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1
Content available A new procedure for the design of iterative learning controllers using a 2D systems formulation of processes with uncertain spatio-temporal dynamics
Cichy B., Gałkowski K., Dąbkowski K., Aschemann H., Rauh A.
Control and Cybernetics
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2013
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Vol. 42, no. 1
9--26
EN
Iterative Learning Control (ILC) is well established in control of linear and nonlinear dynamic systems, both as to underlying theory and experimental validation. This approach specifically aims at applications with the same operation repeated over finite time intervals and reset taking place between subsequent executions (the trials). The main principle behind ILC is to suitably use information from previous trials in selection of the input signal in the current trial with the objective of performance improvement from trial to trial. In this paper, new computationally efficient results are presented for an extension of the ILC approach to the uncertain 2D systems that arise from time and space discretization of partial differential equations. This type of application implies the need to use a spatio–temporal setting for the analysis of the control procedure. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). An illustrative example is provided.
2
Content available Particle swarm optimization of an iterative learning controller for the single-phase inverter with sinusoidal output voltage waveform
Ufnalski B., Grzesiak L. M., Gałkowski K.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2013
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Vol. 61, nr 3
649--660
EN
This paper presents the application of a particle swarm optimization (PSO) to determine iterative learning control (ILC) law gains for an inverter with an LC output filter. Available analytical tuning methods derived for a given type of ILC law are not very straightforward if additional performance requirements of the closed-loop system have to be met. These requirements usually concern the dynamics of a response to a reference signal, the dynamics of a disturbance rejection, the immunity against expected level of system and measurement noise, the robustness to anticipated variations of parameters, etc. An evolutionary optimization approach based on the swarm intelligence is proposed here. It is shown that in the case of the ILC applied to the LC filter, a cost function based on mean squares can produce satisfactory tuning effects. The efficacy of the procedure is illustrated by performing the optimization for various noise levels and various requested dynamics.
3
Content available Robust control of distributed parameter mechanical systems using a multidimensional systems approach
Cichy B., Augusta P., Rogers E., Gałkowski K., Hurak Z.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2010
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Vol. 58, nr 1
67-75
EN
The unique characteristic of a repetitive processes is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration. On each pass an output, termed the pass profile is produced which acts as on forcing function, and hence contributes to, the dynamics of the next pass profile. This leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations that increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by application of standard linear systems control laws and instead they must be treated as two-dimensional (2D) systems where information propagation in two independent directions, termed passto-pass and along the pass respectively, is the defining feature. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control law design algorithms are developed for discrete linear repetitive processes where a plane, or rectangle, of information is propagated in the pass-to-pass direction. The possible use of such a model in the control of distributed parameter systems has been investigated in previous work and this paper considers an extension to allow for uncertainty in the model description.
4
Content available remote On the development of SCILAB compatible software for the analysis and control of repetitive processes
Hładowski Ł., Cichy B., Gałkowski K., Rogers E.
International Journal of Applied Mathematics and Computer Science
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2008
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Vol. 18, no. 3
377-387
EN
In this paper further results on the development of a SCILAB compatible software package for the analysis and control of repetitive processes is described. The core of the package consists of a simulation tool which enables the user to inspect the response of a given example to an input, design a control law for stability and/or performance, and also simulate the response of a controlled process to a specified reference signal.
5
Content available remote Robust stabilization of discrete linear repetitive processes with switched dynamics
Bochniak J., Gałkowski K., Rogers E., Kummert A.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no. 4
441-462
EN
Repetitive processes constitute a distinct class of 2D systems, i.e., systems characterized by information propagation in two independent directions, which are interesting in both theory and applications. They cannot be controlled by a direct extension of the existing techniques from either standard (termed 1D here) or 2D systems theories. Here we give new results on the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.
6
Content available Układy wielowymiarowe
Gałkowski K., Paszke W., Sulikowski B.
Pomiary Automatyka Kontrola
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2003
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R. 49, nr 2/3
53-58
PL
W pracy zawarty jest rys historyczny oraz przegląd podstawowych problemów teoretycznych i możliwości zastosowania praktycznych układów wielowymiarowych (nD). Omówiono też nowe trendy i otwarte, nierozwiązane do tej pory problemy badawcze w tej dziedzinie.
EN
The history, theoretical basics and practical applications of multidimensional (nD) systems are briefly revisited. New directions and current open problems are discussed too.
7
Content available remote Linear Repetitive Process Control Theory Applied to a Physical Example
Gałkowski K., Rogers E., Paszke W., Owens D. H.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no. 1
87-99
EN
In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.
8
Content available remote From Continuous to Discrete Models of Linear Repetitive Processes
Gramacki A., Gramacki J., Gałkowski K., Rogers E., Owens D. H.
Archives of Control Sciences
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2002
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Vol. 12, no. 1/2
151-185
EN
Differential linear repetitive processes are a distinct class of 2D linear systems which pose problems which cannot (except in a few very restrictive special cases) be solved by application for computer aided annalysis and simulation. One such problem area is the construction of accurate numerically well conditioned discrete approximations of the dynamics of differential processes which could, as one example of number of immediate applications areas, from the basis for digital implementation of control laws. In this paper, we undertake a detailed investigation of the critical problems which arise when attempting to construct usefull discrete approximations of the dynamics of differential linear repetitive processes and develop solutions to them. Numerical examples to support the results obtained are also given using a specially developed MATLAB based toolbox.
9
Stability and controllability properties of extended discrete linear repetitive processes.
Gałkowski K., Sulikowski B., Paszke W., Rogers E., Owens D.
Prace Naukowe Instytutu Cybernetyki Technicznej Politechniki Wrocławskiej. Konferencje
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2001
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Vol. 103, nr 47
5-14
EN
This paper develops an extension of the state space model for discrete linear repetitive processes which, in addition to their theoretical interest, are also relevant to robotics applications. In particular, the effects of an additional term in the basie state space model of these processes, which represents a direct cross-dependence between successive passes, are investigated. The main results given are the extensions of the existing 2D global-state, and ID equivalent state space model approaches to stability and controllability analysis of this new model. Finally, the role of MATLAB based numerical analysis in this context is also illustrated.
10
Content available remote Non-standard State-space Models for 2D Systems
Gałkowski K., Theodorou N., Tzafestas S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 1
91-101
EN
In this paper, non-standard 2D state space models of the Roesser type and their equivalence under similarity and elementary operations are discussed. Non-standard models cover a wider repertory of systems than traditional ones of both theoretical and practical importance.
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