1,310 research outputs found
Stabilisation and control design by partial output feedback and by partial interconnection
No full textWe study stabilisation and control design by partial output feedback on the one hand and by partial interconnection according to Willems on the other hand. This article is based on the paper Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules by I. Blumthaler and U. Oberst, and the same technique is used. Both discrete and continuous behaviours and various notions of stability are treated simultaneously. In the case of partial output feedback, we require that both the compensator and the feedback behaviour have proper transfer matrices without presuming properness of the plant. We obtain conditions ensuring the existence of such stabilising compensators which perform additional control tasks like, for instance, tracking, and an algorithm for constructing a large class of such compensators. In the case of stabilisation by interconnection no input–output structures of plant or compensator are assumed, but the controlled behaviour is endowed with a canonical input–output structure. Again we demand this input–output behaviour to have proper transfer matrix. For this situation we obtain necessary and sufficient conditions for the existence of compensators solving the given control task, and a constructive parametrisation of all of them
A new parametrization of observers
No full textThis paper extends and generalizes recent results on the characterization and parametrization of observers for linear systems in the behavioral framework. We formulate the results in the language of quotient signal modules that was developed by Oberst and first used in the context of observer theory by the first author. The resulting characterization of observers in terms of a generalized internal model principle is both elegant and concise. It includes all such results known to the authors as special cases, including the classical results for linear time-invariant state space systems. Moreover, this new characterization of observers leads to a clean and simple one-to-one parametrization result with only free parameters. This new parametrization allows to decide certain additional observer properties (such as input/output structure or nonintrusiveness) purely by inspection
Stabilization and control design by partial output feedback
No full textWe consider a (not necessarily proper) plant input/output behavior which shall be stabilized by a proper controller via partial output feedback such that also the feedback behavior is a proper input/output behavior. In addition a control task like tracking or disturbance rejection shall be performed. The setting includes both the continuous and the discrete time case, and stability is defined with respect to a set T of stable polynomials. The standard choice for T yields asymptotic stability.
Our approach relies on the fact that the signal module is an injective cogenerator over the ring of operators and this property is preserved under localization with respect to the set T.
We present a condition ensuring the existence of proper compensators such that the feedback behavior is proper and stable and such that the given control task is performed. If this condition is satisfied we construct a large class of such compensators
Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules
No full textControl design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks, the systems being generally described by their transfer matrices or by Rosenbrock equations and more recently also as behaviors. Our approach to controller design uses, in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators, a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature: (1) We use an injective cogenerator signal module FF over the polynomial algebra D=F[s]D=F[s] (F an infinite field), a saturated multiplicatively closed set T of stable polynomials and its quotient ring DTDT of stable rational functions. This enables the simultaneous treatment of continuous and discrete systems and of all notions of stability, called T -stability. We investigate stabilizing control design by output feedback of input/output (IO) behaviors and study the full feedback IO behavior, especially its autonomous part and not only its transfer matrix. (2) The new technique is characterized by the permanent application of the injective cogenerator quotient signal module DTFTDTFT and of quotient behaviors BTBT of DFDF-behaviors BB. (3) For the control tasks of tracking, disturbance rejection, model matching, and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors, parametrize all such compensators as IO behaviors and not only their transfer matrices and give new algorithms for their construction. Moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior. The properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case, and that of the compensator enables its realization by Kalman state space equations or elementary building blocks. We note that every behavior admits an IO decomposition with proper transfer matrix, but that most of these decompositions do not have this property, and therefore we do not assume the properness of the plant. (4) The new technique can also be applied to more general control interconnections according to Willems, in particular to two-parameter feedback compensators and to the recent tracking framework of Fiaz/Takaba/Trentelman. In contrast to these authors, however, we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms
The consensus problem in the behavioral approach
No full textIn this paper we investigate the multi-agent consensus problem in a broad context, by assuming both for
the agents and for the distributed controllers higher order input–output dynamic models.
The behavioral approach developed by Jan Willems seems to be the most appropriate set-up where to
investigate this general problem.
