Search results

A distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.

A solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.

So far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.

There are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.

There are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.

The proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.

The proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system’s state vector and by the last sampled value of the control input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems that can be transformed to the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions.

The purpose of this paper is to establish an intelligent framework to generate the data representatives in snapshot simulation in order to construct the online reduced-order model based on the generated data information. It could greatly reduce the computational time in snapshot simulation and accelerate the computational efficiency in the real-time computation of reduced-order modeling.

The snapshot simulation, which generates the data to construct reduced-order models (ROMs), usually is computationally demanding. In order to accelerate the snapshot generation, this paper presents a discrete element interpolaiton method (DEIM)-embedded hybrid simulation approach, in which the entire snapshot simulation is partitioned into multiple intervals of equal length. One of the three models: the full order model (FOM), local ROM, or local ROM-DEIM which represents a hierarchy of model approximations, fidelities and computational costs, will be adopted in each interval.

The outcome of the proposed snapshot simulation is an efficient ROM-DEIM applicable to various online simulations. Compared with the traditional FOM and the hybrid method without DEIM, the proposed method is able to accelerate the snapshot simulation by 54.4%–63.91% and 10.5%–27.85%, respectively. In the online simulation, ROM-DEIM only takes 4.81%–8.56% of the computational time of FOM, while preserving excellent accuracy (with relative error <1%).

1. A DEIM-embedded hybrid snapshot simulation methodology is proposed to accelerate snapshot data generation and reduced-order model (ROM)-DEIM development. 2. The simulation alternates among FOM, ROM and ROM-DEIM to adaptively generate snapshot data of salient subspace representation while minimizing computational load. 3. The DEIM-embedded hybrid snapshot approach demonstrates excellent accuracy (<1% error) and computational efficiency in both online snapshot simulation and online ROM-DEIM verification simulation.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

The purpose of this paper is to propose a new linear-nonlinear data preprocessing-based hybrid model to achieve a more accurate result at a lower cost for wind power forecasting. For this purpose, a decomposed based series-parallel hybrid model (PKF-ARIMA-FMLP) is proposed which can model linear/nonlinear and certain/uncertain patterns in underlying data simultaneously.

To design the proposed model at first, underlying data are divided into two categories of linear and nonlinear patterns by the proposed Kalman filter (PKF) technique. Then, the linear patterns are modeled by the linear-fuzzy nonlinear series (LLFN) hybrid models to detect linearity/nonlinearity and certainty/uncertainty in underlying data simultaneously. This step is also repeated for nonlinear decomposed patterns. Therefore, the nonlinear patterns are modeled by the linear-fuzzy nonlinear series (NLFN) hybrid models. Finally, the weight of each component (e.g. KF, LLFN and NLFN) is calculated by the least square algorithm, and then the results are combined in a parallel structure. Then the linear and nonlinear patterns are modeled with the lowest cost and the highest accuracy.

The effectiveness and predictive capability of the proposed model are examined and compared with its components, based models, single models, series component combination based hybrid models, parallel component combination based hybrid models and decomposed-based single model. Numerical results show that the proposed linear-nonlinear data preprocessing-based hybrid models have been able to improve the performance of single, hybrid and single decomposed based prediction methods by approximately 66.29%, 52.10% and 38.13% for predicting wind power time series in the test data, respectively.

The combination of single linear and nonlinear models has expanded due to the theory of the existence of linear and nonlinear patterns simultaneously in real-world data. The main idea of the linear and nonlinear hybridization method is to combine the benefits of these models to identify the linear and nonlinear patterns in the data in series, parallel or series-parallel based models by reducing the limitations of the single model that leads to higher accuracy, more comprehensiveness and less risky predictions. Although the literature shows that the combination of linear and nonlinear models can improve the prediction results by detecting most of the linear and nonlinear patterns in underlying data, the investigation of linear and nonlinear patterns before entering linear and nonlinear models can improve the performance, which in no paper this separation of patterns into two classes of linear and nonlinear is considered. So by this new data preprocessing based method, the modeling error can be reduced and higher accuracy can be achieved at a lower cost.

This study seeks to explore the nature of a data‐generating process for four dollar exchange rates.

Using a discrete parametric modeling approach, an efficient test statistic was computed for nonlinearity in terms of variance of the residuals of the linear and nonlinear autoregressive models by Akaike Information Criterion, and a surrogate data analysis was conducted.

It shows that a nonlinear autoregressive model outperforms a linear stochastic model in certain subsamples of baht, pound, ringgit, and yen dollar exchange rates. However, when the test statistics using different model orders and the data for the entire samples are estimated, it appears that the nonlinear model has a better performance than the linear model in fitting Thai and Malaysian currencies. The nonlinear model performs better than the linear model in the case of the UK pound in two thirds of the models, but the linear models completely outperform the nonlinear models for the yen data.

More financial and economic time series will be explored to employ the methodology used in the study, and tests for possible presence of nonlinear deterministic dynamics (chaos) in the exchange rates series will be conducted based on the present findings in further study.

These findings suggest that the assumption of linear stochastic process as the underlying dynamics for all currencies examined in this study may not be justifiable.

To the best of the authors' knowledge, this study is the first attempt to use the test statistic based on the information‐theoretical method in testing nonlinearity in financial and economic time series.

The present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).

The authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.

Compared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.

Once models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.

MTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.

The operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.

Nonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

This paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.

As the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases.

Compared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately.

The nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model.

This paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles.

Based on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed.