Lassi Paunonen

Internal Model Theory for Distributed Parameter Systems

In this paper we consider robust output regulation of distributed parameter systems and the internal model principle. The main purpose is to generalize the internal model principle by Francis and Wonham for infinite-dimensional systems and clarify the relationships between different generalizations of the internal model. We also construct a signal generator capable of generating infinite-dimensional polynomially increasing signals.

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

Reduced Order Internal Models in Robust Output Regulation

p

Designing Controllers With Reduced Order Internal Models

-copy internal model and the

Controller Design for Robust Output Regulation of Regular Linear Systems

\mathcal{G}

Perturbation of strongly and polynomially stable Riesz-spectral operators

-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.

Optimal energy decay in a one-dimensional coupled wave–heat system

In this paper, we consider robust output regulation and the internal model principle for infinite-dimensional linear systems. We concentrate on a problem where the control law is required to be robust with respect to a restricted class of perturbations. We show that depending on the class of admissible perturbations, it is often possible to construct a robust controller with a smaller internal model than the one given by the internal model principle. In addition, we also look for minimal classes of perturbations that make the full internal model necessary. We introduce a straightforward way of testing for robustness of the control law for a given set of perturbations. The test in particular shows that the robustness is only dependent on the way the perturbations affect the transfer function of the plant at the frequencies of the exosystem. The theoretic results are applied to designing controllers for a one-dimensional wave equation and for a system consisting of three independent shock absorber models.

Output regulation theory for distributed parameter systems with unbounded control and observation

In this technical note we study robust output tracking for autonomous linear systems. We introduce a new approach to designing robust controllers using a recent observation that a full internal model is not always necessary for robustness. Especially this may be the case if the control law is only required to be robust with respect to a specific predetermined class of uncertainties in the parameters of the plant. The results are illustrated with an example on robust output tracking for coupled harmonic oscillators.

Robustness of polynomial stability with respect to unbounded perturbations

We present three dynamic error feedback controllers for robust output regulation of regular linear systems. These controllers are i) a minimal order robust controller for exponentially stable systems, ii) an observer-based robust controller, and iii) a new internal model based robust controller structure. In addition, we present two controllers that are by construction robust with respect to predefined classes of perturbations. The results are illustrated with an example where we study robust output tracking of a sinusoidal reference signal for a 2-D heat equation with boundary control and observation.

Periodic output regulation for distributed parameter systems

Abstract In this paper we consider bounded and relatively bounded finite rank perturbations of a Riesz-spectral operator generating a polynomially stable semigroup of linear operators on a Hilbert space. We concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half-plane of the complex plane and approaches the imaginary axis asymptotically. We present conditions on the perturbing operator such that the spectrum of the perturbed operator is contained in the open left half-plane of the complex plane and additional conditions for the strong and polynomial stabilities of the perturbed semigroup. We consider two applications of the perturbation results. In the first example we apply the results to the perturbation of a polynomially stabilized one-dimensional wave equation. In the second example we consider the perturbation of a closed-loop system consisting of a distributed parameter system and an observer-based feedback controller solving the robust output regulation problem related to an infinite-dimensional signal generator.