The purpose of this paper is to study the design of robust control for a flexible beam. First, the finite element method (FEM) is used to formulate the ordinary differential equations (ODEs) of the dynamic system of the beam model, and a controller is designed via the H-inf control theory. From the computer simulation results, the following conclusions could be drawn. 1. The developed controller is capable of precision positioning and tolerating external disturbance. 2. The robust stability for the system is assured. Furthermore, robust control of linear one-dimensional systems is extended here to two-dimensional systems. The finite difference method (FDM) is applied to partial differential equations (PDEs) to obtain the so-called Roesser discrete state-space model. We discussed the application of H¡Û control for two-dimensional systems and the design of H-inf controller is formulated into a convex optimization problem characterized by linear matrix inequalities (LMIs). Finally, the solutions of the LMIs are then used to construct a two-dimensional H¡Û controller.

Submitted by FREDERIC CONRAD JANZEN null (fcjanzen@utfpr.edu.br) on 2016-11-13T01:59:49Z No. of bitstreams: 1 Positioning and vibration control of a flexible structure in slewing motion by applying Shape Memory Alloys.pdf: 10393447 bytes, checksum: 905f7c805c63133af1f576ad7ebbfd4b (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-11-17T18:09:27Z (GMT) No. of bitstreams: 1 janzen_fc_dr_bauru.pdf: 10393447 bytes, checksum: 905f7c805c63133af1f576ad7ebbfd4b (MD5) / Made available in DSpace on 2016-11-17T18:09:27Z (GMT). No. of bitstreams: 1 janzen_fc_dr_bauru.pdf: 10393447 bytes, checksum: 905f7c805c63133af1f576ad7ebbfd4b (MD5) Previous issue date: 2016-09-19 / Estruturas flexíveis com movimento de rastreamento tem sido encontradas com frequência cada vez maior em diversos tipos de aplicações, por serem mais eficientes do que suas concorrentes rígidas. O estudo desses sistemas é importante por conta das vibrações advindas da redução de massa das estruturas. Muitos trabalhos têm sido publicados apresentado técnicas de controle aplicadas na redução dos efeitos dessas vibrações. Vários trabalhos demonstram a aplicação de materiais inteligentes como atuadores para esse tipo de aplicação. Sendo assim, o presente trabalho apresenta uma proposta para o controle do posicionamento angular e da vibração de uma estrutura flexível em movimento de rastreamento. Para tal, atuadores compostos de um material inteligente conhecido como Liga com Memoria de Forma são empregados para o controle da vibração da estrutura flexível. Com relação ao controle, a técnica de controle conhecida como Equações de Ricatti Dependentes dos Estados (SDRE) é aplicada para o controle. Com o objetivo de analisar a dinâmica do sistema com o controle proposto considera-se a modelagem matemática do sistema e sua validação através do desenvolvido de um protótipo experimental. Simulações numéricas são realizadas para analisar a viabilidade do controle proposto e testes experimentais são realizados com a finalidade de validar o modelo teórico e a proposta de controle. / Flexible structures with slewing motion has been found with increasing frequency in various types of applications, because they are more efficient than their rigid competitors. The study of these systems is important because of the vibrations coming from the mass reduction of structures. Many works have been published presenting control techniques applied in reducing the effects of these vibrations. Several studies demonstrate the application of intelligent materials as actuators for this application. This paper presents a proposal for controlling the angular positioning and vibration of a flexible structure in slewing motion. For such compounds an intelligent actuator materials known as Shape Memory Alloy is employed to control the vibration of the flexible structure. To control the system, the control technique known as State Dependent Ricatti Equation (SDRE), is applied to the control. In order to analyse the dynamics of the system with the proposed control the mathematical modelling of the system is considered and its validation by developed an experimental prototype. Numerical simulations are carried out to analyse the viability of the control and experimental tests are performed in order to validate the theoretical model and the proposed control.

No / Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control (AVC) algorithm for a flexible beam system simulated using the finite difference (FD) method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments.

Orientador: Prof. Dr. André Fenili / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2015. / No presente trabalho, é investigado o modelo matemático de uma viga não linear com seção retangular em rotação. Foi considerado, no modelo, curvatura linear e condições de contorno de viga livre-engastada. Para simulação, considera-se ainda ângulo de ataque constante e as não linearidades resultantes do acoplamento entre a velocidade angular do eixo de rotação e vibração transversal da viga. As forças externas de arrasto e sustentação ao longo do comprimento da viga foram modeladas utilizando teoria de faixas. Estas forças são funções não lineares da velocidade transversal da viga e da velocidade angular do eixo de rotação. As equações de governo para a viga foram discretizadas no espaço utilizando-se o método das diferenças finitas. Isso resulta em uma sistema de equações diferenciais para os valores nodais da discretização espacial da viga. Esse conjunto de equações diferenciais é integrado numericamente no domínio do tempo utilizando-se um método de Runge-Kutta de quarta ordem. / In this work, we investigate the mathematical model of a nonlinear beam with rectangular cross section in rotation. It was considered, in the model, linear curvature and boundary conditions of clamped-free. To simulation, still considered constant attack angle and the nonlinearities resulting from the coupling between the angular velocity of the rotation axis and transverse vibration of the beam. The external drag and lift forces along the length of the beam were modeled as turbulent drag and potential generated by the lift force. These forces are dependent on the speed of nonlinear excitations acting on the beam. The solution in space wasobtained from the finite difference method using 5 points, and the solution in the time from the Runge- Kutta method of 4th order.

Orientador: Prof. Dr. Juan Pablo Julca Avila / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2015. / Atualmente, os risers rígidos em catenária ou SCRs (Steel Catenary Risers), que são tubos longos de aço, apresentam-se como a melhor solução técnico-econômica na transferência de petróleo e gás desde o solo marinho até uma plataforma flutuante. Os SCRs são de fácil fabricação, resistem altas pressões internas e hidrostáticas e também resistem altas temperaturas. Porém, cuidado especial deve-se tomar no cálculo dos momentos fletores e força axial interna no ponto de contato com o solo marinho, sendo estes parâmetros cruciais no projeto. Por outro lado, devido a que os SCRs interagem com o solo marinho, a plataforma à qual está conectada, correntezas e com o escoamento interno, a teoria de SCRs é complexa e não tem sido totalmente desenvolvida, requerendo para seu estudo a teoria de vigas curvas, tópicos de mecânica dos sólidos e dos fluidos, dinâmica não-linear, mecânica de ondas e mecânica dos solos. Este trabalho tem como principal objetivo o desenvolvimento e implementação de uma ferramenta computacional para análise estática e dinâmica bidimensional de risers rígidos e flexíveis dispostos em catenária em contato com o solo marinho. A discretização espacial do riser é feita usando elementos finitos não lineares tipo de viga, incluindo grandes deslocamentos e rotações. A formulação co-rotacional é utilizada para o tratamento da não linearidade geométrica. O método iterativo-incremental de Newton-Raphson é usado para resolver as equações de equilíbrio estático e dinâmico. A integração no tempo das equações dinâmicas é feita usando o esquema implícito de Newmark. A fim de garantir a estabilidade do esquema numérico implementado quando são impostos deslocamentos no topo do riser pelo método de penalização, é introduzido nas equações dinâmicas um termo de amortecimento estrutural para a filtragem das frequências espúrias induzidas por este tipo de excitação. O solo marinho é modelado como uma fundação elástica-linear do tipo Winkler e o método de penalização é usado para a imposição da condição de não penetração. Simulações estáticas e dinâmicas de problemas geometricamente não lineares foram conduzidas para a avaliação do elemento de viga plana implementado neste trabalho. Os resultados obtidos foram comparados com resultados da literatura para a validação do código. A ferramenta computacional foi aplicada satisfatoriamente para resolver problemas estáticos e dinâmicos de risers rígidos e flexíveis. / Steel catenary risers (SCR) are slender steel pipes that hang free in the ocean, this represents the best technical and economical solution for the oil and gas transfer from the seabed to the floating platform. SCRs are of easy manufacturing, high internal and external pressure resistance and also high temperature resistance. Special care should be taken in the calculation of the bending and tension stresses at the touch down point (TDP) as this parameters are of main importance in the calculation of fatigue resistance. On the other side, as the riser interacts with many other elements as seawater currents, internal flow, floating platform and seabed SCRs theory is complex and is not yet well developed, requiring for its study deep knowledge of curved beam theory, solid and fluid mechanics, non-linear dynamics, wave theory and soil mechanics. The main objective of this work is the development and implementation of a computational tool for the static and dynamic two-dimensional analysis of steel catenary and flexible risers, special attention is given to the seabed contact phenomena, to this end, numerical methods for the solution of dynamic equations were implemented into a MATLAB code. The spacial discretization of the riser geometric domain was made by finite element procedures, the large deflections and rotations, inherent to risers geometric non linearity, were treated by means of the co-rotational formulation. The incremental-iterative Newton-Raphson scheme is used to solve the equations of static and dynamic equilibrium. Time domain integration is made using Newmarks implicit method. To guarantee the numerical stability of the implemented code when imposed a time-varying nodal displacement by the penalty method an structural damping is introduced. This damping filters spurious frequencies induced by the penalty method. The seabed is modeled as an elastic foundation of Winkler type, once again the penalty method is used to enforce the non-penetration condition. Static and dynamic simulations of beams with geometrical non linearity were conducted in order to test the stability and accuracy of the implemented code. These results were compared with those available in specialized literature in order to validate the code. This computational tool was successfully applied to the static and dynamic analysis of steel catenary risers.

