Al-Mg alloys spontaneously infiltrate into porous ceramic preform in a nitrogenous atmosphere above 750 °C with Mg either pre-alloyed or introduced at the interface to initiate the process. The governing process variables are temperature, alloy composition, atmosphere and particle size of the porous preform. The present study investigates the flow kinetics of Al-Mg melts into porous Al2O3 preforms as a function of particle size of the preform from the standpoint of a physical phenomena fluid flow through a non-uniform capillary. Pressureless infiltration involves two major stages: (a) initiation associated with an incubation period and, (b) continuation where the melt infiltrates the preform. Long (~1 hr) and irreproducible incubation periods are typically observed in the Al- Mg/Al2O3 system when the samples are slowly heated in N2 atmosphere. Such lengthy periods prior to infiltration also lead to excessive Mg loss from the system. In order to accurately measure infiltration rates during the continuation stage, the incubation period was minimized by upquenching samples in air under self-sealing conditions. Interrupted experiments reveal that infiltration occurs within 5 mins. Different phenomena are expected to dictate the capillary rise kinetics through the porous ceramic post-incubation (more specifically, retard the melt movement) (a) triple-point ridging of the melt meniscus on the alumina surface (meniscus pinning) (b) interfacial reaction limited wetting and infiltration (c) pore size and distribution of the porous ceramic (d) melt (Al-Mg) / atmosphere (N2) reaction to form products inside the pore space (decrease in permeability) (e) time-dependent loss of Mg from the system (time-dependent contact angle) Some of the above phenomena viz., fluid flow inside the porous medium and chemical reaction of the melt with the reinforcement are invariably coupled in a complex manner. The contribution of each phenomenon to the kinetics of infiltration (a) and (e) was investigated separately. Triple-line ridging Al sessile drops on alumina substrate spread 4-5 orders of magnitude slower than that predicted by hydrodynamic equilibrium. The melt is pinned by ridges leading to spreading rates of 0.4-4 mm/hr in contrast to viscous drag controlled spreading rates of 1-10 mm/sec. In order to detect ridging in the Al-Mg/Al2O3 reactive couple, uniform Al2O3 capillaries were infiltrated. Experiments were conducted under sealed configuration with metal on both sides of the capillary and Mg turnings at the interface. The uniform capillary itself was placed inside an alumina preform and the assembly upquenched to 800-900 °C to minimize evaporative loss of Mg. Examination of the inner walls of the capillary after leaching away the infiltrated metal shows rough, granular features on the polycrystalline Al2O3 surface. No continuous ridges were seen. EDS of the granular phase suggested stoichiometry of spinel, MgAl2O4, formed as a result of the reaction between the melt and the capillary. From interrupted experiments the average infiltration rate inside the uniform capillary was calculated to be in the ballpark range of 2-6 µm/sec (which is a lower limit to the meniscus velocity), an order of magnitude faster than the spreading rates observed during triple-line ridging (0.1 – 1 µm/sec) indicating that the melt front pinning was not the operative mechanism for influencing infiltration kinetics. Pore size distribution of porous medium Additionally, infiltration was found to be faster in uniform channels (fractures in a preform, annular spaces and aligned pores in freeze-cast preforms) compared to the randomly packed bed itself. The effect of pore size on infiltration kinetics was studied by varying the particle size of the packed bed. Experiments were conducted for two systems (a) non-reactive liquid polyethylene glycol PEG 600 (b) reactive Al-Mg melts into packed alumina beds as a function of particle size and temperature. The PEG 600 / Al2O3 ‘model’ system was used to benchmark the effect of pore size and distribution of the particle bed on flow kinetics from a purely physical standpoint. Typically, a Washburn type of ‘parabolic’ kinetics was observed for the non-reactive couple and the ‘effective’ hydrodynamic radius, reff was extracted. (For a uniform capillary, reff and the physical radius of the capillary are the same). Surprisingly, the ‘Washburn’ radius was found to be 1-2 orders of magnitude smaller than the average pore size and even smaller than the minimum average pore size of the compact. The ‘Washburn’ radii for infiltration of Al-Mg melts was a further order of magnitude smaller than the corresponding values for infiltration of non-reactive PEG 600 through the same packed beds. Non-uniform capillary model To predict the infiltration kinetics through porous media, a sinusoidal capillary model was developed based on the pore size distribution. The input parameters for the model were the average pore neck size and average pore bulge size, which were extracted from the experimentally