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Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC. [ABSTRACT FROM AUTHOR]

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.)

The tracking control of a non-linear fractional-order system (FOS) is highly tedious since cumulative approximation errors are encountered during the control process. Hence, to cope with that problem, several controllers have been adopted previously, such as backstepping controllers, sliding mode controllers, dynamic surface controllers, etc. These controllers have successfully reduced the approximation errors in the integer order non-linear system. However, the performance of those effective controllers in fractional-order non-linear systems is evaluated in this paper. The controllers such as the backstepping controller, sliding mode controller, dynamic surface controller and fuzzy dynamic surface controller are examined on FOS to verify the stability of control systems. As a result, the backstepping controller has performed better than other controllers in the case of actuator errors but still has the problem of the increased number of derivative terms and greater complexity in repeated calculations. The tracking error of the backstepping controller has been reduced to 0.0358 with 1.58 s of response time. [ABSTRACT FROM AUTHOR]

The proportional integral derivative (PID) controller continues to be the most popular and widely used in the industry despite the development of various artificial intelligence-based controllers due to its simplicity and ease of use. Setting PID parameters, especially in non-linear systems, is still a significant problem. This study presents a cascade PID tuning technique based on the teaching–learning-based optimization (TLBO) algorithm. The proposed method is tested for the position control of a non-linear ball and beam system. A comparative analysis of the proposed method is done with the conventional tuning method and particle swarm optimization-tuned cascade PID controller. The optimization was carried out using integral time absolute error, integral time error, and integral square error as objective functions. It was observed that the evolutionary algorithm-based controller tuned by TLBO gives a much better response regarding rise time, settling time, and overshoot. To test the effectiveness and validity of the proposed controller robust analysis of the proposed controller is carried out with a step disturbance applied at t = 3 s. The comparative study proves that TLBO-tuned response is better than other controllers. Sensitivity analysis of the proposed controller is also performed by varying system parameters. [ABSTRACT FROM AUTHOR]

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.

The paper is devoted to the study of optimal control of a hyperbolic system, where the control enters the system through the boundary. The hyperbolic system is the wave equation on a smooth and open domain, where the boundary condition involves the normal derivative at the boundary of z, the time derivative of z times a constant k, and a nonlinear term control. Here, z is the state and u is the control, satisfying some boundedness condition depending on k. The functional cost consists of the energy and the difference between the solution of the system at final time, and a desired state in $ L^2 $ L 2 -norm. For a closed convex set, we prove the existence of an optimal control that minimises the cost functional using a priori estimates. Then, using the differentiability of the cost functional with respect to the control, we establish the characterisation by deriving necessary conditions that an optimal control must satisfy. A numerical approach is successfully illustrated by simulations. [ABSTRACT FROM AUTHOR]

This paper presents a combination of both the Takagi–Sugeno–Kang fuzzy controller and the advantage of reinforcement learning for the reduction in the effect of external disturbances and system uncertainties. A neural network is used for the implementation of a critic network; the parameters are updated using the Lyapunov criteria for avoiding local minima problems. The fewer learning parameters used helps online tuning of the controller by the critic network based on the reward function. MATLAB/Simulink is used for simulation of the proposed system under different conditions in the investigation of the performance of the proposed controller. The actor parameters are updated based on the change in the reward function error and a control function. Five different conditions, namely, no-load condition, sudden load-torque changes, system parameter uncertainty, sudden phase interruption, and the impact of noise have been studied. The proposed method was found to meet the high-speed response with the tracking error of ±2.23% for the tracking reference trajectory and tracking error of ±2.5% under constant load-torque disturbance. The test results were compared with two benchmark controllers for the verification of the effectiveness of the proposed controller. Simulation results showed the proposed method providing an adaptive and precise speed response. Therefore, it is suitable for non-linear and uncertain applications. [ABSTRACT FROM AUTHOR]

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]

One of the common non-linear process control problems is the continuous stirred tank reactor problem and the reactor is applied widely in chemical process industries. It is of high importance to develop a suitable controller scheme for the concentration and temperature control of the considered non-linear continuous stirred tank reactor (CSTR) model. In this paper, a novel wavelet neural network (WNN) controller model is developed to carry out the control action and to meet the performance requirements of the system model. The developed wavelet neural network model is tuned for its weights employing the proposed deterministic grey wolf optimizer algorithm and its input is fed from the Mamdani fuzzy model. The optimal number of rules to be formulated for the fuzzy rule base model is computed using the deterministic grey wolf optimizer (DGWO) which is the variant of the classic grey wolf optimizer (GWO). WNN controller devise, based on the inputs from the fuzzy model and weights from DGWO, is designed to perform control action on the non-linear CSTR model. The concentration and temperature control is carried out by the proposed controller and the responses are obtained. Also, the respective time response specifications are evaluated for the developed WNN controller. Simulation experiments prove the effectiveness of the proposed controller for the considered non-linear CSTR model in comparison with that of the existing controllers from the literature. [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.

