Several Types Of Nonlinearities Research Articles

On Development of Two-Wheeled Balancing Robot Adaptive Control System on Basis of Second Lyapunov Approach with Tunable Step Size

The problem of a two-wheeled balancing robot control is the scope of this research. Such plants are unstable, and their mathematical description includes several types of nonlinearities: rising to the power of the robot state coordinates and the trigonometric functions application. Moreover, such objects are non-stationary, i.e. they change the values of their parameters (mass, position of the center of mass and the coefficient of friction of the wheels on the road surface). The existing control systems of balancing robots (in most cases, these are optimal LQ algorithms and PID controllers) are not able to provide compensation of significant parametric disturbances, although they have a certain robustness with respect to them. All above mentioned problems make it reasonable to apply adaptive control algorithms to such plants. So we propose an adaptive control system based on the second Lyapunov method and the use of a reference model. To build such an adaptive controller in this study: 1) a mathematical description of the reference dynamics of the robot (at nominal values of its parameters) is made; 2) the LQ regulator parameters are calculated according to the theory of optimal control; 3) an adaptation loop of the parameters of the obtained controller, which does not require the plant model, is developed on the basis of the second Lyapunov method. The resulting adaptation loop is supplemented with a variable step size, which is recalculated on the basis of data about the current and previous values of the reference of the robot state coordinates. Experimental validation of the adaptive controller is made with the help of both mathematical and physical models of the balancing robot. Considering the experiments with the mathematical model, the mass of the robot is increased from two to 13.5 times. As for the physical model, the mass is doubled. The experimental results show the efficiency of the developed system in comparison with the optimal LQ-regulator in terms of the integral quadratic transient quality index.

The optimization of a hydroformed tube

The shaping by hydroforming process involves several complex phenomena and presents several types of nonlinearities (geometric, material,...). The development of a hydroforming operation requires a lot of testing to determine with precision the optimum loads of trips and get a room without defects. Advances in digital tools have enabled manufacturers to simulate and optimize their production facilities before launching the production in order to minimize the maximum rate of defective parts.

INTERACTION OF NONLINEAR NUMERICAL MODEL OF SFRC SLAB AND NONLINEAR NUMERICAL SUBSOIL MODEL

Experimental measurements of the concrete slab in interaction with subsoil are compared with numerical analysis based on Finite Element Method FEM. Experimental measurements are conducted with usingan experimental device constructed at the Faculty of Civil Engineering VSB – Technical University of Ostrava. In the article, several types of nonlinearities enter into FEM analysis. Subsoil-structure interaction requires an iterative solution procedure - and therefore structural nonlinearity. Material nonlinearity was used in the numerical model of the slab. This model also allows the creation and development of cracks in concrete - similar as during the experimental load test. Material nonlinearity was also used in the numerical model subsoil - to ensure of apposite subsoil behavior. The purpose of this paper is to compare resulting deformation of the slab with values observed during experimental loading test. It was concluded that the good agreement between the experimental results and numerical simulation was observed.

Elementary functions for constructing exact solutions to nonlinear partial differential equations with applications to nonlinear Schrödinger type and MHD equations

In this paper we present an improvement to those methods based on the using of elementary functions like exponential, trigonometric and hyperbolic functions in obtaining exact solutions to nonlinear partial differential equations (NPDEs). The improved method is applied to stable nonlinear Schrödinger (NLS), unstable NLS, generalized NLS, High-order NLS and derivative NLS equations. New solutions for these equations are obtained. The obtained solutions are more general than a wide class of previous solutions. Solutions of a derivative NLS equation that describes the large-amplitude solitons propagating in an arbitrary direction in a high-β hall plasma are also obtained. Moreover, the method is applied to magnetohydrodynamics (MHD) equations describing an ideal incompressible flow in the steady state. One of the most important advantages of the solution method presented here is it deals with several types of nonlinearities associated with PDEs without making a transformation of the original equation to another one.

Explicit dynamics simulation of blade cutting of thin elastoplastic shells using “directional” cohesive elements in solid-shell finite element models

The intentional or accidental cutting of thin shell structures by means of a sharp object is of interest in many engineering applications. The process of cutting involves several types of nonlinearities, such as large deformations, contact, crack propagation and, in the case of laminated shells, delamination. In addition to these, a special difficulty is represented by the blade sharpness, whose accurate geometric resolution would require meshes with characteristic size of the order of the blade curvature radius. A computational finite element approach for the simulation of blade cutting of thin shells is proposed and discussed. The approach is developed in an explicit dynamics framework. Solid-shell elements are used for the discretization, in view of possible future inclusion in the model of delamination processes. Since a sharp blade can interfere with the transmission of cohesive forces between the crack flanks in the cohesive process zone, standard cohesive interface elements are not suited for the simulation of this type of problems unless extremely fine meshes, with characteristic size comparable to the blade curvature radius, are used. To circumvent the problem, the use of a new type of directional cohesive interface element, previously proposed for the simulation of crack propagation in elastic shells, is further developed and reformulated for application to the cutting of elastoplastic thin structures, discretized by solid-shell elements. The proposed approach is validated by means of application to several cutting problems of engineering interest.

Adaptive Robust Precision Motion Control of Linear Motors With Integrated Compensation of Nonlinearities and Bearing Flexible Modes

To realize the high performance potential of linear motor drive systems, various nonlinearities inherited to the system and their compensations have been extensively studied during the past decade. However, existing research tends to focus on one or several types of nonlinearities at a time and thus do not offer a complete overall solution. This paper studies precision motion control of linear motors in the presence of parameter variations and disturbances. An adaptive robust control (ARC) algorithm with simultaneous compensation of all significant nonlinearities is developed. Those nonlinearities include Coulomb friction, cogging force, and nonlinear electromagnetic field effect. The proposed ARC with and without nonlinearity compensation have also been implemented on the Y-axis of a linear-motor-driven industrial gantry. Comparative experimental results show that the proposed ARC algorithm with simultaneous compensation of all significant nonlinearities achieves better motion tracking performance than existing ones. In addition, high-frequency structural flexible modes due to bearing, which are neglected in the previous researches, are explicitly identified experimentally, and their effects are carefully examined. Theoretical analysis is then conducted to generate a set of practically useful guidelines on the tuning of controller gains to optimize the achievable performance in practice.

