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This study presented the design and implementation of a spatial Hinf controller to suppress the free and forced vibrations of a cantilevered smart beam. The smart beam consists of a passive aluminum beam with surface bonded PZT (Lead-Zirconate-Titanate) patches. In this study, the PZT patches were used as the actuators and a laser displacement sensor was used as the sensor. In the first part of the study, the modeling of the smart beam by the assumed-modes method was conducted. The model correction technique was applied to include the effect of out-of-range modes on the dynamics of the system. Later, spatial system identification work was performed in order to clarify the spatial characteristics of the smart beam. In the second part of the study, a spatial Hinf controller was designed for suppressing the first two flexural vibrations of the smart beam. The efficiency of the controller was verified both by simulations and experimental implementation. As a final step, the comparison of the spatial and pointwise Hinf controllers was employed. A pointwise Hinf controller was designed and experimentally implemented. The efficiency of the both controllers was compared by simulations.

This thesis represents the work that has been done by the author in the area of vibration analysis and control of smart structures during his PhD candidature. The research was concentrated on flexible structures, using piezoelectric materials as actuators and sensors. The thesis consists of four major parts. The first part (Chapter 2) is the modelling of piezoelectric laminate structures using modal analysis and finite element methods. The second part (Chapter 4) involves the model correction of pointwise and spatial models of resonant systems. The model correction solution compensates for the errors associated with the truncation of high frequency modes. The third part (Chapter 5) is the optimal placement methodology for general actuators and sensors. In particular, optimal placement of piezoelectric actuators and sensors over a thin plate are considered and implemented in the laboratory. The last part (Chapters 6 to 8) deals with vibration control of smart structures. Several different approaches for vibration control are considered. Vibration control using resonant, spatial H-2 and H-infinity control is proposed and implemented on real systems experimentally. It is possible, for certain modes, to obtain the very satisfactory result of up to 30 dB vibration reduction. / PhD Doctorate

Process models are always associated with uncertainty, due to either inaccurate model structure or inaccurate identification. If left unaccounted for, these uncertainties can significantly affect the model-based decision-making. This thesis addresses the problem of model-based optimization in the presence of uncertainties, especially due to model structure error. The optimal solution from standard optimization techniques is often associated with a certain degree of uncertainty and if the model-plant mismatch is very significant, this solution may have a significant bias with respect to the actual process optimum. Accordingly, in this thesis, we developed new strategies to reduce (1) the variability in the optimal solution and (2) the bias between the predicted and the true process optima. Robust optimization is a well-established methodology where the variability in optimization objective is considered explicitly in the cost function, leading to a solution that is robust to model uncertainties. However, the reported robust formulations have few limitations especially in the context of nonlinear models. The standard technique to quantify the effect of model uncertainties is based on the linearization of underlying model that may not be valid if the noise in measurements is quite high. To address this limitation, uncertainty descriptions based on the Bayes’ Theorem are implemented in this work. Since for nonlinear models the resulting Bayesian uncertainty may have a non-standard form with no analytical solution, the propagation of this uncertainty onto the optimum may become computationally challenging using conventional Monte Carlo techniques. To this end, an approach based on Polynomial Chaos expansions is developed. It is shown in a simulated case study that this approach resulted in drastic reductions in the computational time when compared to a standard Monte Carlo sampling technique. The key advantage of PC expansions is that they provide analytical expressions for statistical moments even if the uncertainty in variables is non-standard. These expansions were also used to speed up the calculation of likelihood function within the Bayesian framework. Here, a methodology based on Multi-Resolution analysis is proposed to formulate the PC based approximated model with higher accuracy over the parameter space that is most likely based on the given measurements. For the second objective, i.e. reducing the bias between the predicted and true process optima, an iterative optimization algorithm is developed which progressively corrects the model for structural error as the algorithm proceeds towards the true process optimum. The standard technique is to calibrate the model at some initial operating conditions and, then, use this model to search for an optimal solution. Since the identification and optimization objectives are solved independently, when there is a mismatch between the process and the model, the parameter estimates cannot satisfy these two objectives simultaneously. To this end, in the proposed methodology, corrections are added to the model in such a way that the updated parameter estimates reduce the conflict between the identification and optimization objectives. Unlike the standard estimation technique that minimizes only the prediction error at a given set of operating conditions, the proposed algorithm also includes the differences between the predicted and measured gradients of the optimization objective and/or constraints in the estimation. In the initial version of the algorithm, the proposed correction is based on the linearization of model outputs. Then, in the second part, the correction is extended by using a quadratic approximation of the model, which, for the given case study, resulted in much faster convergence as compared to the earlier version. Finally, the methodologies mentioned above were combined to formulate a robust iterative optimization strategy that converges to the true process optimum with minimum variability in the search path. One of the major findings of this thesis is that the robust optimal solutions based on the Bayesian parametric uncertainty are much less conservative than their counterparts based on normally distributed parameters.

Tato diplomová práce se zabývá elektromagnetickou analýzou a modelováním asynchronního stroje s plným rotorem. Tato práce tedy zahrnuje literární rešerši na téma vysokootáčkových elektrických strojů s porovnáním s klasickými elektrickými stroji s převodovkou a popisem jejich výhod či nevýhod, rozdělení vysokootáčkových elektrických strojů s plnými rotory a srovnání jejich výhod či nevýhod, kde se tato práce nejvíce soustřeďuje na vysokootáčkové asynchronní stroje s plnými rotory a jejich použití v průmyslu. Dále se tato práce zabývá metodami výpočtu elektrických asynchronních strojů s plnými rotory. Proto jsou zde uvedeny a popsány metody výpočtu stroje mezi které patří analytické metody i metoda konečných prvků. Vzhledem k povaze elektrických strojů s plnými rotory je hlavně kladen důraz v této práci na výpočet stroje pomocí metody konečných prvků ve 2D prostoru s využitím korekčních činitelů konců plných rotorů, které jsou zde velmi detailně popsány a rozděleny. Na základě dostupné literatury je vypočítaný elektrický stroj s plným rotorem pomocí MKP analýzy. Elektromagnetický výpočet stroje je automatizován pomocí skriptu vytvořeného v Pythonu. Dalším hlavním cílem této práce je popis tzv. náhradních modelů, uvedení jejich výhod či nevýhod, použití v jiných průmyslových odvětvích a hlavně použití náhradních modelů na elektrický stroj s plným rotorem. S využitím náhradních modelů je dále optimalizovaný vybraný asynchronní stroj s plným rotorem a to pomocí programů SymSpace a Optimizer. Pro samotnou optimalizaci byly uvažovány 3 návrhy stroje, které byly na závěr mezi sebou porovnány a to hlavně z hlediska jejich elektromagnetického výkonu.

Im Mittelpunkt der 3. Tagung des Sonderforschungsbereichs Transregio 96 am 29. und 30.Oktober 2013 am Werkzeugmaschinenlabor der RWTH Aachen standen die verschiedenen Lösungsansätze der einzelnen Teilprojekte bei der Durchführung der experimentellen Untersuchungen zur Verifizierung von Simulationsergebnissen bzw. zur Ableitung von Modellparametern. Es wurden vier Themenblöcke behandelt: • Ermittlung von thermisch relevanten Prozessparametern • Experimentelle Methodik zur Analyse von Teilsystemen in Werkzeugmaschinen • Methodische Rahmenbedingungen bei der Ermittlung von thermisch relevanten Parametern • Verfahren zur Verformungs- und Verlagerungsmessung