2003 (Volume 13)
Robust compensator control of aerobic continuous fermentation processes with state estimation
(Bulgarian Academy of Sciences, Bulgaria)
(Technical University, Bulgaria)
(Bulgarian Academy of Sciences, Bulgaria)
The paper deals with robust compensator control of continuous aerobic fermentation processes described by a set of non-linear differential equations. For design purposes the non-linear model is transformed into a linear one with interval parameters. The robust state-space compensator is designed according to the internal model principle. Biomass concentration is estimated on-line by an observer. Substrate concentration is obtained by model-based or indirect measurement. The theoretical results are verified by simulations in different cases. Robustness and simple realisation are important features of the proposed algorithms.
keywords: fermentation processes, non-linear model, biomass and substrate concentration estimation, robust compensator control, simulation.
An iterative identification based on the Youla-Kucera parameterisation without model reduction
|Stefan Kozka, Jan Mikles and Miroslav Fikar|
(Slovak University of Technology, Slovak Republic)
The aim of this paper is to present an iterative identification of the plant in the presence of feedback using input-output data, based on the Youla-Kucera parameterisation. When a reduced complexity model is identified then the controller is designed. Here the identified model is just a vehicle for the computation of a controller. The proposed iterative algorithm contains suitably selected filters and ensures that the model reduction of the identified model is not necessary as in the standard approach. This iterative approach simplifies the identification task of the Youla-Kucera parameter as only its numerator has to be estimated. An experiment with a continuous stirred tank reactor (CSTR), which represents a non-linear single input - single output (SISO) system, illustrate this feature. LQ controller design is used for stabilisation.
keywords: iterative identification, identification for control, continuous system, model reduction.
An approach to decentralized adaptive control
|Karel Perutka and Vladimir Bobal|
(Tomas Bata University, Czech Republic)
The paper presents a way of control of decentralized two inputs two outputs (TITO) systems. The base of the approach is usage of the set of one-dimensional self-tuning controllers with reduced orders, being tuned simultaneously, in contrast to methods using relays in feedback. A method of the recursive least squares with directional forgetting factor applied to the continuous-time system is used as the identification algorithm for the self-tuning controllers. It obtains data using the differential filters. Verification was done in MATLAB-SIMULINK on the systems with "P" and "V" structures. Two methods of tuning the controllers were used: the suboptimal linear quadratic tracking method, and the dynamics inversion method. This approach gives good results, and enables to use arbitrary method of tuning the controllers, in particular, to apply the approaches of control of SISO systems (single input single output), which are quite common for the multi-variable systems.
keywords: adaptive control, continuous time systems, decentralized control, dynamics inversion method, recursive least squares, suboptimal control.
The reachable sets concept applied to a class of min-max optimization problems
(Polish Academy of Sciences, Poland)
A multi-criteria control problem over the infinite time horizon for periodical system is considered. Our aim is to solve problems of this type using the known idea of reachable sets. The worst case approach applied concerns e.g. a system of water resources distribution. The min-max optimisation problem obtained occurs to fit naturally the scheme of reachable sets concept. Applicability of this concept to that particular case is discussed and the algorithm is presented.
keywords: reachable sets, min-max optimization, reference point method, periodical control problem.
Multivariable CRHPC (constrained receding-horizon predictive control) algorithm with improved numerical properties
|Maciej Ławryńczuk and Piotr Tatjewski|
(Warsaw University of Technology, Poland)
This paper is concerned with the stabilising constrained receding-horizon predictive control algorithm (CRHPC) for multivariable processes. The optimal input profile is calculated by means of a new method the purpose of which is to avoid inverting usually ill-conditioned matrices. Additionally, relatively simple formulae for calculating free and forced output predictions for the ARX process model, as well as the analytical stabilising control law in the unconstrained case are derived, without the necessity of solving a matrix Diophantine equation.
keywords: model predictive control, stabilising terminal constraint, singular value decomposition, least-squares methods,ARX models.
On the stability of one dimensional discrete-time jump linear systems
|Adam Czornik, Aleksander Nawrat and Szymon Rabsztyn|
(Silesian University of Technology, Poland)
In this paper we present necessary and sufficient conditions for
- moment stability and almost sure stability of one-dimensional discrete-time linear systems subject Markovian jumps. We show that if the Markov chain is ergodic then almost sure stability is equivalent to
-moment stability for certain
keywords: jump linear systems, almost sure stability, moment stability.
Direct stable fuzzy adaptive control of a class of SISO nonlinear systems
|Salim Labiod and Mohamed Seghir Boucherit|
(Ecole Nationale Polytechnique, Algeria)
For a class of unknown nonlinear single-input single-output (SISO) systems a stable direct adaptive controller which uses standard fuzzy systems is presented. The proposed scheme includes a proportional-integral-type adaptation law. Global boundedness of the overall adaptive system and tracking within a desired precision are established with the new adaptive scheme. This adaptive scheme allows for the incorporation of linguistic information from human experts directly into the controller. Simulations performed on two examples illustrate the approach and exhibit its performance.
keywords: fuzzy systems, fuzzy control, adaptive control, nonlinear systems.