Optimal Universal Controllers for Roll Stabilization

Roll stabilization is an important problem of ship motion control. This problem becomes especially difficult if the same set of actuators (e.g. a single rudder) has to be used for roll stabilization and heading control of the vessel, so that the roll stabilizing system interferes with the ship autopilot. Finding the "trade-off" between the concurrent goals of accurate vessel steering and roll stabilization usually reduces to an optimization problem, which has to be solved in presence of an unknown wave disturbance. Standard approaches to this problem (loop-shaping, LQG, $H_{\infty}$-control etc.) require to know the spectral density of the disturbance, considered to be a \colored noise". In this paper, we propose a novel approach to optimal roll stabilization, approximating the disturbance by a polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic optimization problems in presence of polyharmonic disturbances can be solved by means of the theory of universal controllers developed by V.A. Yakubovich. An optimal universal controller delivers the optimal solution for any uncertain amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that provides a realistic vessel's model, we compare our design method with classical approaches to optimal roll stabilization. Among three controllers providing the same quality of yaw steering, OUC stabilizes the roll motion most efficiently

Boundary second-order sliding-mode control of an uncertain heat process with unbounded matched perturbation

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Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

Observation and control of PDE with disturbances

In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties

Observation and control of PDE with disturbances

In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Robust H

This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Stability analysis of coupled ordinary differential systems with a string equation: application to a drilling mechanism

Cette thèse porte sur l'analyse de stabilité de couplage entre deux systèmes, l'un de dimension finie et l'autre infinie. Ce type de systèmes apparait en physique car il est intimement lié aux modèles de structures. L'analyse générique de tels systèmes est complexe à cause des natures très différentes de chacun des sous-systèmes. Ici, l'analyse est conduite en utilisant deux méthodologies. Tout d'abord, la séparation quadratique est utilisée pour traiter le côté fréquentiel de ce système couplé. L'autre méthode est basée sur la théorie de Lyapunov pour prouver la stabilité asymptotique de l'interconnexion. Tous ces résultats sont obtenus en utilisant la méthode de projection de l'état de dimension infinie sur une base polynomiale. Il est alors possible de prendre en compte le couplage entre les deux systèmes et ainsi d'obtenir des tests numériques fiables, rapides et peu conservatifs. De plus, une hiérarchie de conditions est établie dans le cas de Lyapunov. L'application au cas concret du forage pétrolier est proposée pour illustrer l'efficacité de la méthode et les nouvelles perspectives qu'elle offre. Par exemple, en utilisant la notion de stabilité pratique, nous avons montré qu'une tige de forage controlée à l'aide d'un PI est sujette à un cycle limite et qu'il est possible d'estimer son amplitude.This thesis is about the stability analysis of a coupled finite dimensional system and an infinite dimensional one. This kind of systems emerges in the physics since it is related to the modeling of structures for instance. The generic analysis of such systems is complex, mainly because of their different nature. Here, the analysis is conducted using different methodologies. First, the recent Quadratic Separation framework is used to deal with the frequency aspect of such systems. Then, a second result is derived using a Lyapunov-based argument. All the results are obtained considering the projections of the infinite dimensional state on a basis of polynomials. It is then possible to take into account the coupling between the two systems. That results in tractable and reliable numerical tests with a moderate conservatism. Moreover, a hierarchy on the stability conditions is shown in the Lyapunov case. The real application to a drilling mechanism is proposed to illustrate the efficiency of the method and it opens new perspectives. For instance, using the notion of practical stability, we show that a PI-controlled drillstring is subject to a limit cycle and that it is possible to estimate its amplitude