1,286 research outputs found
Quantum Internal Model Principle: Decoherence Control
In this article, we study the problem of designing a Decoherence Control for
quantum systems with the help of a scalable ancillary quantum control and
techniques from geometric control theory, in order to successfully and
completely decouple an open quantum system from its environment. We
re-formulate the problem of decoherence control as a disturbance rejection
scheme which also leads us to the idea of Internal Model Principle for quantum
control systems which is first of its kind in the literature.
It is shown that decoupling a quantum disturbance from an open quantum
system, is possible only with the help of a quantum controller which takes into
account the model of the environmental interaction. This is demonstrated for a
simple 2-qubit system wherein the effects of decoherence are completely
eliminated. The theory provides conditions to be imposed on the controller to
ensure perfect decoupling. Hence the problem of decoherence control naturally
gives rise to the quantum internal model principle which relates the
disturbance rejecting control to the model of the environmental interaction.
Classical internal model principle and disturbance decoupling focus on
different aspects viz. perfect output tracking and complete decoupling of
output from external disturbances respectively. However for quantum systems,
the two problems come together and merge in order to produce an effective
platform for decoherence control. In this article we introduce a seminal
connection between disturbance decoupling and the corresponding analog for
internal model principle for quantum systems.Comment: Submitted to IEEE Transactions on Automatic Control, Mar 15 2010. A
basic introduction appeared in 46th IEEE CDC 2007. Acknowledgements: The
authors would like to thank the Center for Quantum Information Science and
Technology at Tsinghua University, R.-B. Wu, J. Zhang, J.-W. Wu, M. Jiang,
C.-W. Li and G.-L. Long for their valuable comments and suggestion
The Internal Model Principle for Systems with Unbounded Control and Observation
In this paper the theory of robust output regulation of distributed parameter
systems with infinite-dimensional exosystems is extended for plants with
unbounded control and observation. As the main result, we present the internal
model principle for linear infinite-dimensional systems with unbounded input
and output operators. We do this for two different definitions of an internal
model found in the literature, namely, the p-copy internal model and the
-conditions. We also introduce a new way of defining an internal
model for infinite-dimensional systems. The theoretic results are illustrated
with an example where we consider robust output tracking for a one-dimensional
heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie
A fractional representation approach to the robust regulation problem for SISO systems
The purpose of this article is to develop a new approach to the robust
regulation problem for plants which do not necessarily admit coprime
factorizations. The approach is purely algebraic and allows us dealing with a
very general class of systems in a unique simple framework. We formulate the
famous internal model principle in a form suitable for plants defined by
fractional representations which are not necessarily coprime factorizations. By
using the internal model principle, we are able to give necessary and
sufficient solvability conditions for the robust regulation problem and to
parameterize all robustly regulating controllers.Comment: 13 pages, 1 figure, to appear in Systems & Control Letter
Advances In Internal Model Principle Control Theory
In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability.
The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes.
A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers
Approximate robust output regulation of boundary control systems
We extend the internal model principle for systems with boundary control and
boundary observation, and construct a robust controller for this class of
systems. However, as a consequence of the internal model principle, any robust
controller for a plant with infinite-dimensional output space necessarily has
infinite-dimensional state space. We proceed to formulate the approximate
robust output regulation problem and present a finite-dimensional controller
structure to solve it. Our main motivating example is a wave equation on a
bounded multidimensional spatial domain with force control and velocity
observation at the boundary. In order to illustrate the theoretical results, we
construct an approximate robust controller for the wave equation on an annular
domain and demonstrate its performance with numerical simulations.Comment: 29 pages, 4 figure
Demonstration of the Internal Model Principle by Digital
A key topic in classical control theory is the Internal Model Principle (IMP). A particular case of the IMP for tracking periodic references or attenuating periodic disturbances in closed-loop control systems is a technique called repetitive control. This work proposes and describes an educational laboratory plant to show the students the advantages of repetitive controllers in systems with periodic references or disturbances. The plant has been designed to be low cost, easy to build, and subject to periodic disturbances with a clear physical explanation. More specifically, it consists of a pulsewidth modulation (PWM) electronic amplifier, a small dc motor, and a magnetic setup that generates a periodic load torque under constant mechanical speed operation. The control objective for the closed-loop control system is to regulate the mechanical speed to a constant value in spite of the periodic load torque disturbance. In order to accomplish this performance specification, a detailed design of a digital repetitive controller is presented, and some basic experimental results are provided to prove its good behavior. The paper also includes some repetitive control concepts and facts that teaching experience shows as essential to understand the design process.Peer Reviewe
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