689 research outputs found
The application of Discrete sliding mode control in parabolic PDE dynamics
In this paper, the problem of applying Discrete Sliding Mode Control (DSMC) on spatially finite-dimensional systems arising from discretization of bi-variate Partial Differential Equations (PDEs) describing spatio-temporal systems is studied. To this end, heat transfer PDE is discretized to create 2D discrete dynamics and eventually this 2D spatiotemporal discrete form is represented in 1D vectorial form. In order to study the effect of discrepancy between original PDE dynamics and their discrete schemes, an uncertainty term is also considered for the obtained discrete dynamics. According to the notion of strong stability and, in addition, using scaling matrices (similarity transformation), a new method for considering the stability of discrete-time systems in the presence of general uncertainty term (matched and unmatched) is developed. It is also shown that the proposed method in this paper can be used for the case with spatial constraints on the actuation. Consequently, as special cases, the problem of spatially piece-wise constant, sparse and also boundary control input are studied. © 2013 Engineers Australia
Sliding mode control for a nonlinear phase-field system
In the present contribution the sliding mode control (SMC) problem for a
phase-field model of Caginalp type is considered. First we prove the
well-posedness and some regularity results for the phase-field type state
systems modified by the state-feedback control laws. Then, we show that the
chosen SMC laws force the system to reach within finite time the sliding
manifold (that we chose in order that one of the physical variables or a
combination of them remains constant in time). We study three different types
of feedback control laws: the first one appears in the internal energy balance
and forces a linear combination of the temperature and the phase to reach a
given (space dependent) value, while the second and third ones are added in the
phase relation and lead the phase onto a prescribed target. While the control
law is non-local in space for the first two problems, it is local in the third
one, i.e., its value at any point and any time just depends on the value of the
state.Comment: Key words: phase field system, nonlinear boundary value problems,
phase transition, sliding mode control, state-feedback control la
A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
In this paper, we consider input-output properties of linear systems
consisting of PDEs on a finite domain coupled with ODEs through the boundary
conditions of the PDE. This framework can be used to represent e.g. a lumped
mass fixed to a beam or a system with delay. This work generalizes the
sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a
recently developed concept of fundamental state and the associated
boundary-condition-free representation. The conditions of the generalized KYP
are tested using the PQRS positive matrix parameterization of operators
resulting in a finite-dimensional LMI, feasibility of which implies prima facie
provable passivity or L2-gain of the system. No discretization or approximation
is involved at any step and we use numerical examples to demonstrate that the
bounds obtained are not conservative in any significant sense and that
computational complexity is lower than existing methods involving
finite-dimensional projection of PDEs
Challenges in Optimal Control of Nonlinear PDE-Systems
The workshop focussed on various aspects of optimal control problems for systems of nonlinear partial differential equations. In particular, discussions around keynote presentations in the areas of optimal control of nonlinear/non-smooth systems, optimal control of systems involving nonlocal operators, shape and topology optimization, feedback control and stabilization, sparse control, and associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, also aspects of control of fluid structure interaction problems as well as problems arising in the optimal control of quantum systems were considered
Sliding Mode Observers for Distributed Parameter Systems: Theory and Applications
Many processes in nature and industry can be described by partial differential equations. PDEs employ quantities such as density, temperature, velocity, etc. and their partial derivatives to model these phenomena. However, in the case of distributed parameter systems, it is not always possible to have access to the states of the systems due to technical difficulties such as lack of sensors. Therefore, there is the need for state observers to estimate the states of the system only having the output of the system available. In this research, the theory of sliding mode and variable structure systems are employed in order to design observers for different classes of distributed parameter systems such as advection equation, Burgers’ equation, Euler equations, etc. Some contributions of this research are: suggesting the state transformation which allows the arbitrary design of sliding manifold in sliding mode observer, developing some formulae for observer gain, discussing the shock wave situation and its properties and solutions, designing sliding mode observer and anomaly detection system for a system of advection equations
Robust stabilization of the current profile in tokamak plasmas using sliding mode approach in infinite dimension
International audienceThis paper deals with the robust stabilization of the spatial distribution of tokamak plasmas current profile using a sliding mode feedback control approach. The control design is based on the 1D resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretization. Numerical simulations are provided and the tuning of the controller parameters that would reject uncertain perturbations is discussed. Closed loop simulations performed on realistic test cases using aphysics based tokamak integrated simulator confirm the relevance of the proposed control algorithm in view of practical implementation
Observer design for multivariable transport-reaction systems based on spatially distributed measurements
This paper is concerned with the design of observers for a class of one-dimensional multi-state
transport-reaction systems considering distributed in-domain measurements over the spatial domain.
A design based on the Lyapunov method is proposed for the stabilization of the estimation error
dynamics. The approach uses positive definite matrices to parameterize a class of Lyapunov functionals
that are positive in the Lebesgue space of integrable square functions. Thus, the stability conditions can
be expressed as a set of LMI constraints which can be solved numerically using sum of squares (SOS)
and standard semi-definite programming (SDP) tools. In order to evaluate the proposed methodology,
a state observer is designed to estimate the variables of a nonisothermal tubular reactor model.
Numerical simulations are presented to demonstrate the potentials of the proposed observer.Campus Arequip
Sliding modes for a phase-field system
In the present contribution the sliding mode control (SMC) problem for a phase-field model
of Caginalp type is considered. First we prove the well-posedness and
some regularity results for the phase-field type state systems modified by the state-
feedback control laws. Then, we show that the chosen SMC laws force the system to
reach within finite time the sliding manifold (that we chose in order that one of the
physical variables or a combination of them remains constant in time). We study
three different types of feedback control laws: the first one appears in the internal
energy balance and forces a linear combination of the temperature and the phase to
reach a given (space dependent) value, while the second and third ones are added
in the phase relation and lead the phase onto a prescribed target ~. While the
control law is non-local in space for the first two problems, it is local in the third
one, i.e., its value at any point and any time just depends on the value of the state
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