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检索条件"主题词=distributed parameter systems"

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Robust stability of the time varying singular distributed parameter system in hilbert space

Robust stability of the time varying singular distributed pa...

引用

Chinese Control Conference (CCC)

作者： Zhaoqiang Ge Xi'an Jiaotong University Xi'an Shaanxi CN

Perturbation and robust exponential stability of the time varying singular distributed parameter system are discussed via functional analysis and operator theory in Hilbert space. The perturbation principle of generalized evolution operators and the sufficient condition concerning the robust exponential stability of the time varying singular distributed parameter system are obtained, in which the exponential stability for the time varying singular distributed parameter system is not destroyed, if we perturb the equation by linear operator. The perturbation are assumed to have unbounded structure and the smallest perturbation which destroys exponential stability is determined.

关键词： distributed parameter systems Time-varying systems Hilbert space Control theory Robustness Robust stability

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Optimization of spatially distributed systems with spatially local controllers and partial connectivity 53

Optimization of spatially distributed systems with spatially...

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53rd IEEE Annual Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781467360906

This paper presents two different design approaches of networked distributed controllers for a class of partial differential equations. Such a work attempts to reduce controller complexity by opting to control a spatially distributed process by a network of interconnected control units. This approach reduces the need to use a centralized controller that must fuse sensory information by the distributed sensors and then dispense the controllers to the spatially distributed process via the spatially distributed actuators. In the first approach, the controller gains used to implement the local controllers by the controller units, along with the actuator and sensor location and the network connectivity are optimized by formulating the optimization problem into a minimization problem of an appropriately chosen performance measure of the closed-loop system. This takes the form of a parameterized operator Lyapunov equation whose optimal solution provides the optimal (proportional) controller gains, the optimal locations of the actuators and sensors, and the optimal network connectivity. The second approach considers the adaptation of the gains of the distributed controllers using Lyapunov-redesign methods to extract their adaptation. The well-posedness and convergence properties of the proposed controllers are summarized and numerical studies examining various aspects of the proposed work are presented.

关键词： distributed parameter systems distributed local controllers networked systems gain adaptation

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LMI parametrization of Lyapunov Functions for Infinite-Dimensional systems: A Framework

LMI parametrization of Lyapunov Functions for Infinite-Dimen...

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American Control Conference

作者： Peet, Matthew M. Arizona State Univ Sch Matter Transport & Energy Tempe AZ 85287 USA

ISBN: (纸本)9781479932740

In this paper, we present an algorithmic approach to the construction of Lyapunov functions for infinite-dimensional systems. This paper unifies and significantly extends many previous results which have appeared in conference and journal format. The unifying principle is that any linear parametrization of operators in Hilbert space can be used to construct an LMI parametrization of positive operators via squared representations. For linear systems, we get positive linear operators and hence quadratic Lyapunov functions. For nonlinear systems, we get nonlinear operators and hence non-quadratic Lyapunov functions. Special cases of these results include positive operators defined by multipliers and kernels which are: polynomial;piecewise-polynomial;or semi-separable and apply to systems with delay;multiple spatial domains;or mixed boundary conditions. We also introduce a set of efficient software tools for creating these functionals. Finally, we illustrate the approach with numerical examples.

关键词： Delays Hilbert space Kernel Lyapunov methods Polynomials Vectors Delay systems distributed parameter systems LMIs

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Guidance of a moving sensor used in state estimation of a flexible beam 53

Guidance of a moving sensor used in state estimation of a fl...

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53rd IEEE Annual Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781467360906

In certain applications involving structural systems, the use of multiple high end sensors may prove to be prohibitive. The alternative would be to use fewer, or even a single sensing device that is capable of moving across the span of the structural system. In this work, a one dimensional flexible beam, described by an Euler-Bernoulli partial differential equation is considered. It is assumed that a velocity sensor obtaining pointwise (in space) velocity measurements is capable of moving across the beam. A Luenberger observer whose filter gain is expressed as a function of the moving sensor location is proposed. Using Lyapunov redesign methods, similar to those employed in adaptive systems, the guidance of the moving sensor is obtained and which solely depends on the state estimation error at the current sensor position. The guidance policy is performance-based and steers the sensor to spatial regions with larger estimation errors. Extensions of the proposed guidance laws take into account the motion dynamics of a mobile sensor. Extensive numerical studies examine the feasibility of a mobile sensor used for the improved state estimation of a flexible beam.

