Visualizing non-linear control system performance by means of multidimensional scaling

This paper addresses the use of multidimensional scaling in the evaluation of controller performance. Several nonlinear systems are analyzed based on the closed loop time response under the action of a reference step input signal. Three alternative performance indices, based on the time response, Fourier analysis, and mutual information, are tested. The numerical experiments demonstrate the feasibility of the proposed methodology and motivate its extension for other performance measures and new classes of nonlinearities.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Relaxation times in a bistable system with parametric, white noise: Theory and experiment

We consider the effects of external, multiplicative white noise on the relaxation time of a general representation of a bistable system from the points of view provided by two, quite different, theoretical approaches: the classical Stratonovich decoupling of correlations and the new method due to Jung and Risken. Experimental results, obtained from a bistable electronic circuit, are compared to the theoretical predictions. We show that the phenomenon of critical slowing down appears as a function of the noise parameters, thereby providing a correct characterization of a noise-induced transition.

System identification using a linear combination of cumulant slices

In this paper we develop a new linear approach to identify the parameters of a moving average (MA) model from the statistics of the output. First, we show that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, thisresult is used to obtain a new well-conditioned linear methodto estimate the MA parameters of a non-Gaussian process. Theproposed method presents several important differences withexisting linear approaches. The linear combination of slices usedto compute the MA parameters can be constructed from dif-ferent sets of cumulants of different orders, providing a generalframework where all the statistics can be combined. Further-more, it is not necessary to use second-order statistics (the autocorrelation slice), and therefore the proposed algorithm stillprovides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while mostlinear methods developed so far give totally erroneous estimates if the order is overestimated, the proposed approach doesnot require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of thealgorithm and the improvement in performance with respect to existing methods.

Centralized Motion Control of a Linear Tooth Belt Drive: Analysis of the Performance and Limitations

A centralized robust position control for an electrical driven tooth belt drive is designed in this doctoral thesis. Both a cascaded control structure and a PID based position controller are discussed. The performance and the limitations of the system are analyzed and design principles for the mechanical structure and the control design are given. These design principles are also suitable for most of the motion control applications, where mechanical resonance frequencies and control loop delays are present. One of the major challenges in the design of a controller for machinery applications is that the values of the parameters in the system model (parameter uncertainty) or the system model it self (non-parametric uncertainty) are seldom known accurately in advance. In this thesis a systematic analysis of the parameter uncertainty of the linear tooth beltdrive model is presented and the effect of the variation of a single parameter on the performance of the total system is shown. The total variation of the model parameters is taken into account in the control design phase using a Quantitative Feedback Theory (QFT). The thesis also introduces a new method to analyze reference feedforward controllers applying the QFT. The performance of the designed controllers is verified by experimentalmeasurements. The measurements confirm the control design principles that are given in this thesis.

Investigation of the composition of linear alkylbenzenes with emphasis on the identification and quantitation of some trace compounds using GS/MS system in both electron impact and chemical ionization modes

Linear alkylbenzenes, LAB, formed by the Alel3 or HF catalyzed alkylation of benzene are common raw materials for surfactant manufacture. Normally they are sulphonated using S03 or oleum to give the corresponding linear alkylbenzene sulphonates In >95 % yield. As concern has grown about the environmental impact of surfactants,' questions have been raised about the trace levels of unreacted raw materials, linear alkylbenzenes and minor impurities present in them. With the advent of modem analytical instruments and techniques, namely GCIMS, the opportunity has arisen to identify the exact nature of these impurities and to determine the actual levels of them present in the commercial linear ,alkylbenzenes. The object of the proposed study was to separate, identify and quantify major and minor components (1-10%) in commercial linear alkylbenzenes. The focus of this study was on the structure elucidation and determination of impurities and on the qualitative determination of them in all analyzed linear alkylbenzene samples. A gas chromatography/mass spectrometry, (GCIMS) study was performed o~ five samples from the same manufacturer (different production dates) and then it was followed by the analyses of ten commercial linear alkylbenzenes from four different suppliers. All the major components, namely linear alkylbenzene isomers, followed the same elution pattern with the 2-phenyl isomer eluting last. The individual isomers were identified by interpretation of their electron impact and chemical ionization mass spectra. The percent isomer distribution was found to be different from sample to sample. Average molecular weights were calculated using two methods, GC and GCIMS, and compared with the results reported on the Certificate of Analyses (C.O.A.) provided by the manufacturers of commercial linear alkylbenzenes. The GC results in most cases agreed with the reported values, whereas GC/MS results were significantly lower, between 0.41 and 3.29 amu. The minor components, impurities such as branched alkylbenzenes and dialkyltetralins eluted according to their molecular weights. Their fragmentation patterns were studied using electron impact ionization mode and their molecular weight ions confirmed by a 'soft ionization technique', chemical ionization. The level of impurities present i~ the analyzed commercial linear alkylbenzenes was expressed as the percent of the total sample weight, as well as, in mg/g. The percent of impurities was observed to vary between 4.5 % and 16.8 % with the highest being in sample "I". Quantitation (mg/g) of impurities such as branched alkylbenzenes and dialkyltetralins was done using cis/trans-l,4,6,7-tetramethyltetralin as an internal standard. Samples were analyzed using .GC/MS system operating under full scan and single ion monitoring data acquisition modes. The latter data acquisition mode, which offers higher sensitivity, was used to analyze all samples under investigation for presence of linear dialkyltetralins. Dialkyltetralins were reported quantitatively, whereas branched alkylbenzenes were reported semi-qualitatively. The GC/MS method that was developed during the course of this study allowed identification of some other trace impurities present in commercial LABs. Compounds such as non-linear dialkyltetralins, dialkylindanes, diphenylalkanes and alkylnaphthalenes were identified but their detailed structure elucidation and the quantitation was beyond the scope of this study. However, further investigation of these compounds will be the subject of a future study.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

Case based reasoning as an extension of fault dictionary methods for linear electronic analog circuits diagnosis

El test de circuits és una fase del procés de producció que cada vegada pren més importància quan es desenvolupa un nou producte. Les tècniques de test i diagnosi per a circuits digitals han estat desenvolupades i automatitzades amb èxit, mentre que aquest no és encara el cas dels circuits analògics. D'entre tots els mètodes proposats per diagnosticar circuits analògics els més utilitzats són els diccionaris de falles. En aquesta tesi se'n descriuen alguns, tot analitzant-ne els seus avantatges i inconvenients. Durant aquests últims anys, les tècniques d'Intel·ligència Artificial han esdevingut un dels camps de recerca més importants per a la diagnosi de falles. Aquesta tesi desenvolupa dues d'aquestes tècniques per tal de cobrir algunes de les mancances que presenten els diccionaris de falles. La primera proposta es basa en construir un sistema fuzzy com a eina per identificar. Els resultats obtinguts son força bons, ja que s'aconsegueix localitzar la falla en un elevat tant percent dels casos. Per altra banda, el percentatge d'encerts no és prou bo quan a més a més s'intenta esbrinar la desviació. Com que els diccionaris de falles es poden veure com una aproximació simplificada al Raonament Basat en Casos (CBR), la segona proposta fa una extensió dels diccionaris de falles cap a un sistema CBR. El propòsit no és donar una solució general del problema sinó contribuir amb una nova metodologia. Aquesta consisteix en millorar la diagnosis dels diccionaris de falles mitjançant l'addició i l'adaptació dels nous casos per tal d'esdevenir un sistema de Raonament Basat en Casos. Es descriu l'estructura de la base de casos així com les tasques d'extracció, de reutilització, de revisió i de retenció, fent èmfasi al procés d'aprenentatge. En el transcurs del text s'utilitzen diversos circuits per mostrar exemples dels mètodes de test descrits, però en particular el filtre biquadràtic és l'utilitzat per provar les metodologies plantejades, ja que és un dels benchmarks proposats en el context dels circuits analògics. Les falles considerades son paramètriques, permanents, independents i simples, encara que la metodologia pot ser fàcilment extrapolable per a la diagnosi de falles múltiples i catastròfiques. El mètode es centra en el test dels components passius, encara que també es podria extendre per a falles en els actius.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.