Estruturas flexíveis estão sujeitas a excitações desconhecidas que podem causar danos. Um dos possíveis artifícios para lidar com este problema é a teoria de controle de sistemas dinâmicos. Em particular, uma técnica que suscita o interessa para aplicação nesta classe de sistemas é o controle ótimo, devido às suas boas propriedades de resposta e factibilidade, podendo ser aplicado até através de circuitos analógicos. O contratempo desta técnica é a necessidade de um número de sensores igual ao número de estados do sistema, o que para estruturas é inviável. Como uma alternativa, pode se empregar os procedimentos usuais de restrição de realimentação do sinal medido. No entanto, estes casos não consideram o projeto das matrizes de saída e entrada, fator determinante para o controle de vibrações em estruturas. O objetivo deste trabalho é preencher esta lacuna. Inicialmente, são introduzidos alguns conceitos das teorias de controle ótimo, dinâmica estrutural e sobre métodos de discretização em séries. Em seguida, determinam-se as condições necessárias de otimalidade considerando como variáveis de otimização o ganho e as posições dos sensores e atuadores. Determinadas as condições, investigam-se os principais desafios para solução destas equações, dados pela existência de parâmetros que estabilizem o sistema e a dependência do ponto ótimo em relação à condição inicial do sistema. O primeiro é resolvido a partir da especificação do sistema linear para uma forma modal e utilizando funções de controle de Lyapunov, o que adicionalmente proporciona o resultado de que o controle colocalizado é um controle ótimo. Para o segundo são propostas duas soluções, sendo uma utilizada para determinar as posições dos atuadores para projetar um controle LQR com desempenho satisfatório, e a outra para determinar os ganhos e posições dos sensores de modo a obter um controle com realimentação de saída com desempenho próximo ao LQR projetado. Os resultados obtidos a partir da aplicação da metodologia desenvolvida em exemplos da dinâmica estrutural revelaram um desempenho notável. Mesmo para uma razão pequena entre o número de sensores pelo número de estados obteve-se um desempenho equivalente ao LQR, exibindo também propriedades robustez consideráveis em relação às variáveis de otimização. Conclui-se que a metodologia desenvolvida é uma boa alternativa para as técnicas de controle LQR e LQG. / Flexible structures are subject to unknown excitations that may cause damage. One of the possible artifices to deal with this problem is the control theory of dynamical systems. In particular, a technique that raises the interest for application in this class of systems is the optimal control, due to its good properties of response and feasibility, as it can be applied even through analog circuits. A drawback of this technique is the need for a number of sensors equal to the number of states, which for structures is impracticable. As an alternative, the usual procedures of using only measured signals for feedback can be employed. However, these cases do not consider the design of the input and output matrices, a determining factor for vibration control in structures. The purpose of this paper is to fill this gap. Initially, some concepts of the theories of optimal control, structural dynamics and series discretization methods are introduced. Then, the optimality conditions are determined considering the gain and locations of sensors and actuators as the optimization variables. Given these conditions, we investigate the main challenges to solve these equations, given by the existence of parameters that stabilize the system and the dependence of the optimum point in relation to the initial condition of the system. The first one is solved from the specification of the linear system to a modal form and using Lyapunov control functions, which additionally provides the result that the collocated control is an optimal control. For the second two solutions are proposed, one being used to determine the positions of the actuators to design a LQR control with satisfactory performance, and the other to determine the gains and positions of the sensors in order to obtain an output feedback control with close performance to the designed LQR. The results obtained from the application of the methodology developed in structural dynamics examples revealed a remarkable performance. Even for a small ratio between the number of sensors by the number of states a performance equivalent to the LQR was obtained, also exhibiting considerable robustness properties in relation to the optimization variables. It is concluded that the developed methodology is a good alternative for LQR and LQG control techniques.

No description available.

