two Degree of Freedom Helicopter (2DOFH). For this purpose, a control scheme based on a feedback linearization combined with a Generalized Proportional Integral (GPI) controller is used. In order to implement linearization by feedback, it is required to know and have access to all the physical 2DOFH parameters, however, angular velocity and viscous friction are often not available. Commonly, state observers are used to know the angular velocity, however, estimating friction results out to be more complex. Therefore, we propose the use of a Convolutional Neural Network (CNN) to estimate viscous friction and angular velocity. The variables estimated by the CNN are entered into both the GPI and feedforward controllers. Thus, the system is brought to a linear representation that directly relates the GPI control to the dynamics of perturbations and non-model parameters. Finally, results of numerical simulations are shown that validate the robustness of our scheme in the presence of disturbances in the tail rotor, as well as the advantages of using a feedforward control based on a CNN.

The motivation of this paper comes from the fact that $\mathcal {L}_{p}-$ stability and $\mathcal {L}_{p}-$ gain, using the classical signal norms, is not well-defined for arbitrary continuous weighted homogeneous systems. However, using homogeneous signal norms it is possible to show that every internally stable homogeneous system has a globally defined finite homogeneous $\mathcal {L}_{p}-$ gain, for $p$ sufficiently large. If the system has a homogeneous approximation, the homogeneous $\mathcal {L}_{p}-$ gain is inherited locally. Homogeneous $\mathcal {L}_{p}-$ stability can be characterized by a homogeneous dissipation inequality, which in the input affine case can be transformed to a homogeneous Hamilton-Jacobi inequality. An estimation of an upper bound for the homogeneous $\mathcal {L}_{p}-$ gain can be derived from these inequalities. Homogeneous $\mathcal {L}_{\infty }-$ stability is also considered and its strong relationship to Input-to-State stability is studied. These results are extensions to arbitrary homogeneous systems of the well-known situation for linear time-invariant systems, where the Hamilton-Jacobi inequality reduces to an algebraic Riccati inequality. A natural application of finite-gain homogeneous $\mathcal {L}_{p}-$ stability is in the study of stability for interconnected systems. An extension of the small-gain theorem for negative feedback systems and results for systems in cascade are derived for different homogeneous norms. Previous results in the literature use classical signal norms, hence, they can only be applied to a restricted class of homogeneous systems. The results are illustrated by several examples.

This paper presents an input–output linearization (IOL) control strategy to achieve PFC (power factor correction) and output voltage constant in a boost converter. The method transforms the nonlinear system to a linear one in new coordinates by the appropriate nonlinear coordinate transformation and state feedback, ultimately allowing the controller to be designed according to the classical linear control theory. An example implementation is simulated using PSIM software. The simulation results show that the phases of input voltage and input current are consistent, and the output voltage remains constant under load step changes. A set of experimental devices are set up to verify the control method, and the results are consistent with the simulation. Thus, the method is proved to be effective in achieving PFC and provides robust constant voltage output in the boost converter.

The main objective of this paper is to improve the identification efficiency of non-linear systems using the Kalman filter (KF), which is optimised with the Artificial Electric Field (AEF) algorithm. The conventional KF suffers from the proper tuning of its parameters, which leads to a divergence problem. This issue has been solved to a great extent by the meta-heuristic AEF algorithm assisted Kalman filter (AEF-KF). This paper proposes three steps for the identification of the systems while solving the problem as mentioned above. Firstly, it converts the identification model to a measurement problem. Next, the AEF algorithm optimises the KF parameters by considering the fitness function with the KF equations. The third step is to identify the model using conventional KF algorithm with the optimised KF parameters. To evaluate the performance of the proposed method, parameter estimation error, mean squared error (MSE), fitness (FIT) percentage, statistical information and percentage improvement are considered as the performance metrics. To validate the performance of the proposed method, five distinct non-linear models are identified with the Volterra model using KF and the AEF-KF techniques under various noisy input conditions. Besides, the practical applicability of the proposed approach is also tested on two non-linear benchmark systems using experimental data sets. The obtained simulation results confirm the efficacy and robustness of the proposed identification method in terms of the convergence speed, computational time and various performance metrics as compared to KF, Kalman smoother (KS) which is optimised using different state-of-the-art evolutionary algorithms and also other existing recently reported similar types of stochastic algorithms based approaches. • The proposed AEF-KF method resolves the proper tuning problem of Kalman filter. • The role of AEF algorithm is to obtain the optimised set of all the KF parameters. • The proposed method is insensitive to various additive noise input levels. • Simulations carried out on five Volterra models along with two benchmark systems. • AEF-KF outperforms KF and all other reported results with higher convergence speed. [ABSTRACT FROM AUTHOR]

