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| 2. |
- Berbyuk, Viktor, 1953
(författare)
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Dynamics and optimal control of biotechnical systems "Man-Prosthesis"
- 1997
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Ingår i: IUTAM Symposium on Interaction Between Dynamics and Control in Advanced Mechanical Systems, Ed. D. van Campen, Kluwer Academic Publishers, 1997. - Dordrecht : Springer Netherlands. ; , s. 35-42
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Konferensbidrag (refereegranskat)abstract
- In the paper, a mathematical model is proposed for investigating the controlled motion of human locomotion system (HLS) with an above-knee prosthesis. To provide insight into the interaction between dynamics and control in biotechnical system Man-Prosthesis the energy optimal control problem of the HLS wearing a lower limb prosthesis has been considered. The algorithm is based on special conversion of the optimal control problem for a nonlinear dynamical system which models HLS into a standard nonlinear programming problem. A number of energy-optimal control problems of human locomotion with an artificial leg, and optimization problems for the constructive parameters of the prostheses under different boundary conditions and constraints have been solved. The numerical results obtained were compared with experimental data for normal human locomotion. The energy-optimal elastic and viscoelastic characteristics of the ankle and knee joints of the prostheses have been determined.
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| 3. |
- Berbyuk, Viktor, 1953
(författare)
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On complete controllability of linear nonstationary systems
- 1993
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Ingår i: Journal of Soviet Mathematics. - 0090-4104. ; 67:2, s. 2973-2975
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Tidskriftsartikel (refereegranskat)abstract
- The concept of controllability is connected with the transfer of a dynamic system from one state to another by means of a control. An important problem in the theory of control systems is the search for necessary and sufficient conditions for complete controllability of dynamic systems. By using of the first integrals of the equations of unperturbed motion the necessary and sufficient conditions for complete controllability of linear nonstationary dynamic systems have been proposed.
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| 4. |
- Berbyuk, Viktor, 1953
(författare)
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The use of first integrals to synthesize the energetically optimal control of a nonlinear system
- 1997
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Ingår i: Journal of Mathematical Sciences. - 1573-8795 .- 1072-3374. ; 86:2, s. 2642-2645
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Tidskriftsartikel (refereegranskat)abstract
- In the paper a method of solving problems of optimal control of the motion of nonlinear dynamical systemswith respect to energy expenditure given a fixed time and fixed ends of the phase trajectory has been proposed. The method is based on the use of first integrals of the equations of free motion. The application of the method isillustrated by examples.
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| 6. |
- Diehl, Stefan, et al.
(författare)
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Analytical and numerical description of the settling process in the activated sludge operation
- 1990
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Ingår i: Instrumentation, control, and automation of water and wastewater treatment and transport systems : proceedings of the 5th IAWPRC Workshop held in Yokohama and Kyoto, Japan, 26 July-3 August 1990. - 0080407765 ; , s. 471-478
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Konferensbidrag (refereegranskat)abstract
- The secondary clarifier or settler is crucial for the whole activated sludge operation. Consequently, it is important to obtain a reliable analytical model as well as a useful numerical method, which can be used in the automatic control of the settling process. Discontinuities (shocks) appear physically, and an analytical description as well as a stable numerical algorithm must be able to handle these discontinuities. A model based on the Kynch theory of sedimentation is used, where the settling flux is a function only of the local concentration and is assumed to have one inflexion point. For such non-convex flux functions, the settling process is qualitatively the same, independent of further assumptions on the shapes of the settling functions. Using the theory of nonlinear conservation laws, the main results obtained are: how to calculate transient and asymptotic behavior; how to control the concentration profile of the settler, in particular the depth of the sludge blanket, for a given load; and, a numerical algorithm which automatically preserves shocks and gives the physically correct solution according to the analytical treatment. The algorithm can be applied on any flux function (with more than one inflexion point).
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| 8. |
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| 9. |
- Jeppsson, Ulf, et al.
(författare)
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An evaluation of a dynamic model of the secondary clarifier
- 1996
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Ingår i: Water Science and Technology. - : IWA Publishing. - 0273-1223. ; 34:5, s. 19-26
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Tidskriftsartikel (refereegranskat)abstract
- The main objective of the paper is to support and illustrate recent theoretical results on the mathematical modelling of the secondary clarifier. A new settler model is compared with a traditional layer model by means of numerical simulations. Emphasis is put on the numerical solution's ability to approximate the analytical solution of the conservation law written as a non-linear partial differential equation. The new settler model is consistent in this respect. Another important conclusion is that a layer model dividing the settler into only ten layers (normally used in settler models) is too crude an approximation to capture the detailed dynamic behaviour of the settler. All simulations presented are performed with the settler models coupled to the IAWQ Activated Sludge Model No. 1.
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| 10. |
- Jeppsson, Ulf, et al.
(författare)
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On the modelling of the dynamic propagation of biological components in the secondary clarifier
- 1996
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Ingår i: Water Science and Technology. - : IWA Publishing. - 0273-1223. ; 34:5, s. 85-92
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Tidskriftsartikel (refereegranskat)abstract
- When coupling a model of the biological reactor to a model of the settler, difficulties appear because of the different representations used for the particulate material. A combined model of the entire activated sludge process needs to include an algorithm for the dynamic propagation of the biological components of the particulate material through the secondary clarifier. In particular, this is of importance for an accurate description of the sludge that is recycled to the biological reactor. Two one-dimensional algorithms have been evaluated by means of numerical simulations. The first algorithm investigated is the one by Otterpohl and Freund in 1992 and some inherent problems of this method are discussed. For example, it will produce oscillating solutions as the number of layers in the settler model increases. Therefore, an alternative algorithm is proposed. It is based on a percentage vector that describes the different particulate biological components as fractions of the total suspended solids concentration. The vector is updated for every layer in the settler model by a robust numerical method. The algorithm is derived analytically, is computationally efficient and does not exhibit any oscillatory behaviour.
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