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Piezoelectric actuators have proven to be useful in suppressing disturbances and shape control of flexible structures. Large space structures such as solar arrays are susceptible to large amplitude vibrations while in orbit. Moreover, Shape control of many high precision structures such as large membrane mirrors and space antenna is of great importance. Since most of these structures need to be ultra-light-weight, only a limited number of actuators can be used. Consequently, in order to obtain the most effcient control system, the locations of the piezoelectric elements as well as the feedback gain should be optimized. These optimization problems are generally non-convex. In addition, the models for these systems typically have a large number of degrees of freedom. Researchers have used numerous optimization criteria and optimization techniques to find the optimal actuator locations in structural shape and vibration control. Due to the non-convex nature of the problem, evolutionary optimization techniques are extensively used. However, One drawback of these methods is that they do not use the gradient information and so convergence can be very slow. Classical gradient-based techniques, on the other hand, have the advantage of accurate computation; however, they may be computationally expensive, particularly since multiple initial conditions are typically needed to ensure that a global optimum is found. Consequently, a fast, yet global optimization method applicable to systems with a large number of degrees of freedom is needed. In this study, the feedback control is chosen to be an optimal linear quadratic regulator. The optimal actuator location problem is reformulated as a convex optimization problem. A subgradient-based optimization scheme which leads to the global solution of the problem is introduced to optimize the actuator locations. The optimization algorithm is applied to optimize the placement of piezoelectric actuators in vibration control of flexible structures. This method is compared with a genetic algorithm, and is observed to be faster in finding the global optimum. Moreover, by expanding the desired shape into the structure’s modes of vibration, a methodology for shape control of structures is presented. Applying this method, locations of piezoelectric actuators on flexible structures are optimized. Very few experimental studies exist on shape and vibration control of structures. To the best knowledge of the author, optimal actuator placement in shape control has not been experimentally studied in the past. In this work, vibration control of a cantilever beam is investigated for various actuator locations and the effect of optimal actuator placement is studied on suppressing disturbances to the beam. Also using the proposed shape control method, the effect of optimal actuator placement is studied on the same beam. The final shape of the beam and input voltages of actuators are compared for various actuator placements.

Piezoelectric actuators have proven to be useful in suppressing disturbances and shape control of flexible structures. Large space structures such as solar arrays are susceptible to large amplitude vibrations while in orbit. Moreover, Shape control of many high precision structures such as large membrane mirrors and space antenna is of great importance. Since most of these structures need to be ultra-light-weight, only a limited number of actuators can be used. Consequently, in order to obtain the most effcient control system, the locations of the piezoelectric elements as well as the feedback gain should be optimized. These optimization problems are generally non-convex. In addition, the models for these systems typically have a large number of degrees of freedom. Researchers have used numerous optimization criteria and optimization techniques to find the optimal actuator locations in structural shape and vibration control. Due to the non-convex nature of the problem, evolutionary optimization techniques are extensively used. However, One drawback of these methods is that they do not use the gradient information and so convergence can be very slow. Classical gradient-based techniques, on the other hand, have the advantage of accurate computation; however, they may be computationally expensive, particularly since multiple initial conditions are typically needed to ensure that a global optimum is found. Consequently, a fast, yet global optimization method applicable to systems with a large number of degrees of freedom is needed. In this study, the feedback control is chosen to be an optimal linear quadratic regulator. The optimal actuator location problem is reformulated as a convex optimization problem. A subgradient-based optimization scheme which leads to the global solution of the problem is introduced to optimize the actuator locations. The optimization algorithm is applied to optimize the placement of piezoelectric actuators in vibration control of flexible structures. This method is compared with a genetic algorithm, and is observed to be faster in finding the global optimum. Moreover, by expanding the desired shape into the structure’s modes of vibration, a methodology for shape control of structures is presented. Applying this method, locations of piezoelectric actuators on flexible structures are optimized. Very few experimental studies exist on shape and vibration control of structures. To the best knowledge of the author, optimal actuator placement in shape control has not been experimentally studied in the past. In this work, vibration control of a cantilever beam is investigated for various actuator locations and the effect of optimal actuator placement is studied on suppressing disturbances to the beam. Also using the proposed shape control method, the effect of optimal actuator placement is studied on the same beam. The final shape of the beam and input voltages of actuators are compared for various actuator placements.

