Stability of positive-position feedback controllers with low-frequency restrictions

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Precise tip positioning of a flexible manipulator using resonant control

A single-link flexible manipulator is fabricated to represent a typical flexible robotic arm. This flexible manipulator is modeled as a SIMO system with the motor-torque as the input and the hub angle and the tip position as the outputs. The two transfer functions are identified using a frequency-domain system identification method. A feedback loop around the hub angle response with a resonant controller is designed to damp the resonant modes. A high gain integral controller is also designed to achieve zero steady-state error in the tip position response. Experiments are performed to demonstrate the effectiveness of the proposed control scheme

Modelo de referência para seguimento robusto de referências senoidais

Este trabalho define uma estrutura para o modelo de referência em projetos de controle que visam seguimento robusto de referências senoidais e rejeição de suas harmônicas. Modelos de referência são especialmente úteis em métodos de controle baseado em dados, onde não é possível contar com um modelo matemático do processo a ser controlado, limitando-se aos seus dados de entrada e saída, o que motiva sua denominação. A partir de uma estrutura predeterminada do controlador, dos dados da planta e um modelo de referência é possível estimar um controlador ótimo, que aproxime ao máximo o processo em malha fechada do modelo de referência. São propostas estratégias de escolha para os polos e zeros da estrutura definida para o modelo de referência, baseadas em desempenhos desejados em malha fechada, projetados com base em características predominantes estimadas do processo. Desenvolve-se, então, um algoritmo de otimização para testar diferentes modelos de referências com diferentes polos. Desse algoritmo obtém-se os modelos com melhores desempenhos em malha fechada com os respectivos controladores — da classe proporcionalmúltiplo- ressonante — projetados por meio do método de controle baseado em dados virtual reference feedback tuning. Realiza-se, então, um estudo de caso em que, após análise de seus resultados, pode-se concluir que a priorização do seguimento e rejeição de sinais senoidais interferem nos requisitos desejados, que polos dominantes complexos otimizam o desempenho, enquanto os demais polos devem ser adotados no limiar do critério de dominância e que a introdução de mais harmônicas eleva, consideravelmente, o nível de dificuldade do projeto.This work defines a structure for the reference model in control designs that aim for robust tracking of sinusoidal references and rejection of their harmonics. Reference models are especially useful in data-driven control methods, where it is not possible to count on a mathematical model of the process to be controlled, being limited to its input and output data, which motivates its denomination. From a predetermined controller structure, the plant data, and a reference model it is possible to estimate an optimal controller, which brings the closed-loop process as close as possible to the reference model. It proposes choice methods for the poles and zeros of this structure, based on desired closed-loop performance, designed according to estimated predominant characteristics of the process. An optimization algorithm is then developed to test different reference models with different poles. From this algorithm we obtain the models with the best closed loop performance with their respective controllers — of the proportional-multi-resonant class — designed by means of the virtual reference feedback tuning method. A case study is then carried out in which, after analyzing its results, can be concluded that the prioritization of tracking and rejection of sinusoidal signals interferes with the desired requirements, that complex dominant poles optimize the performance, while the other poles should be adopted at the threshold of the dominance criterion, and that the introduction of more harmonics raises, considerably, the level of difficulty of the project

Tuning of resonant controllers based on the frequency response

Resonant controllers are introduced to fulfil the increased demand for controllers capable to follow or reject periodic signals with superior performance than conventional PID ones. The main characteristic of these controllers is the infinite gain in the frequency of interest, which can lead to stability problems and makes their tuning more complex. This work presents the computation of resonant controllers parameters based on a frequency response method, using stability margins and sensitivity functions as indicators of performance and stability for the controlled system. In addition, the combination with a phase-lead compensator is proposed to allow better performance in an augmented bandwidth. The method is extended for multiple frequency modes in order to deal with higher harmonic content, resulting in the multi-resonant controller. The proposed method is tested using different classes of processes found in typical control problems in order to illustrate its wide applicability.Controladores ressonantes são introduzidos para atender à demanda crescente por controladores capazes de seguir ou rejeitar sinais periódicos com desempenho superior ao dos controladores PID convencionais. A principal característica destes controladores é o ganho infinito na frequência de interesse, o que pode levar a problemas de estabilidade e torna o seu projeto e sintonia mais complexos. Este trabalho apresenta um método para a sintonia dos parâmetros de controladores ressonantes baseada em um método de resposta em frequência, usando as margens de estabilidade e as funções sensibilidade como indicadores de desempenho e estabilidade para o sistema controlado. Além disso, a combinação com um compensador de avanço de fase é proposta para possibilitar desempenho superior em uma maior largura de banda. O método é então estendido para múltiplos modos de frequência a fim de considerar sinais de referência ou perturbação com maior conteúdo harmônico, resultando no controlador multirressonante. O método proposto é testado usando diferentes classes de processos encontrados em problemas típicos de controle para demonstrar sua vasta aplicabilidade

