Repetitive Model Predictive Control (RMPC) incorporates the idea of Repetitive Control (RC) into Model Predictive Control (MPC) to take full advantage of the constraint handling, multivariable control features of MPC in periodic processes. The RMPC achieves perfect asymptotic tracking/rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance exactly. Even a small mismatch between the actual period of process and the controller period can deteriorate the RMPC performance significantly. The period mismatch occurs either from an inaccurate estimation of actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of sampling time. An extension of RMPC called Robust Repetitive Model Predictive Control (R-RMPC) is proposed for such cases where period length cannot be predetermined accurately, or where period is not an integer multiple of sampling time. This robust RMPC borrows the idea of using weighted, multiple memory loops in RC for robustness enhancement. The modified RMPC is more robust in the sense that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that R-RMPC achieves significant improvement over the standard RMPC in case of a slight period mismatch. The effectiveness of this Robust RMPC is demonstrated by applying it to a mechanical motion tracking machine whose function is to follow a constant trajectory while rejecting periodic disturbances of an uncertain period.

In a roll-to-roll web system lateral motion of a web caused by disturbances, which are often periodic, results in poor product quality. To reduce the effect of such disturbances, two control strategies are applied. First, the internal model principle is used to reject a sinusoidal disturbance. Second, repetitive control theory is used to reject a general periodic disturbance. We provide the synthesis procedure for both strategies, and demonstrate its use in several simulation studies on a five-roller web system. The simulation results show that the effect of disturbances, either sinusoidal or triangular, on lateral motion are significantly reduced with the internal model controller or the modified repetitive controller.

In a roll-to-roll web system lateral motion of a web caused by disturbances, which are often periodic, results in poor product quality. To reduce the effect of such disturbances, two control strategies are applied. First, the internal model principle is used to reject a sinusoidal disturbance. Second, repetitive control theory is used to reject a general periodic disturbance. We provide the synthesis procedure for both strategies, and demonstrate its use in several simulation studies on a five-roller web system. The simulation results show that the effect of disturbances, either sinusoidal or triangular, on lateral motion are significantly reduced with the internal model controller or the modified repetitive controller.

Abstract In this thesis a set of new algorithms is introduced for Iterative Learning Control (ILC) and Repetitive Control (RC). Both areas of study are relatively new in control theory, and the common denominator for them is that they concentrate on controlling systems that include either reference signals or disturbances which are periodic. This provides opportunities for using past information or experience so that the control system learns the control action that results in good performance in terms of reference tracking or disturbance rejection. The first major contribution of the thesis is the algebraic analysis of ILC systems. This analysis shows that in the discrete-time case ILC algorithm design can be considered as designing a multivariable controller for a multivariable static plant and the reference signal that has to be tracked is a multivariable step function. Furthermore, the algebraic analysis reveals that time-varying algorithms should be used instead of time-invariant ones in order to guarantee monotonic convergence of the error in norm. However, from the algebraic analysis it is not clear how to select the free parameters of a given ILC algorithm. Hence in this thesis optimisation methods are used to automate this design phase. Special emphasis is placed on the so called Norm-Optimal Iterative Learning Control (NOILC) that was originally developed in (Amann:1996) as a new result it is shown that a convex modification of the existing predictive algorithm will result in a considerable improvement in convergence speed. Because the NOILC algorithm is computationally quite complex, a new set of Parameter-Optimal ILC algorithms are derived that converge under certain assumptions on the original plant. Three of these new algorithms will result in monotonic convergence to zero tracking error for an arbitrary discrete-time, linear, time-invariant plant. This a very strong property that has been earlier reported for only a small number of ILC algorithms. In the RC case it is shown that an existing RC algorithm that has been widely analysed and used in the research literature is in fact highly unrobust if the algorithm is implemented using sampled-data processing. Consequently, in this thesis a new optimality based discrete-time RC algorithm is derived, which converges to zero tracking error asymptotically for an arbitrary linear, time-invariant discrete-time plant under mild controllability and observability conditions.

