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

The objective of this dissertation is to develop a practical methodology for designing full and reduced order H[infinity] filter for plants with polytopic model uncertainty. Because the polytopic model description is convex, it is amenable to a Linear Matrix Inequality (LMI) formulation. Reduced order filters are desirable in applications where fast data processing is necessary. To improve robustness to model uncertainties, this dissertation reformulates an H2 filter design technique as a reduced order H[infinity] filter design methodology. Lyapunov functions are replaced with parameter-dependent Lyapunov functions to provide less conservative results. As the problem is formulated as an LMI, an admissible filter with suitable dynamic behavior can be obtained from the solution of a convex optimization problem. The advantages of this approach over earlier approaches are highlighted in a simple computational example. This filtering technique is used to design a fault detection filter. Robust fault detection filter (RFDF) design is formulated as a multi-objective H[infinity] optimization for a polytopic uncertain system. The order of the RFDF is reduced using LMI techniques and the detection performance is compared with the full order filter. An adaptive threshold is used to reduce the number of false alarms. Examples are presented to illustrate effectiveness of the order reduction. / Thesis (Ph.D.)--Wichita State University, Dept. of Electrical and Computer Engineering. / Includes bibliographic references (leaves 70-76). / "May 2006."

The main topic of this thesis is to exhibit how robust control techniques can be applied to real time systems. Presently, the control techniques used in the industry are very simple even when applied to complex systems; these techniques are intuitive and not necessarily systematic. Moreover, the notion of optimality of robustness is absent. Control design procedures are mostly based on SISO techniques, thus, overlooking the intrinsic multivariable aspect of the design that a MIMO system requires. In this thesis a modern control technique is presented to manipulate a 3DOF birotor helicopter in real time. The objective of this research is to demonstrate the performance of more efficient control algorithms to control these kinds of systems. The robust method proposed in this thesis is an H infinity controller which exhibits robustness to plant model uncertainties, and good disturbance and noise rejection.

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.

For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

For a long time determining the stability issue of characteristic polynomials has played avery important role in Control System Engineering. This thesis addresses the traditionalcontrol issues such as stabilizing a system with any certain controller analyzingcharacteristic polynomial, yet a new perspective to solve them. Particularly, in this thesis,Proportional-Integral-Derivative (PID) controller is considered for a fixed structuredcontroller. This research aims to attain controller gain set satisfying given performancespecifications, not from the exact mathematical model, but from the empirical data of thesystem. Therefore, instead of a characteristic polynomial equation, a speciallyformulated characteristic rational function is investigated for the stability of the systemin order to use only the frequency data of the plant. Because the performance satisfactionis highly focused on, the characteristic rational function for the investigation of thestability is mainly dealt with the complex coefficient polynomial case rather than realone through whole chapters, and the mathematical basis for the complex case is prepared.For the performance specifications, phase margin is considered first since it is avery significant factor to examine the system’s nominal stability extent (nominal performance). Second, satisfying H norm constraints is handled to make a more robustclosed loop feedback control system. Third, we assume undefined, but bounded outsidenoise, exists when estimating the system’s frequency data. While considering theseuncertainties, a robust control system which meets a given phase margin performance, isattained finally (robust performance).In this thesis, the way is explained how the entire PID controller gain setssatisfying the given performances mentioned in the above are obtained. The approachfully makes use of the calculating software e.g. MATLAB® in this research and isdeveloped in a systematically and automatically computational aspect. The result ofsynthesizing PID controller is visualized through the graphic user interface of acomputer.

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 1990. / Thesis Advisor(s): Collins, Daniel J. Second Reader: Schmidt, Louis V. "September 1990." Description based on title screen as viewed on December 29, 2009. DTIC Identifier(s): Flight control systems, control theory, computer files, theses, input output processing, F-18 aircraft. Author(s) subject terms: Modern control theory, H infinity control theory, H2 control theory, multivariable robustness, F-18 control design or synthesis, super augmented aircraft. Includes bibliographical references (p. 110). Also available in print.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2003. / On t.p. "[infinity]" appears as the infinity symbol. Includes bibliographical references (leaves 88-92). Also available in electronic version. Access restricted to campus users.

Includes bibliographical references (p. 121-124).