measured pore size distribution. The flow was assumed to be quasi-steady state and laminar. Hagen-Poiseuille’s equation was employed to calculate the total pressure drop, which was equated with the instantaneous pressure drop across the meniscus. The meniscus velocity within the non-uniform capillary was solved numerically based on the instantaneous pressure drop. The infiltration profile for the sinusoidal capillary displayed jumps associated rise in the narrow segments of the profile while the rise through the broad segment was considerably slow. The overall infiltration profile could be fitted by a parabolic Washburn-type equation. The ‘effective’ hydrodynamic radius of such a sinusoidal capillary was found to be 2-3 orders of magnitude smaller than the average capillary size and even smaller than the narrowest opening of the sinusoidal capillary. The overall kinetics was limited by flow through the broad segment of the profile where the capillary driving force is the lowest coupled with a large viscous retarding force due to the narrow feeding segment thereby leading to extremely slow flow rates. The calculated ‘effective’ radius of the sinusoidal capillary (reff = 0.03 µm) based on the pore size distribution of the 25-37 µm (1.4-10.8 µm) packed bed was similar to the experimentally observed ‘effective’ radius for flow in the non-reactive couple (reff = 0.06 µm) implying good agreement between experiments and modeling. The model was extended for the case of pressure infiltration of Al melts into SiC & TiC compacts reported in the literature, under conditions where chemical reactions are negligible. A good agreement to within a factor of 4 between the observed kinetics and the ones predicted by the current model is observed. In order to understand the origin of this ‘unphysical’ radius dictating capillary rise, the physics of flow through a stepped capillary was analysed. The kinetics of flow through the wide segment could be expressed by an ‘effective’ drodynamic radius r 4min based on geometrical parameters of the stepped capillary as: reff= r3max (Wetting situation) where rminand rmax are the radii of the narrow and broad segments of the capillary. The ‘effective’ radius from the above equation matched well with the numerically derived ‘effective’ radius for flow through the stepped capillary. A r 2 similar expression for flow under applied pressure was derived as: reff= min rmax (non- wetting situation) which is strictly correct for large values of applied pressure. Chemical reactions influencing infiltration kinetics: Upquenched samples (time-dependent contact angle due to Mg loss) The previous investigation of fluid flow in porous media from a purely physical standpoint reveals the dominant role of the pore size and distribution in the porous medium in controlling infiltration kinetics. This however, is accurate only if chemical factors are minimized. In case of the upquenched experiments for the Al-Mg/Al2O3 system, the ‘effective’ radius was determined to be an order of magnitude smaller than that for the PEG 600/Al2O3 couple implying additional chemical factors influencing flow kinetics in this reactive system. Experiments with Mg turnings mixed with the powder bed shows faster infiltration compared to the ones where the entire Mg was placed at the interface showing that local availability of Mg was responsible for slower infiltration kinetics. Diminishing Mg at the melt front, leads to increase of surface tension and increase in contact angle. This was modeled by incorporating a kinetics (time-dependent) contact angle into the sinusoidal capillary model developed for non-reactive infiltration. The infiltration kinetics was found to be retarded in the case of a kinetic contact angle. Thus, both flow retardation through a packed bed and time-dependent variations of contact angle due to Mg loss from the system are responsible for slow pressureless infiltration kinetics of Al-Mg melts inside Al2O3 preforms. The infiltration kinetics predicted by the sinusoidal capillary model thus defines an upper envelope to the rate of infiltration and subsequent composite formation for such a process governed by fluid flow; all other factors if present in effect, retard the kinetics further. Samples processed in N2 atmosphere (reduced permeability due to AlN formation) The more practical case of composite fabrication (PRIMEXTM process) by pressureless infiltration of Al-Mg melts in a flowing N2 containing atmosphere was also examined. The kinetics of infiltration of Al-Mg melts in a flowing N2-H2 atmosphere (pO2 ~ 10-20atm) for different particle sizes of the packed bed was investigated. A large scatter in the infiltrated heights was observed and the absolute infiltration rates could not be established. Moreover, incubation periods were seen to range from 1-2 hours for different particle sizes. Post-incubation, the infiltration kinetics for a wide range of particle sizes was found to be approximately an order of magnitude slower than that for the upquenched