By making use of the behavioral approach, we will show that the consensus problem can be naturally
rephrased as a special case of stabilization problem: the stabilization pertains only a part of the system
variables (the outputs) and it is achieved through regular full interconnection of the agent models and
of the controllers. It turns out that if the communication among agents is described by a weighted,
undirected and connected graph, then a necessary and sufficient condition for the consensus problem to
be solvable is that the output is stabilizable from the input in the agents model. In this respect, the theory
here developed for higher-order input–output models naturally extends the results about consensus
derived in the state-space approach
A generalized tracking and disturbance rejection problem for multidimensional behaviors
No full textIn this paper we study a generalized tracking and disturbance rejection problem for multidimensional behaviors. Given a multidimensional plant, our first goal is to design a compensator to be connected to the plant through regular partial interconnection, in such a way that the overall controlled system is autonomous and stable, when no exogenous signal acts on the system. On the other hand, when exogenous signals affect the controlled system evolution, we want to impose that a suitable linear combination of the overall system trajectories is "negligibile" in a sense we will clarify within the paper. This problem setup formalizes a number of classical control problems, first of all tracking of some (reference) signal together with rejection of another (disturbance) signal. The adopted approach is extremely general and it is based on the idea of describing all behavior trajectories as the sum of a "transient signal" and a "steady state" component, a decomposition that relies on Gabriel's localization theory. Necessary and sufficient conditions for the problem solvability are provided, and the compensators that satisfy the control goal are characterized in terms of an internal model condition. Furthermore, a parameterization of all such compensators is provided
Control Design Problems for Multidimensional Behaviours
No full textIn this paper we study a generalized tracking
and disturbance rejection problem for multidimensional linear
behaviours. Given a multidimensional plant, our first goal is
to design a compensator to be connected to the plant through
regular partial interconnection, in such a way that the overall
controlled system is autonomous and stable, when no exogenous
signal acts on the system. On the other hand, when exogenous
signals affect the controlled system evolution, we want to
impose that a suitable linear combination of the overall system
trajectories is “negligibile” in a sense we will clarify within the
paper. This problem set-up formalizes a number of classical
control problems, first of all tracking of some (reference)
signal together with rejection of another (disturbance) signal.
The adopted approach is extremely general and it is based
on the idea of describing all behaviour trajectories as the
sum of a “transient signal” and a “steady state” component,
a decomposition that relies on Gabriel’s localization theory.
Necessary and sufficient conditions for the problem solvability
are provided, and the compensators that satisfy the control goal
are characterized in terms of an internal model condition
The consensus problem in the behavioral approach
No full textIn this paper we present some preliminary results about the consensus problem in the behavioral approach. Specifically, we consider a group of N homogeneous agents whose dynamics are described by the same (linear and time-invariant) behavioral model, involving inputs, measurable variables and target variables. We assume that the agents' mutual communication is described by some (not necessarily symmetric) adjacency matrix. In this set-up we have derived necessary and sufficient conditions for a group of homogenous dynamic controllers, making use of the weighted information received by each agent about the other agents' dynamics, for the N agents to achieve consensus on the target variables dynamics (under regularity constraints on the overall interconnection). Such conditions have been extended to the case when consensus is searched for both the target and the measurable variables. Finally, it is shown that the paper results encompass, as a special case, the classical situation when the agents' dynamics are described by state-space models and the target (measurable) variables are the state (output) variables
Ingrid Ylva och tornet i Bjälbo
No full textThe article discusses the background to the erection of the huge church tower in Bjälbo, Östergötland, Sweden. It also focuses on medieval women as founders of churches. The author maintains that new dendrochronological dating of the tower could mean that founder of this building piece was not one of the male members of the important Bjälbo dynasty, but Ingrid Ylva the mother of Birger Jarl
Ingrid Winterbach: Novelist (Interview)
No full textWinner of the prestigious Hertzog Prize for Literature for Niggie (2002)Ingrid Winterbach is the author of eight novels, three of which have been translated into English and two into Dutch. The translation of her fourth novel, Karolina Ferreira (1993) as The Elusive Moth (2005), and subsequently, Niggie as To Hell with Cronjé (2007) and Die boek van toeval en toeverlaat (2006) as The Book of Happenstance (2008), have brought this author to the attention of a wider South African readership
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