Investigation into vibration assisted micro milling: theory, modelling and applications

PhD ThesisPrecision micro components are increasingly in demand for various engineering industries, such as biomedical engineering, MEMS, electro-optics, aerospace and communications. The proposed requirements of these components are not only in high accuracy, but also in good surface performance, such as drag reduction, wear resistance and noise reduction, which has become one of the main bottlenecks in the development of these industries. However, processing these difficult-to-machine materials efficiently and economically is always a challenging task, which stimulates the development and subsequent application of vibration assisted machining (VAM) over the past few decades. Vibration assisted machining employs additional external energy sources to generate high frequency vibration in the conventional machining process, changing the machining (cutting) mechanism, thus reducing cutting force and cutting heat and improving machining quality. The current awareness on VAM technology is incomplete and effective implementation of the VAM process depends on a wide range of technical issues, including vibration device design and setup, process parameters optimization and performance evaluation. In this research, a 2D non-resonant vibration assisted system is developed and evaluated. Cutting mechanism and relevant applications, such as functional surface generation and microfluidic chips manufacturing is studies through both experimental and finite element analysis (FEA) method. A new two-dimensional piezoelectric actuator driven vibration stage is proposed and prototyped. A double parallel four-bar linkage structure with double layer flexible hinges is designed to guide the motion and reduce the displacement coupling effect between the two directions. The compliance modelling and dynamic analysis are carried out based on the matrix method and lagrangian principle, and the results are verified by finite element analysis. A closed loop control system is developed and proposed based on LabVIEW program consisting of data acquisition (DAQ) devices and capacitive sensors. Machining experiments have been carried out to evaluate the performance of the vibration stage and the results show a good agreement with the tool tip trajectory simulation results, which demonstrates the feasibility and effectiveness of the vibration stage for vibration assisted micro milling. The textured surface generation mechanism is investigated through both modelling and experimental methods. A surface generation model based on homogenous matrices transformation is proposed by considering micro cutter geometry and kinematics of vibration assisted milling. On this basis, series of simulations are performed to provide insights into the effects of various vibration parameters (frequency, amplitude and phase difference) on the generation mechanism of typical textured surfaces in 1D and 2D vibration-assisted micro milling. Furthermore, the wettability tests are performed on the machined surfaces with various surface texture topographies. A new contact model, which considers both liquid infiltration effects and air trapped in the microstructure, is proposed for predicting the wettability of the fish scales surface texture. The following surface textures are used for T-shaped and Y-shaped microchannels manufacturing to achieve liquid one-way flow and micro mixer applications, respectively. The liquid flow experiments have been carried out and the results indicate that liquid flow can be controlled effectively in the proposed microchannels at proper inlet flow rates. Burr formation and tool wear suppression mechanisms are studied by using both finite element simulation and experiment methods. A finite element model of vibration assisted micro milling using ABAQUS is developed based on the Johnson-Cook material and damage models. The tool-workpiece separation conditions are studied by considering the tool tip trajectories. The machining experiments are carried out on Ti-6Al-4V with coated micro milling tool (fine-grain tungsten carbides substrate with ZrO2-BaCrO4 (ZB) coating) under different vibration frequencies (high, medium and low) and cutting states (tool-workpiece separation or nonseparation). The results show that tool wear can be reduced effectively in vibration assisted micro milling due to different wear suppression mechanisms. The relationship between tool wear and cutting performance is studied, and the results indicate that besides tool wear reduction, better surface finish, lower burrs and smaller chips can also be obtained as vibration assistance is added

Resonant control of structural vibration using charge-driven piezoelectric actuators

Driving piezoelectric actuators by charge, or current rather than voltage is known to significantly reduce the hysteretic nature of these actuators. Although this feature of piezoelectric transducers has been known to the researchers for some time, still voltage amplifiers are being used as the main driving mechanism for piezoelectric devices. This is due to the perceived difficulty in building charge/current amplifiers capable of driving highly capacitive loads such as piezoelectric actuators. Recently, a new charge amplifier has been proposed which is ideal for driving piezoelectric loads used in applications such as active damping of vibration. Consequently, it is now possible to effectively, and accurately control the charge deposited on the electrodes of a piezoelectric transducer, and thereby avoid hysteresis altogether. This paper further investigates properties of piezoelectric transducers driven by charge sources when used with resonant controllers for structural vibration control applications. The paper reports experimental results of a multivariable resonant controller implemented on a piezoelectric laminate cantilever beam