[pt] No presente trabalho estuda-se a aplicação do controle estrutural na proteção de estruturas submetidas a carregamentos dinâmicos contra níveis de vibração indesejáveis que possam causar desconforto e, até mesmo, comprometer a segurança e integridade da edificação. Os três tipos de controle estrutural, passivo, ativo e híbrido, são analisados de forma a evidenciar as vantagens do uso do controle híbrido. O mecanismo de controle utilizado é o denominado amortecedor de massa sintonizado (AMS), devido à sua vasta aplicação na Engenharia Civil, tendo uma grande quantidade sido instalada em edifícios, pontes e chaminés industriais para controle de vibrações causadas pelo vento. Verifica-se a influência da não- linearidade da rigidez do AMS no comportamento do sistema principal. A utilização de amortecedores de massa sintonizados múltiplos é também estudada como uma forma de vencer certas limitações quanto à robustez deste tipo de sistema e melhorar sua performance. Analisa-se por fim o comportamento e eficiência do amortecedor de massa híbrido (AMH), em relação ao AMS passivo. Para cálculo da força de controle são utilizados os seguintes algoritmos: controle ótimo linear clássico, controle ótimo instantâneo e controle ótimo não-linear. Uma estratégia para definição das matrizes de ponderação, utilizadas no algoritmo de controle ótimo instantâneo, que minimizem a amplitude da resposta harmônica permanente é apresentada. Exemplos numéricos são apresentados ao longo de todo o trabalho. Verifica-se que a utilização do controle híbrido é mais eficiente que os controles passivo e ativo isolados, requerendo forças de magnitude inferiores, o que reduz bastante o custo deste tipo de sistema. O sistema de controle híbrido se mostrou eficiente na redução de vibrações causadas por carregamentos cujas freqüências eram diversas das consideradas no projeto do sistema de controle passivo. Verificou-se, ainda que o mesmo se comportou de forma satisfatória no caso de discrepância na freqüência natural da estrutura. / [en] In this work the use of structural control is studied to protect dynamically loaded building structures against undesirable vibration levels, which can cause human discomfort and, even more, compromise the building safety and integrity. The three types of structural control, passive, ative and hybrid, are analysed to show the advantages of hybrid control in reducing undesirable vibration levels. The chosen control mechanism is the so called tuned mass damper (TMD), due to its large application in Civil Engineering, having a great number of these devices been installed in buildings, bridges and industrial chimneys to control structural vibrations induced by wind loads. It is also verified the influence of TMD non linear stiffness on the main system behaviour. The use of multiple tuned mass dampers is studied as a possible way of improving the TMD robustness and performance. The hybrid mass damper (HMD) behaviour and efficiency comparing to the passive mass damper is analysed in detail. To calculate the control force the following control algorithms are used: classical optimum linear control, instantaneous optimum control and non-linear optimum control. A strategy to define the weighting matrices used in the instantaneous optimum control algorithm that minimizes the harmonic response amplitude is presented. Several numerical examples are presented aalong the work. The results show that the hybrid control is more efficient that the passive or active control used separately, requiring smaller forces reducing in this way the cost of the control system. The hybrid control system showed to be more efficient in reducing vibrations caused by loadings which had different frequencies from that considered on the passive control design. Moreover it was shown that hybrid control has a satisfactory perfomance when discrepancies in natural frequency occur.

This thesis provides analytical and experimental proof-of-concept for a new feedback-controlled sound transmission control module for use in an active segmented partition (ASP) array. The objective of such a module is to provide high transmission loss down to low audible frequencies while minimizing the overall mass of the module. This objective is accomplished in the new module by using actively controlled panels in conjunction with analog feedback controllers. The new module also overcomes two limitations that exist in current ASP modules: the inability to control broadband random-noise and the lack of bidirectional control through the module. Overcoming these limitations represents an important advancement in the research area of actively controlled partitions and broadens the number of potential applications for ASP arrays. Analogous circuit models were developed and used to predict the performance of the new ASP module under feedback control. The preliminary design consists of two loudspeaker drivers mounted back-to-back in a duct, with two decoupled analog feedback controllers connected to reduce the vibration of the loudspeaker cones. It was found that the classical analogous circuit model of a loudspeaker proved inadequate for modeling the low- and mid-frequency transmission loss due to resonance effects of the loudspeaker surround. An enhanced model of a loudspeaker was then used to account for this phenomenon and more accurately predict the transmission loss behavior. An experimental proof-of-concept module was constructed using two 10 cm diameter loudspeaker drivers, two accelerometers, and other off-the-shelf materials. The two analog feedback controllers used in the module were designed and built using measured frequency response function techniques. The passive and active transmission loss of the module was measured using a plane-wave tube. Transmission loss of broadband random-noise in excess of 50 dB was achieved between 100 Hz and 2 kHz. The experimental transmission loss results validated the numerical model and showcased the transmission loss performance of the new module design.

Les granitoïdes associés aux skarn à Cu-Pb-Zn et au W, dérivent, respectivement, de la fusion partiellede roches mafiques à amphiboles dans la croute inférieure et de roches métas-édimentaires riches enmuscovite dans la croute moyenne-supérieure. Ces sources fertiles mobilisées pour la formation de cesplutons a permis la formation de gisements à Cu-Pb-Zn, et W au cours du Jurassique moyen. L’originedans la croûte moyenne de la granodiorite de Tongshanling, associée aux minéralisations à Cu-Pb-Zn, aété montrée par l’étude des enclaves microgranulaires dioritiques qui sont des restites remaniées issuesde la fusion partielle des amphibolites de la croûte inférieure. Le Cu et le Zn associées à ces plutons sontprobablement issus de la croûte inférieure et ces métaux ont probablement étés remobilisés au cours dela fusion partielle. Le Pb issue de la croute supérieur a été collecté lors de l’ascension du magma qui adonné la granodiorite. Lors de leur mise en place ces granitoïdes ont exprimé leur potentielminéralisateur. L’étude structural montre que la géométrie des corps minéralisés et en lien avec ladéformation induite par la mise en place des plutons. Les différentes expressions de la minéralisationdans le district à Cu-Mo-Pb-Zn-Ag de Tongshanling sont génétiquement lié à l’hydrothermalisme et à sonévolution lors du développement du skarn. Le granite de Weijia a cristallisé à partir d’un magma saturéen eau et riche en Fluor. Les facteurs qui ont contrôlé la formation de ce skarn magnésien riche en W,suppose l’existence d’une source enrichie en W dans les sources métasédimentaires et d’un magmariche en Fluor très différentia par cristallisation fractionnée. / The Middle-Late Jurassic Cu-Pb-Zn-bearing and W-bearing granitoids in the Nanling Range were mainlyderived from non-simultaneous partial melting of the mafic amphibolitic rocks in the lower crust and themuscovite-rich metasedimentary rocks in the upper-middle crust, respectively. The fertile sources in theNanling Range are beneficial to the formation of Cu-Pb-Zn and W deposits during Middle-Late Jurassic.The lower-crust origin of the Cu-Pb-Zn-bearing granodiorites is further demonstrated by the dioriticmicrogranular enclaves in the Tongshanling granodiorite which are reworked restite enclaves derivedfrom partial melting of the mafic amphibolitic source. The Cu and Zn associated with these intrusionswere most probably released from the mafic amphibolitic lower crust by partial melting, whereas, Pb wasextracted from the upper crust by ascending granodioritic magmas. The emplacement of these orebearinggranitoid magmas may have a structural connection with the subsequent polymetallicmineralization in some way. For instance, the exoskarn and sulfide-quartz veins in the Tongshanling Cu-Pb-Zn deposit are evidently controlled by magma emplacement-induced wall-rock deformation. Thedifferent mineralization types and ore deposits in the Tongshanling Cu-Mo-Pb-Zn-Ag ore district aregenetically linked together in the same skarn system as the productions of evolution and zonation. TheWeijia granite was crystallized from a F-rich and water-saturated magma. The key factors controlling theoccurrence of unusual magnesian skarn W mineralization during Late Jurassic in the Nanling Rangemainly include a W enriched metasedimentary source, a fluorine-rich magma, a strong crystalfractionation, and a fluorine-rich hydrosaline melt