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Este trabalho apresenta uma comparação entre as estratégias de controle por torque calculado e controle repetitivo aplicadas a manipuladores robóticos. O objetivo no uso desses controladores é para que o manipulador siga referência de trajetória periódica no espaço das juntas. O desenvolvimento e implementação dos controladores são focados no manipulador WAM (Whole Arm Manipulator) da Barrett Technology®Inc. Neste trabalho, também são apresentadas uma formulação do modelo não linear do manipulador e as sínteses dos controladores por torque calculado e repetitivo aplicados ao modelo do manipulador linearizado por realimentação. O controlador por torque calculado é apresentado e sintetizado na sua forma clássica. Para o controlador repetitivo, a síntese parte do princípio do modelo interno com a adição de uma estrutura repetitiva e uma realimentação proporcional e derivativa do erro de seguimento de referência O projeto dos ganhos do controlador repetitivo é feito através de um problema de otimização convexa com restrições na forma de inequações matriciais lineares (ou no inglês: Linear Matrix Inequalities - LMI). A formulação do problema de otimização parte da teoria de estabilidade segundo Lyapunov com um funcional Lyapunov-Krasoviskii, adição de um custo quadrático, para ajuste de desempenho, e de um critério de desempenho transitório dado pela taxa de decaimento exponencial da norma dos estados. É apresentada a comparação entre as estratégias de controle e a validação do controlador repetitivo proposto aplicado ao caso com linearização perfeita e ao caso com o modelo não linear do manipulador. No primeiro caso, é feita a simulação do modelo linear do manipulador com adição de um torque de atrito na junta. No segundo caso, é utilizado o sistema ROS (Robot Operating System) com o programa Gazebo simulando o manipulador WAM considerando erros de linearização, isto é, incertezas paramétricas. / This work presents a comparison between the strategies of computed-torque control and repetitive control applied to robotic manipulators. The main objective in use these controllers with the manipulator is to tracking periodic trajectory in joint space. The development and implementation of controllers are focused on the Whole Arm Manipulator (WAM) of the Barrett Technology®Inc. Also featured are a non-linear model formulation of the manipulator and the synthesis of controllers for computed-torque control and repetitive control applied to the manipulator model linearized by state feedback. The computed-torque controller is presented in its classic form. For the repetitive controller, the synthesis is based on the internal model principle with the addition of a repetitive structure and a proportional-derivative reference tracking error feedback. The design of the repetitive controller gains is done through a convex optimization problem with linear matrix inequalities (LMI) constraints. The formulation of the optimization problem is based on the Lyapunov stability theory using a Lyapunov-Krasoviskii functional, addition of a quadratic cost for performance adjustment and a transient performance criteria given by the exponential decay rate of the states norm. A comparison between the control strategies and the validation of the repetitive controller applied to the case with perfect linearization and the case with the non-linear model of the manipulator are presented. In the first case, is made simulations of the linear model of the manipulator in MATLAB program, with the addition of a disturbance modeling the friction torque at the joint. In the second case, is used the Robot Operating System (ROS) with Gazebo program simulating the WAM nonlinear model. In this case, a possible mismatch between the model used for the feedback linearization and the real system is taken into account.

This thesis applies digital repetitive control to a single-phase DC-to-AC converter, with some proposed designs to improve stability and enhance performance of the converter under various load variations. A practical DC-to-AC converter is required to convert DC power to stable AC power with low harmonic distortion when attached to various linear or nonlinear loads. This thesis combines repetitive control with feedback dithering modulation and optimal state feedback to control the converter. The repetitive control is responsible for regulating output power and eliminating harmonics, while the feedback dithering modulation for switching the power transistors with reduced switching noise and the state feedback for stabilizing the converter under various load variations. The presented control and modulation schemes of the power converter are implemented on an FPGA (Field Programmable Gate Array). The experiments confirm the excellent performance and robustness of the converter, indicating a total harmonic distortion of less than 0.5% for the converter when attached to various linear or nonlinear loads.