关键词： distributed parameter systems state observers second order systems mobile sensor

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Sliding Mode Boundary Control for an Euler-Bernoulli Beam with Boundary Disturbances and parameter Variations

Sliding Mode Boundary Control for an Euler-Bernoulli Beam wi...

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American Control Conference

作者： Karagiannis, Dimitri Radisavlejevic-Gajic, Verica Villanova Univ Dept Mech Engn Ctr Nonlinear Dynam & Control CENDAC Villanova PA 19085 USA

ISBN: (纸本)9781479932740

This work addresses the problem of stability and control of an Euler-Bernoulli beam with sliding-pinned boundary conditions. The control comes in the form of an applied displacement and bending moment on the pinned end. The proposed controller accounts for bounded exogenous disturbances on the pinned end boundary conditions, representing a number of possible practical issues such as model parameter uncertainties or unknown external forces. This controller takes advantage of a technique for stabilizing an Euler-Bernoulli beam through a Schrodinger equation representation and a previously developed integral transformation which provides the opportunity to select arbitrary damping for the system. The contribution of this work is to introduce unknown boundary disturbances into the system boundary terms and the development of a Sliding Mode Controller which effectively drives the system states to an exponentially stable infinite-dimensional sliding surface which then eliminates the system vibration with arbitrary damping. The resulting control efforts developed are continuous functions and therefore do not create a chattering effect on control actuators.

关键词： Boundary conditions Equations Integral equations Kernel Mathematical model Transforms Uncertainty distributed parameter systems Flexible structures Variable-structure/sliding-mode control

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Fault Detection and Isolation of Fornasini-Marchesini 2D systems: A Geometric Approach

Fault Detection and Isolation of Fornasini-Marchesini 2D Sys...

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American Control Conference

作者： Baniamerian, Amir Meskin, Nader Khorasani, Khashayar Concordia Univ Dept Elect & Comp Engn Quebec City PQ Canada

ISBN: (纸本)9781479932740

The fault detection and isolation (FDI) problem for discrete-time two-dimensional (2D) systems represented by the Fornasini-Marchesini model II is investigated in this work. It is shown that the sufficient conditions for solvability of the FDI problem that we have developed recently for the Roesser model is also applicable to this class of 2D systems. In this paper, we are mainly concerned with the necessary conditions. Two sets of necessary conditions for the solvability of the FDI problem are derived. The first necessary condition involves a new set of invariant subspaces that has no one-dimensional (1D) equivalency. The second set which is consistent with its equivalent 1D case is derived, generically (from the algebraic geometry point of view). A numerical example is also provided to illustrate the application of the results.

关键词： Computational modeling Equations Fault detection Geometry Mathematical model Three-dimensional displays Vectors distributed parameter systems Fault detection/accomodation

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A dynamic state observer for real-time reconstruction of the tokamak plasma profile state and disturbances

A dynamic state observer for real-time reconstruction of the...

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American Control Conference

作者： Felici, Federico de Baar, Marco Steinbuch, Maarten Eindhoven Univ Technol Fac Mech Engn Control Syst Technol Grp NL-5600 MB Eindhoven Netherlands

ISBN: (纸本)9781479932740

A dynamic observer is presented which can reconstruct the internal state of a tokamak fusion plasma, consisting of the spatial distribution of current and temperature, from measurements. Today, the internal plasma state is usually reconstructed by solving an ill-conditioned inversion problem using a large number of measurements at one point in time. Such an approach does not take into account the time evolution of the underlying dynamical system (the plasma) and strongly relies on (technically challenging) internal measurements. The observer-based approach presented here includes the dynamics of the plasma current and temperature, modeled by a set of coupled nonlinear 1-D PDEs which are discretized in space and time to yield a finite-dimensional nonlinear model. The observer, which is based on an Extended Kalman Filter, estimates the state of an augmented model which includes additive state disturbances modeled as a random walk. Simulation results demonstrate the effectiveness of this observer in the case of perturbed models and input disturbances.

