There is much interest in the design of feedback controllers for linear systems that minimize the H-infty norm of a specific closed-loop transfer function.  The H-infty optimization problem initiated by Zames (1981), \\cite{zames1981feedback}, has received a lot of interest since its formulation.  In H-infty control theory one uses the H-infty norm of a stable transfer function as a performance measure.  One typically uses approaches in either the frequency domain or a state space formulation to tackle this problem.  Frequency domain approaches use operator theory, J-spectral factorization or polynomial methods while in the state space approach one uses ideas similar to LQ theory and differential games.  One of the key computational issues in the design of H-infty optimal controllers is the determination of the optimal H-infty norm.  That is, determining the infimum of r for which the H-infty norm of the associated transfer function matrix is less than r.  Doyle  et al (1989), presented a state space characterization  for the sub-optimal H-infty control problem.  This characterization requires that the unique stabilizing solutions to  two Algebraic Riccati Equations are positive semi definite as well as satisfying a spectral radius coupling condition.  In this work, we describe an algorithm by Lin et al(1999),  used to calculate the H-infty norm for the state feedback and output feedback control problems.  This algorithm only relies on standard assumptions and divides the problem into three sub-problems. The first two sub-problems rely on algorithms for the state feedback problem formulated in the frequency domain as well as a characterization of the optimal value in terms of the singularity of the upper-half of  a matrix created by the stacked basis vectors of the invariant sub-space of the associated Hamiltonian matrix.  This characterization is verified through a bisection or secant method.  The third sub-problem relies on the geometric nature of the spectral radius of the product of the two solutions to the Algebraic Riccati Equations associated with the first two sub-problems.  Doyle makes an intuitive argument that the spectral radius condition will fail before the conditions involving the Algebraic Riccati Equations fail.  We present numerical results where we demonstrate that the Algebraic Riccati Equation conditions fail before the spectral radius condition fails. / Master of Science

Orientador: Alberto Luiz Serpa / Dissertação (mestrado - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-20T02:35:52Z (GMT). No. of bitstreams: 1 Tapias_RenanMoro_M.pdf: 4789122 bytes, checksum: 0c921b95857d6987a5596ae935a85719 (MD5) Previous issue date: 2012 / Resumo: Esta dissertação aborda técnicas de controle robusto H-infinito para sistemas dinâmicos lineares com incertezas paramétricas. Para obtenção do modelo da estrutura em estudo, utiliza-se o método de elementos finitos. A partir do modelo da estrutura, consideram-se incertezas paramétricas, sendo elas, na frequência natural e no fator de amortecimento. As incertezas paramétricas quando consideradas para projeto do controlador H-infinito são tratadas pela abordagem poli tópica. Essa metodologia utiliza o conceito de Desigualdades Matriciais Lineares (LMI). Ainda na fase de projeto do controlador, filtros de ponderação são utilizados para impor uma certa forma em frequência. As incertezas dos sistemas em estudo são consideradas como sendo tanto variantes como invariantes no tempo. O controlador encontrado por essa metodologia se mostrou robusto a incertezas paramétricas, garantindo estabilidade e boa atenuação de vibração dos modos considerados em projeto / Abstract: The aim of this dissertation is to study the H-infinity robust control techniques for linear dynamic systems with parametric uncertainties. The finite element method was employed to find the model of the flexible structure. When dealing with the model, parametric uncertainties were considered for natural frequencies and for damping of the structure. The parametric uncertainties for the H-infinity controller design are handled in the polytopic approach. This methodology uses the concept of Linear Matrix Inequalities (LMI) for the controller project. Weighting filters were used to impose desired frequency response in the controller design. Systems with uncertainties were considered variant and invariant in time. The controller found using this methodology was robust to parametric uncertainties, ensuring stability and good attenuation of vibration in design the considered modes / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