The aeration process is often the single largest consumer of electricity in a wastewater treatment plant. Aeration in biological reactors provides microorganisms with oxygen which is required to convert ammonium to nitrate. Ammonium is toxic for aqueous ecosystems and contributes to eutrophication. The importance of aeration for the treatment results in combination with the high costs motivates automatic control of the aeration process. This thesis is devoted to ammonium feedback control in municipal wastewater treatment plants. With ammonium feedback control, the aeration intensity is changed based on a measurement of the outlet ammonium concentration. The main focus of the thesis is design, implementation, evaluation and improvement of ammonium PI (proportional-integral) controllers. The benefits of ammonium feedback control are established through long-term experiments at three large wastewater treatment plants in Stockholm, Sweden. With ammonium feedback control, energy savings up to around 10 % were achieved compared to keeping the dissolved oxygen concentration constant. The experiments generated several lessons learned with regard to implementation and evaluation of controllers in full-scale operation. The thesis has established guidelines on how to design ammonium feedback controllers for situations when cost-effective operation is the overall aim. Simulations have demonstrated the importance to limit the dissolved oxygen concentration in the process and under what conditions the energy saving with ammonium feedback control is large. The final part of the thesis treats improvements of ammonium PI control through minor modifications to the control structure or controller. Three strategies were studied: gain scheduling control, repetitive control, and a strategy reacting to oxygen peaks in the last aerobic zone. The strategies all had their benefits but the ammonium feedback controller was the key factor to improved aeration control.

Este trabalho apresenta uma comparação entre as estratégias de controle por torque calculado e controle repetitivo aplicadas a manipuladores robóticos. O objetivo no uso desses controladores é para que o manipulador siga referência de trajetória periódica no espaço das juntas. O desenvolvimento e implementação dos controladores são focados no manipulador WAM (Whole Arm Manipulator) da Barrett Technology®Inc. Neste trabalho, também são apresentadas uma formulação do modelo não linear do manipulador e as sínteses dos controladores por torque calculado e repetitivo aplicados ao modelo do manipulador linearizado por realimentação. O controlador por torque calculado é apresentado e sintetizado na sua forma clássica. Para o controlador repetitivo, a síntese parte do princípio do modelo interno com a adição de uma estrutura repetitiva e uma realimentação proporcional e derivativa do erro de seguimento de referência O projeto dos ganhos do controlador repetitivo é feito através de um problema de otimização convexa com restrições na forma de inequações matriciais lineares (ou no inglês: Linear Matrix Inequalities - LMI). A formulação do problema de otimização parte da teoria de estabilidade segundo Lyapunov com um funcional Lyapunov-Krasoviskii, adição de um custo quadrático, para ajuste de desempenho, e de um critério de desempenho transitório dado pela taxa de decaimento exponencial da norma dos estados. É apresentada a comparação entre as estratégias de controle e a validação do controlador repetitivo proposto aplicado ao caso com linearização perfeita e ao caso com o modelo não linear do manipulador. No primeiro caso, é feita a simulação do modelo linear do manipulador com adição de um torque de atrito na junta. No segundo caso, é utilizado o sistema ROS (Robot Operating System) com o programa Gazebo simulando o manipulador WAM considerando erros de linearização, isto é, incertezas paramétricas. / This work presents a comparison between the strategies of computed-torque control and repetitive control applied to robotic manipulators. The main objective in use these controllers with the manipulator is to tracking periodic trajectory in joint space. The development and implementation of controllers are focused on the Whole Arm Manipulator (WAM) of the Barrett Technology®Inc. Also featured are a non-linear model formulation of the manipulator and the synthesis of controllers for computed-torque control and repetitive control applied to the manipulator model linearized by state feedback. The computed-torque controller is presented in its classic form. For the repetitive controller, the synthesis is based on the internal model principle with the addition of a repetitive structure and a proportional-derivative reference tracking error feedback. The design of the repetitive controller gains is done through a convex optimization problem with linear matrix inequalities (LMI) constraints. The formulation of the optimization problem is based on the Lyapunov stability theory using a Lyapunov-Krasoviskii functional, addition of a quadratic cost for performance adjustment and a transient performance criteria given by the exponential decay rate of the states norm. A comparison between the control strategies and the validation of the repetitive controller applied to the case with perfect linearization and the case with the non-linear model of the manipulator are presented. In the first case, is made simulations of the linear model of the manipulator in MATLAB program, with the addition of a disturbance modeling the friction torque at the joint. In the second case, is used the Robot Operating System (ROS) with Gazebo program simulating the WAM nonlinear model. In this case, a possible mismatch between the model used for the feedback linearization and the real system is taken into account.