Spacecrafts are generally equipped with high precision optical and other sensor payloads. The structures of most of the spacecrafts are light-weight, flexible and have low damping. Vibrations are often induced in the spacecraft body due to the presence of many disturbance sources such as momentum/reaction wheels, control thrusters used for attitude control and cryocoolers etc. Low damping leads to long decay time for vibrations hence during this period the spacecraft sensors cannot be used effectively. One possible solution is to isolate the precision sensor from the rest of the satellite and this strategy has been used for spaceborne telescopes and interferometers that have extremely precise positional and vibratory tolerances imposed on them in order to achieve scientific goals. Another strategy is to isolate the vibration source itself from the spacecraft body. This thesis deals with modelling, analysis and experimentation of a novel low frequency flexible space platform designed to serve as a mount for the disturbance source in order to insulate the source generated vibrations reaching critical areas of the structure. The novel space platform consisting of folded continuous beams, is light-weight and is capable of isolating vibration generated by sources such as reaction/momentum wheels. Finite element analysis of the platform is carried out for static and dynamic load cases. Simulation studies are carried out on flexible beam platform in order to firm up the design for passive vibration isolation. Modal analyses is done to simulate the response of each mode. Active control has been studied by embedding the platform’s beam elements with piezo actuators and sensors. The simulation results show that the space platform can effectively attenuate vibration and further improvement in vibration attenuation is possible with active control. Based on the analysis, a prototype low frequency platform has been designed and fabricated. An experimental validation has been done to test the usefulness of the low frequency platform to act as a mount for reaction wheels and to mitigate the vibration disturbances/effects transmitted from the reaction wheel assembly to structure. Measurements and tests have been conducted at varying wheel speeds to quantify and characterize the amount of isolation to the reaction wheel generated vibrations. The time and frequency domain analysis of test data clearly show that level of isolation is significant and an average of 13 dB of isolation is seen. The level of isolation is different for different isolators and it depends upon the isolator design and wheel speed. Forces and moments measured at the base for wheel with isolator and wheel without isolator clearly demonstrate and confirm a reduction in the disturbance levels of atleast one order. These isolators are further tested successfully for launch dynamic loads in order to confirm the design adequacy to sustain such loads. Results indicate that the flexible mounts of the type discussed in this thesis can be used for effective passive vibration isolation in spacecrafts with reaction/momentum wheels.