samples. Microstructural investigations of the etched samples revealed significant AlN formation at the start of the composite near the preform/billet interface. This reduced the cross-sectional area available for melt flow and possibly led to long incubation periods encountered in the process. AlN formation was also detected in the matrix on the particle surfaces as well as in the interior of the matrix. This reduced the permeability of the compact and increased the hydrodynamic resistance for flow through the porous compact leading to slower infiltration kinetics. Thus both AlN formation in the matrix and Mg loss from the melt retard capillary flow of the melt through the porous ceramic over and above the intrinsic hydrodynamic resistance for flow through the packed bed. Role of atmosphere on the pressureless infiltration process The role of atmosphere in promoting the pressureless infiltration process was examined by using different processing atmospheres such as vacuum, N2-H2 and Ar and combinations thereof. It is known that the pressureless infiltration of Al melts into porous Al2O3 preforms requires both N2 and a critical level of Mg in the system. Samples heated under vacuum and Ar to 900 °C under open conditions did not infiltrate. Rather these showed discoloration related to the formation of MgAl2O4 on the particle surface due to reduction of Al2O3 by Mg vapour. Moreover, samples heated in Ar upto 500 °C followed by heating up in N2-H2 till 900 °C did not infiltrate indicating irreversible changes. Interestingly enough, if the samples were heated in vacuum upto 700 °C followed by N2-H2 at 900 °C, infiltration was observed. Dewetted regions of the compact were seen too adjacent to the preform-billet interface. This indicated a minimum critical partial pressure of N2, which promotes infiltration. From an analysis of the different interfacial energies and their dependence on atmosphere, it was concluded that either an increase in the solid-vapour interfacial energy (~ 10%) or a decrease in the solid-liquid interfacial energy (~ 10%) would lead to a decrease in the contact angle, θ, by 10°, large enough to ensure wettability and infiltration in certain atmospheres. It was also established that Mg infiltrates into porous Al2O3 both in N2-H2 as well as Ar under sealed conditions. So the presence of a minimum partial pressure of N2 favouring wettability was specific to the Al-Mg/Al2O3 system. (pl see the original document for formulas)

Ce manuscrit de thèse porte sur la formation de masques de réseaux denses de nanopiliers ou nanotrous à partir de l'auto-assemblage de copolymères à blocs (CPB) à haute force de ségrégation, pour des applications dans la micro-électronique. Des copolymères à blocs, de type ABA, constitués d'un bloc central de polydiméthylsiloxane (PDMS) et de deux blocs terminaux de polylactide (PLA) ont été synthétisés par polymérisation par ouverture de cycle. Les caractérisations de deux CPB d'intérêt en masse et sous forme de film mince montrent une mesostructure hexagonale sphérique et cylindrique de PLA dans la matrice de PDMS,avec des périodes de 14,3 et 15,5 nm respectivement. Afin de contrôler l'organisation des domaines, les autoassemblages des films minces des deux CPB ont été étudiés en fonction de plusieurs facteurs : paramètres de dépôt et post-traitements (exposition à des vapeurs de solvant et recuit thermique). Dans le cas du réseau hexagonal cylindrique, le contrôle des énergies interfaciales entre le film et le substrat de silicium a été obtenu grâce au greffage d'une couche de copolymères statistique ayant des blocs chimiquement différent des blocs contenus dans le CPB. Par ailleurs, à des fins industrielles, les mesostructures doivent montrer une organisation à grande échelle (plusieurs micromètres) dépourvue de défauts. Dans cette perspective, l'auto-assemblage des CPB a aussi été étudié sur des surfaces à topographie contrôlée (graphoépitaxie) montrant un relief sinusoïdal.

Στην παρούσα διπλωματική εργασία γίνεται μελέτη της ανάλυσης και σύνθεσης ήχου με τη βοήθεια ημιτονοειδών. Ειδικότερα, εξετάζονται οι παράμετροι της ανάλυσης και σύνθεσης και πως αυτες επηρεάζουν την τελική ανακατασκευή του σήματος. Στη συνέχεια γίνεται διερεύνηση της ανάλυσης και σύνθεσης μόνο στις χαμηλές συχνότητες. Με βάση ένα περιορισμένο εύρος ζώνης, γίνεται ανίχνευση των τονικών υψών. Αναπτύσσονται τρεις μέθοδοι κατηγοριοποίησης τους και στη συνέχεια γίνεται μία αξιολόγηση των μεθόδων αυτών μέσω των μέτρων NMR και PEAQ. / In this degree thesis sound analysis and synthesis using sinusoidals is studied. More specifically, parameters of analysis and synthesis are examined and how they affect the final reconstruction of a signal. Further research is conducted for analysis and synthesis at low sound frequencies. Based on a limited bandwidth, pitch detection is taking place on the input signal. Three methods of categorizing frequencies are developed and they are evaluated using the metrics of NMR (Noise to Mask Ratio) and PEAQ (Perceptual Evaluation of Audio Quality).