The vibration control problem for flexible structures is examined within the context of overall controller performance and power reduction. First, the issue of optimal sensor and actuator placement is considered along with its associated control robustness aspects. Then the option of alternately activating subsets of the available devices is investigated. Such option is considered in order to better address the effects of spatiotemporally varying disturbances acting on a flexible structure while reducing the overall energy consumption. Towards the solution to the problem of optimal device placement, three different approaches are proposed. First, a computationally efficient scheme for the simultaneous placement of multiple devices is presented. The second approach proposes a strategy for the optimal placement of sensors and collocated sensor/actuator pairs, taking into account the influence of the spatial distribution of disturbances. The third approach provides a solution to the actuator location problem by incorporating considerations with respect to preferred spatial regions within the flexible structure. Then the second problem named above is considered. Activating a subset of the available and optimally placed actuators and sensors in a flexible structure provides enhanced performance with reduced energy consumption. Such approach of switching on and off different actuating devices, depending on their local-in-time authority, results in a hybrid system. Therefore the proposed work draws on existing results on hybrid systems and includes an additional degree of freedom, whereby both the actuating devices and the control signals allocated to them are switched in and out. To enable this switching an activation strategy, which insures also that stability-under-switching is guaranteed, is required. Three different strategies are considered for such actuators allocation: first a cost-to-go index is considered, then a cost function based on the mechanical energy of the flexible structure and finally a performance index based on the maximum deviation of the transverse displacement. A flexible aluminum plate was chosen to validate and test the proposed approaches. The set up utilized four pairs of collocated piezoceramic patches that serve to provide sensing and actuating capabilities. Extensive numerical simulations were performed for both the placement strategies and the switching policies proposed, in order to predict the behavior of the flexible plate and provide the optimal actuator and sensor locations that were to be affixed on the flexible structure. Finally, to complete the validation process a sequence of experimental tests were performed. The objective of these tests was to compare the performance of the proposed hybrid control system to traditional non switched control schemes. In order to provide a repeatable perturbation, four of the piezoceramic patches were allocated to simulate a spatiotemporally varying disturbance, while the remaining four patches were used as sensors and controlling actuators. The experimental results showed a significant performance improvement for the switched controller over the traditional controller. Moreover the switched controller exhibited improved robustness towards spatiotemporally varying disturbances while the traditional controller showed a significant loss of controller performance. The improvement achieved in vibration control problems could be extended to a wider range of applications. In particular, although this study was concentrated on a rectangular thin plate, the proposed strategies can be applied to emph{any} structure and more generally to any plant whose dynamics can be represented by a second order linear system. For example, by removing the restriction of spatially fixed actuators and sensors, the proposed theory can be applied to the problem of unmanned vehicles control.

"The recent years have seen the innovative system integration of a great many actuator technologies, such as point force actuators for space vehicle applications and the use of single fire actuators; such as pyrocharges to guide a free falling bomb to it’s target. The inherent limitations of these developments, such as nonlinear behavior under extreme environments and/or prolonged/repeated usage leading to a relaxation time component between firing of actuators and inherent system power limitations, have resulted in greater need for sophisticated control algorithms that allow for optimal switching between various actuators in any given embedded configuration so as to achieve the best possible performance of the system. The objective of this investigation is to offer a proof of concept experimental verification of a real time control algorithm, which switches between online piezoelectric actuators, employed for vibration control in an aluminum beam with fixed boundary conditions. In this investigation at a given interval of time, only one actuator is activated and the rest are kept dormant. The reason is to demonstrate the better vibration alleviation characteristics realized in switching between actuators depending on the state of the system, over the use of a single actuator that is always in fire mode. This effect is particularly pronounced in controlling systems affected by spatiotemporal disturbances. The algorithm can be easily adapted for various design configurations or system requirements. The optimality of switching is with respect to the minimal cost of an LQR performance index that corresponds to each actuator. Computer simulations with repeatable disturbance profiles, revealed that this algorithm offered better performance over the non-switched case. Performance measures employed were the time varying total energy norm of the dynamic system and position traces at any particular location on the beam. This algorithm was incorporated on a dSPACE rapid prototyping platform along with suitable hardware. Experimental and simulation results are discussed. "

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.

Conformal airborne antennas have several advantages compared to externally mounted antennas, and they will play an important role in future aircrafts. However, they are subjected to vibration induced deformations which degrade their electromagnetic performances. With the motivation of suppressing such vibrations, use of active vibration control techniques with piezoelectric actuators is investigated in this study. At first, it is aimed to control the first three bending modes of a cantilever beam. In this scope, four different modal controllers / positive position feedback (PPF), resonant control (RC), integral resonant control (IRC) and positive position feedback with feed-through (PPFFT) are designed based on both reduced order finite element model and the system identification model. PPFFT, is a modified version of PPF which is proposed as a new controller in this study. Results of real- time control experiments show that PPFFT presents superior performance compared to its predecessor, PPF, and other two methods. In the second part of the study, it is focused on controlling the first three modes of a rectangular plate with four clamped edges. Best location alternatives for three piezoelectric actuators are determined with modal strain energy method. Based on the reduced order finite element model, three PPFFT controllers are designed for three collocated transfer functions. Disturbance rejection performances show the convenience of PPFFT in multi-input multi-output control systems. Performance of the control system is also verified by discrete-time simulations for a random disturbance representing the in-flight aircraft vibration characteristics.

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.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21091号 / 工博第4455号 / 新制||工||1692(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 五十嵐 晃, 教授 八木 知己, 准教授 古川 愛子 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM