The problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used. The investigated properties include stability of equilibrium points, a chaos of dynamics and non-minimum phase behaviour around an upper position. The presented results refer to the model of a physical (constructed) DIP system.
The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.
This paper presents a robust model free controller (RMFC) for a class of uncertain continuous-time single-input single-output (SISO) minimum-phase nonaffine-in-control systems. Firstly, the existence of an unknown dynamic inversion controller that can achieve control objectives is demonstrated. Afterwards, a fast approximator is designed to estimate as best as possible this dynamic inversion controller. The proposed robust model free controller is an equivalent realization of the designed fast approximator. The perturbation theory and Tikhonov’s theorem are used to analyze the stability of the overall closed-loop system. The performance of the developped controller are verified experimentally in the position control of a pneumatic actuator system.
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.
The Dez dam was commissioned in 1963 and since sediments accumulated in the reservoir up to an elevation of approximately 15m below the intake of the power tunnel. One of the possible measures to improve operation of the reservoir is by heightening of the existing dam. This paper describes the conducted procedure for static and thermal calibration of this 203m dam in Iran based on micro geodesies measurements. Also the nonlinear response of existing dam is investigated under maximum credible earthquake ground motions considering joint behavior and mass concrete cracking and safety of dam is evaluated for possible heightening. For thermal calibration of provided numerical model, transient thermal analysis was conducted and results were compared with thermometers records installed in central block. In addition, for static calibration; thermal distribution within dam body, dam self weight, hydrostatic pressure and silt load applied on the 3D fi nite element model of dam-reservoir-foundation were considered. Results show that the distribution of stresses will be critical within dam for heightening case under seismic loads in MCL.
In many therapeutic applications of a pulsed focused ultrasound with various intensities the finite- amplitude acoustic waves propagate in water before penetrating into tissues and their local heating. Water is used as the matching, cooling and harmonics generating medium. In order to design ultrasonic probes for various therapeutic applications based on the local tissue heating induced in selected organs as well as to plan ultrasonic regimes of treatment a knowledge of pressure variations in pulsed focused nonlinear acoustic beams produced in layered media is necessary. The main objective of this work was to verify experimentally the applicability of the recently developed numerical model based on the Time- Averaged Wave Envelope (TAWE) approach (Wójcik et al., 2006) as an effective research tool for predicting the pulsed focused nonlinear fields produced in two-layer media comprising of water and tested materials (with attenuation arbitrarily dependent on frequency) by clinically relevant axially-symmetric therapeutic sources. First, the model was verified in water as a reference medium with known linear and nonlinear acoustic properties. The measurements in water were carried out at a 25◦C temperature using a 2.25 MHz circular focused (f/3.0) transducer with an effective diameter of 29 mm. The measurement results obtained for 8-cycle tone bursts with three different initial pressure amplitudes varied between 37 kPa and 113 kPa were compared with the numerical predictions obtained for the source boundary condition parameters determined experimentally. The comparison of the experimental results with those simulated numerically has shown that the model based on the TAWE approach predicts well both the spatial-peak and spatial-spectral pressure variations in the pulsed focused nonlinear beams produced by the transducer used in water for all excitation levels complying with the condition corresponding to weak or moderate source-pressure levels. Quantitative analysis of the simulated nonlinear beams from circular transducers with ka ≫ 1 allowed to show that the axial distance at which sudden accretion of the 2nd or higher harmonics amplitude appears is specific for this transducer regardless of the excitation level providing weak to moderate nonlinear fields. For the transducer used, the axial distance at which the 2nd harmonics amplitude suddenly begins to grow was found to be equal to 60 mm. Then, the model was verified experimentally for two-layer parallel media comprising of a 60-mm water layer and a 60-mm layer of 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany). This medium was selected because of its tissue-mimicking acoustic properties and known nonlinearity parameter B/A. The measurements of both, the peak- and harmonic-pressure variations in the pulsed nonlinear acoustic beams produced in two-layer media (water/1.3-butanediol) were performed for the same source boundary conditions as in water. The measurement results were compared with those simulated numerically. The good agreement between the measured data and numerical calculations has shown that the model based on the TAWE approach is well suited to predict both the peak and harmonic pressure variations in the pulsed focused nonlinear sound beams produced in layered media by clinically relevant therapeutic sources. Finally, the pulsed focused nonlinear fields from the transducer used in two-layer media: water/castor oil, water/silicone oil (Dow Corning Ltd., Coventry, UK), water/human brain and water/pig liver were predicted for various values of the nonlinearity parameter of tested media.
Regarding the importance of short circuit and inrush current simulations in the split-winding transformer, a novel nonlinear equivalent circuit is introduced in this paper for nonlinear simulation of this transformer. The equivalent circuit is extended using the nonlinear inductances. Employing a numerical method, leakage and magnetizing inductances in the split-winding transformer are extracted and the nonlinear model inductances are estimated using these inductances. The introduced model is validated and using this nonlinear model, inrush and short-circuit currents are calculated. It has been seen that the introduced model is valid and suitable for simulations of the split-winding transformer due to various loading conditions. Finally, the effects of nonlinearity of the model inductances are discussed in the following.