The problems of inconsistent data sampling frequency, outliers, and coloured noise often exist in system identification, resulting in unsatisfactory identification results. In this study, a novel identification method of input non‐uniform sampling Wiener model with a coloured heavy‐tailed noise is proposed. The lifted Wiener model with coloured noise and outlier value disturbed is constructed. Under the expectation‐maximisation (EM) algorithm framework, the student's t‐distribution is introduced to model the contaminated output data. The variance scale is regarded as a unique latent variable, and the iterative parameter estimation formula of the non‐uniform sampling Wiener model is derived. The idea of the auxiliary model is applied to acquire the unmeasured middle variable and handle the coloured noise variable in the non‐uniformly sampled Wiener model. The Differential Evolution algorithm is used to calculate the intractable part of the Q‐function. The convergence analysis of the proposed algorithm is given. Two numerical examples and one water tank simulation are employed to indicate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In order to handle the non-linear system and the complex disturbance in marine engines, a finite-time convergence active disturbance rejection control (ADRC) technique is developed for the control of engine speed. First, a model for the relationship between engine speed and fuel injection is established on the basis of the mean value engine model. Then, to deal with the load disturbances and model parameter perturbation of the diesel engine, this paper designs an ADRC approach to achieve finite-time stability. Finally, simulation experiments show that the proposed method has better control effect and stronger disturbance rejection ability in comparison with the standard linear ADRC.

Accurate trajectory tracking is a paramount objective when a mobile robot must perform complicated tasks. In high-speed movements, time delays appear when reaching the desired position and orientation, as well as overshoots in the changes of orientation, which prevent the execution of some tasks. One of the aspects that most influences the tracking performance is the control system of the actuators of the robot wheels. It usually implements PID controllers that, in the case of low-cost robots, do not yield a good tracking performance owing to friction nonlinearity, hardware time delay and saturation. We propose to overcome these problems by designing an advanced process control system composed of a PID controller plus a prefilter combined with a Smith predictor, an anti-windup scheme and a Coulomb friction compensator. The contribution of this article is the motor control scheme and the method to tune the parameters of the controllers. It has been implemented in a well-known low-cost small mobile robot and experiments have been carried out that demonstrate the improvement achieved in the performance by using this control system.

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Electrification of non-propulsive aircraft systems has resulted in the increased proliferation of power electronics embedded grids on aircraft. Typically, power converters on these networks are optimised locally without consideration to the wider grid dynamics, which as a result increases the interactive effect between sub-systems. Filters are typically used to decouple these interactive effects, however since weight is a key design factor for aircraft, filters are typically reduced in size, further increasing interactive effects. Recent studies into $H_2$ control, due to its ability to develop decentralised controls whilst considering the global grid dynamic model, have shown to reduce these interactive effects, however studies concentrate only on fixed frequency systems, atypical to modern variable frequency grids on modern aircraft today. In this paper, $H_2$ optimisation is used to optimise a target converter to a pre-designed converter generating the variable frequency AC bus. The proposed method shows that not only are interactions reduced on the target converter for all frequencies but allows the pre-designed system to run as designed without detrimental performance, even during large power transients for full range of frequencies. This paper includes mathematical derivations, key design points, and has been validated and compared against other popular controls by experiment.

In this paper, a mechanical system composed of a thin rotating rod under some constraints is considered. For this system, the total torque of the gravity forces is fixed and the unknown function to be determined is the mass density of the rod. This kind of problem is faced in several engineering applications as in aerospace. The resulting problem is formulated as a non classical integral equation, where the conventional methods of resolution do not apply. Therefore, a special treatment is required to solve the obtained integral equation. First, the obtained integral equation is transformed into a system of mixed integral and linear differential equations with two unknown functions. The latter transformation allows the inspiration of the general expression of the requested functions. Consequently, a highly non linear system with several unknowns is obtained. During the resolution of the latter system several mathematical technics are used. After applying all these technics an analytical solution of the studied integral equation is obtained. Finally, the technical feasibility from an engineering viewpoint of the production of a thin rod with the obtained mass density function is briefly discussed. In this context, the Functionally Graded Material is proposed as a material satisfying the obtained mass density function.

