The aim of this paper is to present a way of ranking the nonlinearities of electrodynamic loudspeakers. For this purpose, we have constructed a nonlinear analytic model which takes into account the variations of the small signal parameters. The determination of these variations is based on a very precise measurement of the electrical impedance of the electrodynamic loudspeaker. First, we present the experimental method to identify the variations of these parameters, then we propose to study theoretically the importance of these nonlinearities according to the input level or the input frequency. We show that the parameter which creates most of the distortions is not always the same and depends mainly on both the input level and the input frequency. Such results can be very useful for optimization of electrodynamic loudspeakers.

In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.

The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.

The article is a continuation of a study on the synthesis of matching multi-terminal networks, also known as compensators. The reactive four-terminal-network compensators for linear loads were introduced in previous publications, but it appeared that they operate effectively with nonlinear loads too. The methods to create a compensator for a mono-harmonic source, which allows complete independence of input from output waveforms, ensuring optimal operating conditions for the source, are presented herein. The work for the first time presents the optimal four-terminal-network compensator applied to a nonlinear load.

Reliable evaluation of stress-strain characteristics can be done only in the laboratory where boundary conditions with respect to stress and strain can be controlled. The most popular laboratory equipment is a triaxial apparatus. Unfortunately, standard version of triaxial apparatus can reliable measure strain not smaller than 0.1 %. Such accuracy does not allow to determine stiffness referred to strain range most often mobilized in situ i.e. 10-3 ÷ 10-1%, in which stiffness distribution is highly nonlinear. In order to overcome this problem fundamental modifications of standard triaxial apparatus should be done. The first one concerns construction of the cell. The second refers to method of measurement of vertical and horizontal deformation of a specimen. The paper compares three versions of triaxial equipment i.e. standard cell, the modified one and the cell with system of internal measurement of deformation. The comparison was made with respect to capability of stiffness measurement in strain range relevant for typical geotechnical applications. Examples of some test results are given, which are to illustrate an universal potential of the laboratory triaxial apparatus with proximity transducers capable to trace stress-strain response of soil in a reliable way.

The implementation of a new, high-performance float flat glass manufacturing technology in Europe, in conjunction with the growing interest in new glass functions expressed by the construction industry, has led to significant developments in the theory of glass structures. Long time research conducted in the EU countries has been concluded by the technical document CEN/TC 250 N 1060, drawn up as a part of the work of the European Committee for Standardization on the second edition of Eurocodes (EC). The recommendations pertaining to the design of glass structures have been foreseen in the second edition of the Eurocodes, in particular the development of a separate design standard containing modern procedures for static calculations and stability of glass building structures (cf. works M. Feldmann, R. Kasper, K. Langosch and other).

In this paper new static analysis methods for glass plates made of monolithic and laminated glass, declared in th document CEN/TC 250 N 1060 (2014) and recommended in the national standarization document CNR-DT 210 (National Research Council of Italy, 2013) are presented. These static analysis methods are not commonly known in our national engineering environment, and thus require popularization and regional verification. Numerical and analytical simulations presented in this paper for rectangular plates made of monolithic and laminated glass and having various support conditions are of this character. The results of numerical calculations constitute a basis for the discussion of new static analysis methods for plates.

The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.

The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.

This paper presents the design of digital controller for longitudinal aircraft model based on the Dynamic Contraction Method. The control task is formulated as a tracking problem of velocity and flight path angle, where decoupled output transients are accomplished in spite of incomplete information about varying parameters of the system and external disturbances. The design of digital controller based on the pseudo-continuous approach is presented, where the digital controller is the result of continuous-time controller discretization. A resulting output feedback controller has a simple form of a combination of low-order linear dynamical systems and a matrix whose entries depend nonlinearly on certain known process variables. Simulation results for an aircraft model confirm theoretical expectations.

Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual method is based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

Electromagnetic mill installation for dry grinding represents a complex dynamical system that requires specially designed control system. The paper presents model-based predictive control which locates closed loop poles in arbitrary places. The controller performs as gain scheduling prototype where nonlinear model – artificial recurrent neural network, is parameterized with additional measurements and serves as a basis for local linear approximation. Application of such a concept to control electromagnetic mill load allows for stable performance of the installation and assures fulfilment of the product quality as well as the optimization of the energy consumption.