Submitted by Morgana Silva (morgana_linhares@yahoo.com.br) on 2016-07-27T16:18:26Z No. of bitstreams: 1 arquivototal.pdf: 1682868 bytes, checksum: e6813f2f2930d8867270563d26fb878c (MD5) / Made available in DSpace on 2016-07-27T16:18:26Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1682868 bytes, checksum: e6813f2f2930d8867270563d26fb878c (MD5) Previous issue date: 2016-02-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work proposes a repetitive-based control for series compensator with the objective of dynamically restore the voltage applied to sensitive and critical loads of power system. The control mitigates voltage sags while also minimize harmonic distortions. Its transfer function is simple to be realized and does not require any harmonic selective filters. The control system acts on sinusoid references and it is implemented in each phase independently. Another important aspect of the proposed system are the optimization strategies to minimize either the voltage injection or the active power injection. One of these strategies is to optimize the magnitude of the compensation voltage sag with the smallest voltage magnitude injection by the series compensator. For this purpose, the compensating voltage injected must be in phase with the voltage supply. Is possible to control the injection of the voltage compensation to minimize active power injection by the series compensator to compensate a voltage sag. To perform the voltage correction with minimum active power injection were developed analytical expressions for the magnitude and angle of the injected voltage. To implement theses strategies, an recursive least-squares algorithm is used to estimate the grid voltage. A laboratory-scale series compensator was developed to validate the method. Simulations and experimental results are presented and show the efficacy of the proposed method. / Este trabalho propõe um controle repetitivo para compensadores série com o objetivo de restaurar dinamicamente a tensão aplicada a cargas sensíveis e críticas de sistemas de energia. O controle pode mitigar afundamentos de tensão ao mesmo tempo que compensa distorções harmônicas. Sua função de transferência é simples de ser implementada e não requer qualquer filtro seletivo de harmônicos. O sistema de controle atua sobre as referências senoidais e deve ser implementado em cada fase independentemente. Um outro aspecto importante do trabalho são as estratégias de otimização para minimizar a tensão de compensação ou a potência ativa fornecida pelo compensador. Um destas estratégias é a otimização pela amplitude, em que a compensação do afundamento de tensão ocorre com a menor injeção de amplitude de tensão por parte do compensador série. Para isso, a tensão injetada pelo compensador deve estar em fase com a tensão da rede afundada. Pode-se, também, controlar a injeção da tensão de compensação para minimizar a potência ativa a ser injetada pelo compensador série para compensar um afundamento de tensão. Para realizar a correção com a mínima injeção de potência ativa utilizou-se expressões analíticas para obter a magnitude e o ângulo da tensão a ser injetada. Na implementação destas estratégias foi utilizado um algoritmo recursivo de mínimos quadrados para estimar a amplitude e fase da tensão da rede. Um sistema compensador série foi montado em laboratório para validar o método. As simulações e resultados experimentais são apresentados e constatam a eficácia do método proposto.