Ce travail de thèse s’inscrit dans le cadre du rejet adaptatif de perturbations sur des structures de contrôle actif de vibrations. L’objectif était de développer des stratégies de commande adaptatives, pour le rejet actif de perturbations, et de les mettre en œuvre sur des procédés réels se trouvant au sein du département Automatique du laboratoire GIPSA-Lab de Grenoble. En première partie, le rejet de perturbations bande étroites inconnues a été traité en utilisant des lois de commande adaptatives en contre réaction basées sur le principe du modèle interne. Ces lois de commande ont été validées expérimentalement sur une plate-forme de suspension active. En deuxième partie, des algorithmes adaptatifs pour l’atténuation de perturbations bande larges par action anticipatrices « feedforward » ont été proposés, analysés, et testés en pratique sur une structure flexible de contrôle actif de vibrations. / This thesis work is a part of adaptive disturbances rejection on some flexible structures in active vibration control (AVC). The objective was to develop adaptive control strategies for the active disturbances rejection, and to implement them on real process located in the Automatic Control Department of GIPSA-Lab in Grenoble. In the first part, the rejection of unknown narrow-band disturbances (Sinusoidal and multi-sinusoidal) was treated using adaptive control laws in « feedback » based on the internal model principle. These control laws have been validated experimentally on an active suspension platform. In the second part, adaptive algorithms for the minimization of the effects of "broadband" disturbances in "feedforward" have been proposed, analyzed and tested in practice on a flexible structure of active vibration control.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

This dissertation presents a numerical study using molecular dynamic simulations that interrogates the polymer structure as it is strained continuously in time and correlates it with the stress developed in it. We investigate the role of external control variables such as temperature, strain-rate, chain length, and density. At temperatures higher than glass transition, stress anisotropy is reduced even though bond stretch is greater at higher temperatures. There is a significant increase in stress level with increasing density. At faster rates of loading stress anisotropy increases. Deformation is mostly due to bond stretch and bond bending rather than overall shape and size. Stress levels increase with longer chain length. Cross-linkers beyond a critical value of functionality cause increased constraint on the motion of monomers and uniaxial stress developed increases. Stacking of chains also plays a dominant role in terms of excluded volume interactions. Low density, high temperature, low values of functionality of cross-linkers, and short chain length, facilitate chain uncoiling and chain slipping in crosslinked polymers. Uniaxial stress in linear polymers, on the other hand, is only mildly in uenced by temperature. Sinusoidal strain loading clearly reveals the viscoelastic nature of polymers. Internal structural parameters of the chains such as bond length, bond angle show hysteresis during loading and unloading. However, parameters representing overall size and shape of chains do not display any hysteresis. Small size magnetic particles and their small volume fractions in polymers show no signi cant e ect of applied external magnetic eld on anisotropic stress. Stress increases with lowering temperature, increasing density, decreasing volume fraction of magnetic particles, and increasing chain length

This diploma thesis deals with the theoretical analysis of the predictive methods of signal interpolation and signal modeling using sinusoidal model. On the basis of this theory the algorithm for the reconstruction of the missing sections in the audio signal is implemented in computing environment MATLAB. Results of mass testing reconstructions are displayed using objective methods SNR and PEMO-Q. Further experiments are carried out on single signals and their evaluation is described.

The vehicle industry have for many years improved the design of car motors and iterated the control systems associated with it. The systems have become very complex and hard to understand because of this work process. It is today very difficult to perform evaluations of the engine's performance or components theoretically at Powertrain Engineering Sweden (PES). This thesis proposes a test method to estimate the robustness, in terms of stability margins, of the air charge throttle control loop using measurement data. Alternative test methods are also presented, for example system identification performed with MATLAB's SITB. The proposed test method superimposes a sine wave upon the control signal in a closed loop system. The control signal is measured after it is superimposed and after it have made one round trip around the loop. These two signals is regarded as sine in and sine out. The phase shift and relation in amplitude are estimated from the measurements and the robustness is presented by Bode plots. The method finds the phase shift from the time difference between the zero-crossings of the input- and output signal. The relation in amplitude is found by looking at the total sum of the absolute value sine wave. Extensive testing with different tunings of the P-part of the air charge controller shows that the proposed method correctly identifies if the systems stability margins have become larger or smaller. For nine measurements with different P-tunings it is seen that the magnitude curves stay separate throughout the whole Bode plot. It is also shown that the gain margins are decreasing for every increase in P-value. The overall results and findings in this thesis are promising and can act as a foundation for future thesis' work to come.