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

The advances in computational and experimental modeling in the area of structural mechanics have stimulated research in a class of hybrid problems that require both of these modeling capabilities to be combined to achieve certain objectives. Real-time substructure (RTS) testing, structural system identification (SSI) and active control techniques fall in the category of hybrid problems that need efficient tools in both computational and experimental phases for their successful implementation. RTS is a hybrid testing method, which aims to overcome the scaling problems associated with the conventional dynamic testing methods (such as shake table test, effective force test and pseudo dynamic test) by testing the critical part of the structure experimentally with minimum compromise on spatio-temporal scaling, while modeling the remaining part numerically. The problem of SSI constitutes an important component within the broader framework of problems of structural health monitoring where, based on the in-situ measurements on the loading and a subset of critical responses of the structure, the system parameters are estimated with a view to detecting damage/degradation. Active control techniques are employed to maintain the functionality of important structures, especially under extreme dynamic loading. The work reported in the present thesis contributes to the areas of RTS, SSI and active control of nonlinear systems, the main focus being the computational aspects, i.e., in developing numerical strategies to address some of the unsolved issues, although limited efforts have also been made to undertake laboratory experimental investigations in the area of nonlinear SSI. The thesis is organized into seven chapters and five appendices. The first chapter contains an overview of the state of the art techniques in dynamic testing, SSI and structural control. The topics covered include effective force test, pseudo dynamic test, RTS test, time and frequency domain methods of nonlinear system identification, dynamic state estimation techniques with emphasis on particle filters, Rao-Blackwellization, structural control methods, control algorithms and active control of nonlinear systems. The review identifies a set of open problems that are subsequently addressed, to an extent, in the thesis. Chapter 2 focuses on the development of a time domain coupling technique, involving combined computational and experimental modeling, for vibration analysis of structures built-up of linear/nonlinear substructures. The numerical and experimental substructures are allowed to interact in real-time. The equation of motion of the numerical substructure is integrated using a step-by-step procedure that is formulated in the state space. For systems with nonlinear substructures, a multi-step transversal linearization method is used to integrate the equations of motion; and, a multi-step extrapolation scheme, based on the reproducing kernel particle method, is employed to handle the time delays that arise while accounting for the interaction between the substructures. Numerical illustrations on a few low dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using RTS testing techniques. The concept of substructuring is extended in Chapter 3 for implementing Rao-Blackwellization, a technique of combining particle filters with analytical computation through Kalman filters, for state and parameter estimations of a class of nonlinear dynamical systems with additive Gaussian process/observation noises. The strategy is based on decomposing the system to be estimated into mutually coupled linear and nonlinear substructures and then putting in place a rational framework to account for coupling between the substructures. While particle filters are applied to the nonlinear substructures, estimation of linear substructures proceeds using a bank of Kalman filters. Numerical illustrations for state/parameter estimations of a few linear and nonlinear oscillators with noise in both the process and measurements are provided to demonstrate the potential of the Rao-Blackwellized particle filter (RBPF) with substructuring. In Chapter 4, the concept of Rao-Blackwellization is extended to handle more general nonlinear systems, using two different schemes of linearization. A semi-analytical filter and a conditionally linearized filter, within the framework of Monte Carlo simulations, are proposed for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. The first filter uses a local linearization of the nonlinear drift fields in the process/observation equations based on explicit Ito-Taylor expansions to transform the given nonlinear system into a family of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. In the second filter, the marginalized posterior distribution of an appropriately chosen subset of the state vector is obtained using a particle filter. Samples of these marginalized states are then used to construct a family of conditionally linearized system of equations to obtain the posterior distribution of the states using a bank of Kalman filters. The potential of the proposed filters in state/parameter estimations is demonstrated through numerical illustrations on a few nonlinear oscillators. The problem of active control of nonlinear structural dynamical systems, in the presence of both process and measurement noises, is considered in Chapter 5. The focus of the study is on the exploitability of particle filters for state estimation in feedback control algorithms for nonlinear structures, when a limited number of noisy output measurements are available. The control design is done using the state dependent Riccati equation (SDRE) method. The Bayesian bootstrap filter and another based on sequential importance sampling are employed for state estimation. Numerical illustrations are provided for a few typically nonlinear oscillators of interest in structural engineering. The experimental validation of the RBPF using substructuring (developed in Chapter 3) and the conditionally linearized Monte Carlo filter (developed in Chapter 4), for parameter estimation, is reported in Chapter 6. Measured data available through laboratory experiments on simple building frame models subjected to harmonic base motions is processed using the proposed algorithms to identify the unknown parameters of the model. A brief summary of the contributions made in this thesis, together with a few suggestions for future research, are presented in Chapter 7. Appendix A provides an account of the multi-step transversal linearization method. The derivation of the reproducing kernel shape functions are presented in Appendix B. Appendix C provides the details of the stochastic Taylor expansion and derivation of the covariance structure of Gaussian MSI-s. The performance of a particle filtering algorithm (bootstrap filter) and Kalman filter in the state estimation of a linear system is provided in Appendix D and Appendix E contains the theoretical details of the Rao-Blackwellized particle filter.

科学研究費補助金 研究種目:基盤研究(B)(2) 課題番号:11555183 研究代表者:金武 直幸 研究期間:1999-2001年度