Abstract Background Triple tracer meal experiments used to investigate organ glucose-insulin dynamics, such as endogenous glucose production (EGP) of the liver are labor intensive and expensive. A procedure was developed to obtain individual liver related parameters to describe EGP dynamics without the need for tracers. Results The development used an existing formula describing the EGP dynamics comprising 4 parameters defined from glucose, insulin and C-peptide dynamics arising from triple meal studies. The method employs a set of partial differential equations in order to estimate the parameters for EGP dynamics. Tracer-derived and simulated data sets were used to develop and test the procedure. The predicted EGP dynamics showed an overall mean R 2 of 0.91. Conclusions In summary, a method was developed for predicting the hepatic EGP dynamics for healthy, pre-diabetic, and type 2 diabetic individuals without applying tracer experiments.

We believe high accuracy analytic function approach will no longer be useful in calculating the ground state energy of V(x)=x4-λx6 and similar Hamiltonians.

Some seismic design codes require to determine earthquake motions at ground surface, although we need sometimes a motion at engineering basement of ground. For example, it is necessary for optimal design of structures to introduce effects of soil-structure interaction and to input ground motions to engineering basement, which should satisfy the motions at surface required by a design code. This is simplified as a problem to find a possible input signal of a known non-linear-single-input and single-output (SISO) system with a given output signal. This study proposes a very simple algorithm to find a possible input signal for a known SISO system satisfying a given output signal from the system. The proposed algorithm searches for a possible input signal, whose system response is similar in shape to the given output signal, without any system identifications. Thus, it is not an inversion technique; it is an algorithm used to search for one of the possible input signals. Herein, the proposed algorithm is described and its performance is demonstrated using numerical examples. [ABSTRACT FROM AUTHOR]

This study proposes a hybrid method to control dynamic time-varying plants that comprises a neural network controller and a cerebellar model articulation controller (CMAC). The neural-network controller reduces the range and quantity of the input. The cerebellar-model articulation controller is the main controller and is used to compute the final control output. The parameters for the structure of the proposed network are adjusted using adaptive laws, which are derived using the steepest-descent gradient approach and back-propagation algorithm. The Lyapunov stability theory is applied to guarantee system convergence. By using the proposed combination architecture, the designed CMAC structure is reduced, and it makes it easy to design the network size and the initial membership functions. Finally, numerical-simulation results demonstrate the effectiveness of the proposed method.

• The modified Lie-Hori method is useful to solve Hamiltonian dissipative problems. • That is exemplified by computing the nutations of a 2-layer Earth with dissipations. • Analytical and numerical results are compared with previous approximate solution. • Corrections to previous solution reach the microarcsecond level for some periods. • That is about the current level of determination of amplitudes from observations. In this research, a modification of the Lie-Hori perturbation method developed by the authors in a recent investigation is used to compute the forced nutations of a non-rigid Earth model, including dissipative processes at the core-mantle boundary. The study is tackled within the Hamiltonian formalism of a two-layer Earth, where the viscous and electromagnetic couplings between mantle and core are introduced via generalized forces. The modified Lie-Hori method is introduced within the framework of the generalized Hamiltonian formalism. It, therefore, allows for calculating first-order perturbations in both conservative and non-conservative systems, while the classical Lie-Hori procedure is not designed to include generalized forces in the kernel to account for dissipative processes. Unlike other methods, this one presents the advantage of keeping the same dimensionality of the original problem, avoiding the doubling of the dimension of the phase space. With this mathematical refinement, differences in the derived nutation amplitudes at the microarcsecond level have been found when compared with the former, first approximation for dissipative systems based on damped oscillators —the only existing previous solution. Those figures are of relevance according to recent recommendations of the International Astronomical Union (IAU) and the International Association of Geodesy (IAG) based on the final report of the Joint Working Group on Theory of Earth rotation and validation. [ABSTRACT FROM AUTHOR]