关键词： Covariance matrices Current measurement Mathematical model Plasma measurements Temperature measurement Tokamaks distributed parameter systems Kalman filtering Observers for nonlinear systems

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Application of Enthalpy-Based Feedback Control Methodology to the Two-Sided Stefan Problem

Application of Enthalpy-Based Feedback Control Methodology t...

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American Control Conference

作者： Petrus, Bryan Bentsman, Joseph Thomas, Brian G. Univ Illinois Dept Mech Sci & Engn Champaign IL 61820 USA

ISBN: (纸本)9781479932740

In [1], the authors introduced a novel control law for the single-phase Stefan problem, a nonlinear partial differential equation, with the eventual goal of applying the result to control of cooling in continuous steel casting. In this paper, the previously published method of controlling the Stefan problem is extended in two key ways that improve the fidelity of the nonlinear PDE as a model of the temperature and solidification of continuous steel casters. First, a non-symmetric temperature distribution is allowed, in which separate Neumann boundary control is applied at either surface. Two convergent control laws are compared in simulation, with one converging significantly faster. Second, saturation of the Neumann boundary control input is considered. Saturation is a significant concern in the actual process. The enthalpy-based algorithm still allows for convergence under saturation. However, as one would expect, severity of the constraints can affect the convergence rate.

关键词： Casting Convergence Liquids Process control Solid modeling Steel Temperature control distributed parameter systems Materials processing

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Adaptive Output Feedback for Oil Drilling Stick-Slip Instability Modeled by Wave PDE with Anti-damped Dynamic Boundary

Adaptive Output Feedback for Oil Drilling Stick-Slip Instabi...

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American Control Conference

作者： Bresch-Pietri, Delphine Krstic, Miroslav MIT Dept Mech Engn Cambridge MA 02139 USA

ISBN: (纸本)9781479932740

We develop an adaptive output-feedback controller for a wave PDE in one dimension with actuation on one boundary and with an unknown anti-damping dynamics on the opposite boundary. This model is representative of drill string torsional instabilities arising in deep oil drilling, for which the model of bottom interaction with the rock is poorly known. The key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system. Our approach is based on employing Riemann variables to convert the wave PDE into a cascade of two delay elements, with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ODE. This enables us to employ a prediction-based design for systems with input delays, suitably converted to the adaptive output-feedback setting. The result's relevance and ability to suppress undesirable torsional vibrations of the drill string in oil well drilling systems is illustrated with simulation example.

关键词： Adaptation models Delays Equations Friction Mathematical model Rocks Torque distributed parameter systems Indirect adaptive control Process control

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Synchronization optimization of networked second order infinite dimensional systems 53

Synchronization optimization of networked second order infin...

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53rd IEEE Annual Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. Fahroo, Fariba Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA AFOSR RTA Computat Math Arlington VA 22203 USA

ISBN: (纸本)9781467360906

We consider optimization aspects for the synchronization control of networked second order infinite dimensional systems. It is assumed that a number of identical such systems are desired to be synchronized and using output feedback controllers, the resulting coupled systems are brought in an aggregate form in order to optimize the synchronization gains. Using a closed-loop energy as the optimization metric, the choice of the synchronization gains reduces to the minimization of the optimization index. This eventually is described by the trace of the solution to a parameterized Lyapunov operator equation. Numerical studies on a network of four one-dimensional cantilevered beams provide insight on the optimization of the proposed synchronization control.

关键词： distributed parameter systems flexible structures second order systems synchronization

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