The ability to describe the nonlinear process dynamics is an essential feature of the Hammerstein model that paved more research and application studies in system identification and control. Using the Hammerstein model, this study shows an alternative approach to identify and control the highly nonlinear pH neutralization process. This Hammerstein model called Laguerre Least Square Support Vector Machines (LLSSVM) models the static nonlinearity with LSSVM and the linear part with Laguerre filter. The identified LLSSVM Hammerstein model performance evaluation with Mean Squared Error (MSE) and Variance Accounted For (VAF) is better than the Linear Laguerre model. We apply the identified LLSSVM Hammerstein model to implement a Nonlinear Model Predictive Controller (NMPC) to control the pH neutralization process. Then evaluated NMPC performance in terms of Integral Squared Error (ISE), Integral Absolute Error (IAE), and Total Variation (TV) and Control Effort (CE) parameters to verify its effectiveness in set-point tracking and disturbance rejection problems. The comparison of the NMPC with the Linear Laguerre Model-based Predictive Controller (LMPC) shows better performance of the NMPC than the LMPC. Results show that the LLSSVM Hammerstein model replicates the pH neutralization process well than the Linear Laguerre model. Also, the identified LLSSVM Hammerstein model provides an efficient NMPC than the LMPC for the pH neutralization process. [ABSTRACT FROM AUTHOR]

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]

Multi‐agent system (MAS) is a common cyber‐physical system (CPS). Due to it often uses a relatively open network platform, it is vulnerable to malicious cyber attacks in the process of system operation, so the control scheme design is critical to ensure the system operation security. In this article, we propose a new resilient neuroadaptive dynamic surface control scheme for non‐linear MASs with potential cyber attacks (false data injection and denial‐of‐service), system uncertainty, unknown control gain, and output constraints which are usually seen on CPSs. In this scheme, the neuroadaptive controller design ensures that all signals of the closed loop system are semi‐globally uniform ultimately bounded when the MAS even exists time‐varying cyber attacks on data links among agents, and the links between controllers, actuators, and sensors. Using Gaussian radial basis function neural network, the system uncertainty, non‐strict feedback terms, unknown control gain, and some cyber attacks are effectively solved and the process of controller design is extremely simplified. Finally, we provide a simulation result to verify the effectiveness and superiority of the proposed control scheme. [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.

This paper investigates a new disturbance observer based non-singular fast terminal sliding mode control technique for the path tracking and stabilization of non-linear second-order systems with compound disturbance. The compound disturbance is comprised of both parametric and non-parametric uncertainties. While warranting fast convergence rate and robustness, it also dominates the singularity and complex-value number issues associated with conventional terminal sliding mode control. Furthermore, due to the estimation properties of the observer, knowledge about the bounds of the uncertainties is not required. The simulation results of two case studies, the velocity and path tracking of an autonomous underwater vehicle and the stabilization of a chaotic Φ6-Duffing oscillator, validate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

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.)

The article presents a mathematical model that simulates the elastic and plastic behaviour of discrete systems representing isotropic materials. The systems consist of one lattice of nodes connected by edges and a second lattice with nodes placed at the centres of the existing edges. The derivation is based on the assumption that the kinematics of the second lattice is induced by the kinematics of the first, and uses stored energies in edges of both lattices to derive a edge forces in the first lattice. This leads to a non-linear system of algebraic equations describing elasticity and plasticity in lattices. A numerical solution to the non-linear system is proposed by providing a matrix formulation necessary for software implementation. An illustrative example is given to justify the formulation and demonstrate the system behaviour. [ABSTRACT FROM AUTHOR]

• Wind and hydro systems are lauded for cost-effectiveness and environmental benefits. • FAT-AOS proposes a novel method for optimizing FOPID controllers efficiently. • FAT-AOS ensures system stability during disturbances, minimizing computational load. • Key metrics validate superior performance in rise time and settling time. • Simulation results in MATLAB confirm improved outcomes over existing approaches. Wind and hydroelectric systems are more cost-effective and environmentally beneficial. A hybrid technique is proposed for the fractional-order proportional-integral-derivative (FOPID) controller to regulate the wind and hydro system. The proposed hybrid technique combines the feedback-artificial-tree (FAT), and atomic-orbital-search (AOS); together known as FAT-AOS approach. The proposed technique is utilized to decide the optimum controller parameters, and it guarantees system constancy in large disturbances using less computation and overshoot by restraining the parameter variation. The FAT is used to predict the optimum gain parameter of FOPID, and minimizing the system error is accomplished with the AOS approach. The performance metrics are peak time, rise time, settling time, and peak overshoot, are analyzed. The performance of the proposed method is done in the MATLAB platform. The simulation result of proposed approach for the rise time as 0.001 sec, settling time is 0.012 sec, and the overshoot percentage is 0.02 %. By comparing the existing methods, like Ant lion optimizer (ALO), Salp swarm algorithm (SSA), Particle swarm optimization (PSO), the proposed approach rise time and settling time overshoot, is less. The comparison proves that the proposed system delivers improved outcome than existing systems. [ABSTRACT FROM AUTHOR]

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]