This paper considers a general approach to fault diagnosis using a generalized Hamiltonian system representation. It can be considered that, in general, nonlinear systems still represent a problem in fault diagnosis because there are results only for a specific class of them. Therefore, fault diagnosis remains a challenging research area despite the maturity of some of the available results. In this work, a type of nonlinear system that admits a generalized Hamiltonian representation is considered; in practice, there are many systems that have this kind of representation. Thereupon, an approach for fault detection and isolation based on the Hamiltonian representation is proposed. First, following the classic approach, the original system is decoupled in different subsystems so that each subsystem is sensitive to one particular fault. Then, taking advantage of the structure, a simple way to design the residuals is presented. Finally, the proposed scheme is validated at the two-degree of freedom (DOF) helicopter of Quanser®, where the presence of faults in sensors and actuators were considered. The results show the efficacy of the proposed scheme. [ABSTRACT FROM AUTHOR]

The paper considers a geometrically non-linear column constructed as an overbraced flat rod system loaded with a force directed towards the positive pole. The analyzed system is characterized by two forms of static equilibrium: rectilinear and curvilinear. It was proved in scientific studies that the loss of rectilinear form can be local and is directly related to the distribution of bending stiffness. In this paper, it is proposed to use elements with a variable cross-section as a way to reduce the phenomenon of local loss of rectilinear static equilibrium. The obtained results allow for the statement that proper shaping of the non-prismatic rod which is a component of the geometrically non-linear system may cause an increase in bifurcation load, and thus limiting the scope of local loss of rectilinear form of static equilibrium. [ABSTRACT FROM AUTHOR]

This study proposes a hybrid method to control dynamic time-varying plants that comprises a neural network controller and a cerebellar model articulation controller (CMAC). The neural-network controller reduces the range and quantity of the input. The cerebellar-model articulation controller is the main controller and is used to compute the final control output. The parameters for the structure of the proposed network are adjusted using adaptive laws, which are derived using the steepest-descent gradient approach and back-propagation algorithm. The Lyapunov stability theory is applied to guarantee system convergence. By using the proposed combination architecture, the designed CMAC structure is reduced, and it makes it easy to design the network size and the initial membership functions. Finally, numerical-simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The identification of thermal systems is an approach particularly well suited to solve inverse heat conduction problems (IHCP) in the case of complex systems where many parameters are unknown and where even the sensors must be modeled in order to obtain accurate results. In this paper, we propose significant advances in the formulation of the mathematical model structure by basing it exclusively on the non-integer order integration operator. We show that this approach is consistent with the heat diffusion process and that it allows to get rid of the step of pre-filtering the experimental signals to the sensors which was necessary when using the derivation operator. Demonstrations are made on the simulated configurations through simple analytical solutions and also a complex real configuration. I generalize the use of the non-integer integration operator in the treatment of non-linear heat conduction problems based on the Volterra series decomposition. We show in particular that the use of a generalized non-integer transfer function gives encouraging and generalizable results for a large class of related problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.

The article aims to document PhaPl that’s a teaching software to plot and research phase portraits of autonomous systems of 2 differential equations on a plane. Interactive computer teaching materials allow to demonstrate tasks describing large number of states of investigated systems clearly and involving students into solving. Plotting and research of phase portraits of autonomous system of 2 differential equations is an important task in “Differential equations” course and other courses that use dynamic systems. The software allows to visualize phase portraits and to perform analysis easily. Plotting of phase portraits needs a lot of routine computations. The software allows teacher to focus on analytical research of autonomous systems of 2 differential equations. The software supports linear and nonlinear autonomous systems of 2 differential equations. The software differs is very different compared with previously known programs: it has very easy graphical user interface and it gives clarity because it demonstrates all steps of solution. To get the full solution, it is enough to just enter a system to research. Initial conditions to plot phase trajectories are chosen automatically. Graphical representation of the phase plane is interactive and allows user to draw additional trajectories with specified initial conditions by mouse hovering over the phase plane. The software is based on popular Free Software (Maxima, Qt4, LaTeX) and it is Free Software itself, thus it is accessible to wider audience, including online students. The software is portable and works on Windows and Linux operating systems. The article describes advantages, disadvantages and peculiar properties of the software, and some aspects of teaching experience. The software is deployed in Moscow State University of Economics, Statistics, and Informatics (MESI), Lomonosov Moscow State University (MSU) since 2013, and in Plekhanov Russian University of Economics since 2016. Further development will be focused on reduction of binary size of the software, portability improvements, and number of analytical results showed.