Não linearidades, mudanças de regime e assimetrias na taxa de inflação brasileira: análise a partir de um modelo SETAR, 1944-2009

O objetivo principal deste estudo é investigar assimetrias e não linearidades na inflação brasileira, descrevendo-a como um processo autorregressivo sujeito a mudanças de regime. A metodologia empregada baseia-se na aplicação de testes para três tipos de não linearidade. Foi estimado um modelo SETAR com dois regimes capaz de descrever o comportamento não linear e assimétrico de um processo autorregressivo. Todos os testes indicaram a não linearidade da inflação brasileira. Os resultados das estimações sugerem a ocorrência de pelo menos dois regimes distintos para a inflação com diferentes processos geradores. O regime de baixa inflação é o menos volátil e o mais persistente. A despeito dos períodos de alta inflação e alta volatilidade, conclui-se que o regime de baixa inflação com baixa volatilidade é uma característica predominante na economia brasileira.

Institutions and parameter heterogeneity

The role of institutions has taken center stage in the empirical growth literature recently, with many innovative approaches and suggestive results. Most of the previous literature has focused on the direct correlation between institutions and growth or its determinants. In this paper, I investigate the indirect effect that institutions may have on growth through parameter heterogeneity. In particular, the quality of a country’s institutions could affect the relationship between growth and its other determinants, such as human and physical capital accumulation, geography, and government policies. After allowing for several types of nonlinearities, the results are generally supportive of Glaeser et al. [Glaeser, E.L., La Porta, R., Lopez-de-Silanes, F., Shleifer, A., 2004. Do institutions cause growth? Journal of Economic Growth, 9 (3), 271–303] in that most of their preferred measures of institutions are not correlated with growth. However, there is some evidence that institutions do matter for policy variables, particularly those associated with trade policy.

Institutions and Parameter Heterogeneity

The role of institutions has taken center stage in the empirical growth literature recently, with many innovative approaches and suggestive results. Most of the previous literature has focused on the direct correlation between institutions and growth or its determinants. In this paper, I investigate the indirect effect that institutions may have on growth through parameter heterogeneity. In particular, the quality of a country's institutions could affect the relationship between growth and its other determinants, such as human and physical capital accumulation, geography, and government policies. After allowing for several types of nonlinearities, the results are generally supportive of Glaeser, La Porta, and Lopez-de-Silanes (2004) in that most of their preferred measures of institutions are not correlated with growth. However, there is some evidence that institutions do matter for policy variables, particularly those associated with trade policy.

Investigation of several types of nonlinearities for use in stereo acoustic echo cancellation

In this paper, we investigate several types of nonlinearities used for the unique identification of receiving room impulse responses in stereo acoustic echo cancellation. The effectiveness is quantified by the mutual coherence of the transformed signals. The perceptual degradation is studied by psycho-acoustic experiments in terms of subjective quality and localization accuracy in the medial plane. The results indicate that, of the several nonlinearities considered, ideal half-wave rectification appears to be the best choice for speech. For music, the nonlinearity parameter of the ideal rectifier must be readjusted. The smoothed rectifier does not require this readjustment, but is a little more difficult to implement.

Boundary element formulation for nonlinear applications in geomechanics

Several types of nonlinearities are considered, using the boundary element method, with emphasis on geomechanical applications. Numerical algorithms to model ‘no-tension’ plastic, viscoplastic and viscoelastic responses are presented. Extension of the method to two-dimensional piecewise homogeneous problems is shown. The overlay technique is adapted for the boundary element formulation to model complex plastic and viscoplastic responses. In particular, the technique is shown to be extremely useful to model time-dependent behaviour. It has also proved suitable for the Bauschinger-effect representation in elastoplastic analysis. Tunnel examples are presented and are shown to be very well suited to solution by boundary elements. The method deals with infinite domains without requiring the definition of an artificial outer boundary. As a result little discretization is needed.

Treatment of nonlinear terms in the numerical solution of partial differential equations for multiphase flow in porous media

Simultaneous flow of two or three immiscible fluids in porous media is modelled by a system of coupled, nonlinear partial differential equations. These equations are reduced to a system of nonlinear algebraic equations through the use of finite-difference approximations for derivatives. Several types of nonlinearities requiring careful analysis exist in this model. Here, we present a systematic study of all available, and some new, methods for the treatment of nonlinearitics in this model. It is believed that the solution techniques presented here may also prove useful for other strongly nonlinear partial differential equations.

Finite element analysis of linear and nonlinear heat transfer

The finite element method is rapidly becoming a popular procedure for the evaluation of thermal stresses in complex structures. In linear analysis the method has been used extensively and has been coupled with stress analysis computer programs in order to automate thermal stress analysis. However, for the method to be effective, efficient numerical techniques need to be used. The purpose of this paper is to survey the recent developments in linear heat transfer analysis and, specifically, to present the techniques that permit the practical analysis of large and complex three-dimensional heat conduction problems. Typical practical problems are described and solution times are presented. In the analysis of systems with nonlinear thermal properties the method has had limited application. In this paper the general formulation of the incremental equations used in nonlinear heat transfer analysis are presented. An efficient numerical solution of the equations is given. Several types of nonlinearities are discussed and the solutions of some typical problems are presented.