This research investigates the harmonic and narrowband disturbance rejection problem for linear time-periodic (LTP) systems. The consequence of disturbances on LTP systems is similar to their linear time-invariant (LTI) counterparts, but is complicated by the interaction of the disturbance and plant acting at different frequencies, which manifests itself in the modulation of the disturbance signal. The result, for an m-periodic plant and disturbance containing a single tone, is that the output contains m tones. Using various disturbance rejection architectures, harmonic and narrowband disturbance rejection is investigated for linear time-periodic plants. Included are classical and multivariable feedback controllers, fixed-gain feedforward designs using finite impulse response (FIR) filters and H-infinity synthesis tools, and adaptive feedforward controllers. The objective of time-periodic, narrowband, disturbance rejection seeks to place a zero in the controlled system's disturbance path and align the zero direction, defined by the null space of the controlled system at the disturbance frequency, with the disturbance. In this research, constraints on controlled system infinity-norms specify nominal performance and robust stability objectives. Periodic controllers are found using existing LTI H-infinity control theory, and causality is satisfied using two techniques which can be added easily to H-infinity solvers: loop-shifting and Q-parameterization. The resulting controllers are high-gain, narrowband-pass, periodic filters; the closed-loop sensitivity has a zero at the disturbance frequency, and the disturbance is in the sensitivity's null space. It is also shown that classical designs do not achieve the same performance levels as periodic controllers. Similar developments are made using the feedforward disturbance rejection architecture. Objectives are given which minimize the weighted infinity-norm of the controlled system. Such feedforward controllers achieve perfect disturbance rejection. A multivariable equivalent of the tapped-delay line is used in the description of periodic FIR filters. In addition, periodic FIR filters are made adaptive using an algorithm similar to filtered-X least mean square (LMS) but modified for periodic systems. / Ph. D.

This thesis investigates Bicoprime Factorisations (BCFs) and their possible uses in robust control theory. BCFs are a generalisation of coprime factorisations, which have been well known and widely used by the control community over the last few decades. Though they were introduced at roughly the same time as coprime factorisations, they have been largely ignored, with only a very small number of results derived in the literature. BCFs are first introduced and the fundamental theory behind them is developed. This includes results such as internal stability in terms of BCFs, parametrisation of the BCFs of a plant and state space constructions of BCFs. Subsequently, a BCF uncertainty structure is proposed, that encompasses both left and right coprime factor uncertainty. A robust control synthesis procedure is then developed with respect to this BCF uncertainty structure. The proposed synthesis method is shown to be advantageous in the following two aspects: (1) the standard assumptions associated with H-infinity control synthesis are directly fulfilled without the need of loop shifting or normalisation of the generalised plant and (2) any or all of the plant's unstable dynamics can be ignored, thus leading to a reduction in the dimensions of the Algebraic Riccati Equations (AREs) that need to be solved to achieve robust stabilisation. Normalised BCFs are then defined, which are shown to provide many advantages, especially in the context of robust control synthesis. When using a normalised BCF of the plant, lower bounds on the achievable BCF robust stability margin can be easily and directly computed a priori, as is the case for normalised coprime factors. Although the need for an iterative procedure is not completely avoided when designing an optimal controller, it is greatly simplified with the iteration variable being scalar. Unlike coprime factorisations where a single ARE needs to be solved to achieve normalisation, two coupled AREs must be satisfied for a BCF to be normalised. Two recursive methods are proposed to solve this problem. Lastly, an example is presented where the theory developed is used in a practical scenario. A quadrotor Unmanned Aerial Vehicle (UAV) is considered and a normalised BCF controller is designed which in combination with feedback linearisation is used to control both the attitude and position of the vehicle.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18402号 / 情博第517号 / 新制||情||91(附属図書館) / 31260 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 山本 裕, 教授 西村 直志, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

This paper presents the development of building up a controlled MEMS acceleration sensor. The first samples have archived a resolution of better than 500 ug and a bandwidth of more than 200 Hz. A theoretical model is built from the physical principles of the complete sensor system, consisting of the MEMS sensor, the charge amplifier and the PWM driver for the sensor element. A reduced order model of the system is used to design a robust control with the Mixed-Sensitivity H-infinity Approach. Limitations for the control design are given since the system contains time delays and an unstable pole imposed by the electrostatic spring softening effect. The theoretical model might be inaccurate or lacks of completeness, because the parameters for the theoretical model building vary from sample to sample or might be not known. A new two-stage identification scheme is deployed to obtain directly the system parameters from the samples. The focus of this paper is the complete system development and identification process including practical tests in a DSP TI-TMS320C3000 environment with 12/14-bit A/D-D/A converters. / Der Artikel beschreibt die Entwicklungsschritte eines geregelten MEMS-Beschleunigungssensors. Die ersten Prototypen erreichten dabei eine Auflösung von weniger als 500 ug und eine Bandbreite von mehr als 200 Hz. Ein theoretisches Modell für den Reglerentwurf wird aus den physikalischen Zusammenhängen des Gesamtsystems, bestehend aus dem mechanischen Sensorelement, dem Ladungsverstärker und der PWM-Treiberstufe, gebildet. Für den Reglerentwurf wird der H-Infinity Mixed-Sensitivity Approach verwendet. Wegen Systemtotzeiten und dem Effekt der elektrostatischen Federerweichung sind Grenzen für die Wahl der Bandbreite zu beachten. Da Parameter für das theoretische Modell stark variieren oder schwer zu bestimmen sind, wird eine 2-Stufen-Identifikationsmethode vorgeschlagen, um ein Modell für den Reglerentwurf zu erhalten. Praktische Tests wurden mit einem DSP TI-TMS320C3000 mit 12/14-Bit A/D-D/A Wandlerstufen durchgeführt.

Extremely large telescopes (ELTs) are the next generation of ground-based reflecting telescopes of optical wavelengths. ELTs possess an aperture of more than 20 meters and share a number of common features, particularly the use of a segmented primary mirror and the use of adaptive optics systems. In 2005, the European Southern Observatory introduced a new giant telescope concept, named the European Extremely Large Telescope (E-ELT), which is scheduled for operation in 2018. The E-ELT will address key scientific challenges and will aim for a number of notable firsts, including discovering Earth-like planets around other stars in the ``habitable zones'' where life could exist, attempting to uncover the relationship between black holes and galaxies, measuring the properties of the first stars and galaxies, and probing the nature of dark matter and dark energy. In 2009, a feasibility study, conducted by National Instruments, proved the feasibility of the real-time (RT) control system architecture for the E-ELT's nearly 1,000 mirror segments with 3,000 actuators and 6,000 sensors. The goal of the RT control system was to maintain a perfectly aligned field of mirrors at all times with a loop-time of 1 ms. The study assumed a prescribed controller algorithm. This research report prescribes the optimal controller algorithms for large segmented telescopes. In this respect, optimal controller designs for the primary mirror of the E-ELT, where optimality is formulated in the [H-2] and [H-infinity] frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance metrics are met. / text

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

abstract: This thesis addresses the design and control of three phase inverters. Such inverters are used to produce three-phase sinusoidal voltages and currents from a DC source. They are critical for injecting power from renewable energy sources into the grid. This is especially true since many of these sources of energy are DC sources (e.g. solar photovoltaic) or need to be stored in DC batteries because they are intermittent (e.g. wind and solar). Two classes of inverters are examined in this thesis. A control-centric design procedure is presented for each class. The first class of inverters is simple in that they consist of three decoupled subsystems. Such inverters are characterized by no mutual inductance between the three phases. As such, no multivariable coupling is present and decentralized single-input single-output (SISO) control theory suffices to generate acceptable control designs. For this class of inverters several families of controllers are addressed in order to examine command following as well as input disturbance and noise attenuation specifications. The goal here is to illuminate fundamental tradeoffs. Such tradeoffs include an improvement in the in-band command following and output disturbance attenuation versus a deterioration in out-of-band noise attenuation. A fundamental deficiency associated with such inverters is their large size. This can be remedied by designing a smaller core. This naturally leads to the second class of inverters considered in this work. These inverters are characterized by significant mutual inductances and multivariable coupling. As such, SISO control theory is generally not adequate and multiple-input multiple-output (MIMO) theory becomes essential for controlling these inverters. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2015