The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle's invariance principle. Stabilisation in a wide range of controller parameters improves the system's robustness. [ABSTRACT FROM AUTHOR]

• Pitch angle control of the wind turbine using the FOFPID controller is proposed and investigated for efficiency in power regulation. • The proposed FOFPID based pitch angle controller achieves convenient control in dynamic wind speed and provides suitable behaviour for a highly non-linear wind turbine system, and hence, was selected to control the pitch angle of a wind turbine. • The pitch angle regulation performance of the FOFPID based pitch angle controller is investigated to establish superiority over PID, FOPID and FPID based pitch angle controllers. • The FOFPID based pitch angle controller is well-tuned by TLBO. TLBO tuned PID, FOPID and FPID controllers are also analysed to control the pitch angle for the first time. A wind energy conversion system (WECS) is a highly nonlinear and coupled system in which the output power depends upon highly uncertain wind speed. Therefore, the quality of produced power becomes a challenging problem for engineers. Pitch angle control is a powerful and widely used power control method to handle wind above the rated wind speed. In this paper, a fractional order fuzzy-proportional-integral-derivative controller is proposed for pitch angle control to preserve the output power of a 2 MW direct-drive WECS at the rated value in dynamic wind conditions. To evaluate the performance of the proposed controller, the rise time, fall time, settling time, overshoot and total harmonic distortion by the proposed controller are compared with conventional and other intelligent controllers. Furthermore, the proposed controller is well-tuned using a teaching-learning based optimization (TLBO) algorithm. The performance of the TLBO is also compared with the genetic algorithm to show effectiveness. [ABSTRACT FROM AUTHOR]

The continuous uninterrupted supply of Natural Gas (NG) is crucial to today's economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton–Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids. [ABSTRACT FROM AUTHOR]

Controlling load–frequency is regarded as one of the most important control-related issues in design and exploitation of power systems. Permanent frequency deviation from nominal value directly affects exploitation and reliability of power system. Too much frequency deviation may cause damage to equipment, reduction of network loads efficiency, creation of overload on communication lines and stimulation of network protection tools, and in some unfavorable circumstances, may cause the network collapse. So, it is of great importance to maintain the frequency at its nominal value. It would be useful to make use of the type 2 fuzzy in modeling of uncertainties in systems which are uncertain. In the present article, first, the simplified 4-block type-2 fuzzy has been used for modeling the fuzzy system. Then, fuzzy system regulations are reduced by 33% with the help of hierarchy fuzzy structure. The simplified type-2 fuzzy controller is optimized using the Cuckoo algorithm. Eventually, the performance of the proposed controller is compared to the Mamdani fuzzy controller in terms of the ISE, ITSE, and RMS criteria.

In this paper, a numerical solution of mass transfer effects on an unsteady free convection flow of an incompressible electrically conducting viscous dissipative fluid past an infinite vertical porous plate under the influence of a uniform magnetic field considered normal to the plate has been obtained. The non-dimensional governing equations for this investigation are solved numerically by using the Ritz finite element method. The effects of flow parameters on the velocity, temperature and concentration fields are presented through the graphs and numerical data for the skin-friction, Nusselt and Sherwood numbers are presented in tables and then discussed.

This paper considers a general approach to fault diagnosis using a generalized Hamiltonian system representation. It can be considered that, in general, nonlinear systems still represent a problem in fault diagnosis because there are results only for a specific class of them. Therefore, fault diagnosis remains a challenging research area despite the maturity of some of the available results. In this work, a type of nonlinear system that admits a generalized Hamiltonian representation is considered; in practice, there are many systems that have this kind of representation. Thereupon, an approach for fault detection and isolation based on the Hamiltonian representation is proposed. First, following the classic approach, the original system is decoupled in different subsystems so that each subsystem is sensitive to one particular fault. Then, taking advantage of the structure, a simple way to design the residuals is presented. Finally, the proposed scheme is validated at the two-degree of freedom (DOF) helicopter of Quanser®, where the presence of faults in sensors and actuators were considered. The results show the efficacy of the proposed scheme.

Throughout this paper, the model, its parameter estimation and a controller for a solution using a DC motor with a gearbox worm, coupled to a non-rigid joint, will be presented. First, the modeling of a non-linear system based on a DC Motor with Worm Gearbox coupled to a non-rigid joint is presented. The full system was modeled based on the modeling of two sub-systems that compose it—a non-rigid joint configuration and the DC motor with the worm gearbox configuration. Despite the subsystems are interdependent, its modelling can be performed independently trough a carefully chosen set of experiments. Modeling accurately the system is crucial in order to simulate and know the expected performance. The estimation process and the proposed experimental setup are presented. This setup collects data from an absolute encoder, a load cell, voltage and current sensors. The data obtained from these sensors is presented and used to obtaining some physical parameters from both systems. Finally, through an optimization process, the remaining parameters are estimated, thus obtaining a realistic model of the complete system. Finally, the controller setup is presented and the results obtained are also presented.

A method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on numerical examples.

We prove the null controllability of a parabolic system. The single control is common to both PDEs, distributed and subject to constraints. The studied model can be applied in dynamics of biological systems or in physics. First we study the problem associated to a similar linearized system. Then appropriate Carleman inequalities and a fixed-point argument are used to prove the null controllability results. [ABSTRACT FROM AUTHOR]

Although associative memory functions realized by CNNs have been widely demonstrated, most of those CNNs models don’t contain external inputs, and rarely have mentioned the implementation of actual circuit. In this work, we demonstrate the associative memory on the basis of three-cell CNNs with external inputs. Both single-associative memory and multi-associative memories can be realized by varying the initial values of the three-cell CNNs. In the physical circuit, different eight patterns can be stored and reconfigured by tuning very few resistances and the pre-stored patterns can be successfully retrieved. [ABSTRACT FROM AUTHOR]

The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this research builds the theoretical background to understand the sharing economy business model. Analytically, the techniques include a classical Markov process of the single channel queueing system, semi-Markov process and semi-regenerative process. It uses the stochastic congruent properties to find the probability distribution of the number of contractors in the sharing economy platform. The obtained explicit formulas demonstrate the usage of functional for the main stochastic characteristics including sharing expenses due to over contracted resources and optimization of their objective function.

Consistent state estimation is a vital requirement in numerous real life applications from localization to multi-source information fusion. The Kalman filter and its variants have been successfully used for solving state estimation problems. Kalman filtering-based estimators are dependent upon system model assumptions. A deviation from defined assumptions may lead to divergence or failure of the system. In this work, we propose a Kalman filtering-based robust state estimation model using statistical estimation theory. Its primary intention is for multiple source information fusion, although it is applicable to most non-linear systems. First, we propose a robust state prediction model to maintain state constancy over time. Secondly, we derive an error covariance estimation model to accept deviations in the system error assumptions. Afterward, an optimal state is attained in an iterative process using system observations. A modified robust MM estimation model is executed within every iteration to minimize the impact of outlying observation and approximation errors by reducing their weights. For systems having a large number of observations, a subsampling process is introduced to intensify the optimized solution redundancy. Performance is evaluated for numerical simulation and real multi sensor data. Results show high precision and robustness of proposed scheme in state estimation.

The continuous uninterrupted supply of Natural Gas (NG) is crucial to today’s economy, with issues in key infrastructure, e.g., Baumgarten hub in Austria in 2017, highlighting the importance of the NG infrastructure for the supply of primary energy. The balancing of gas supply from a wide range of sources with various end users can be challenging due to the unique and different behaviours of the end users, which in some cases span across a continent. Further complicating the management of the NG network is its role in supporting the electrical network. The fast response times of NG power plants and the potential to store energy in the network play a key role in adding flexibility across other energy systems. Traditionally, modelling the NG network relies on nonlinear pipe flow equations that incorporate the demand (load), flow rate, and physical network parameters including topography and NG properties. It is crucial that the simulations produce accurate results quickly. This paper seeks to provide a novel method to solve gas flow equations through a network under steady-state conditions. Firstly, the model is reformulated into non-linear matrix equations, then the equations separated into their linear and nonlinear components, and thirdly, the non-linear system is solved approximately by providing a linear system with similar solutions to the non-linear one. The non-linear equations of the NG transport system include the main variables and characteristics of a gas network, focusing on pressure drop in the gas network. Two simplified models, both of the Irish gas network (1. A gas network with 13 nodes, 2. A gas network with 109 nodes) are used as a case study for comparison of the solutions. Results are generated by using the novel method, and they are compared to the outputs of two numerical methods, the Newton–Raphson solution using MATLAB and SAINT, a commercial software that is used for the simulation of the gas network and electrical grids.