1,056 research outputs found
A robust multi-model predictive controller for distributed parameter systems
12 páginas, 6 figurasIn this work a robust nonlinear model predictive controller for nonlinear convection–diffusion-reaction systems is presented. The controller makes use of a collection of reduced order approximations of the plant (models) reconstructed on-line by projection methods on proper orthogonal decomposition (POD) basis functions. The model selection and model update step is based on a sufficient condition that determines the maximum allowable process-model mismatch to guarantee stable control performance despite process uncertainty and disturbances. Proofs on the existence of a sequence of feasible approximations and control stability are given.
Since plant approximations are built on-line based on actual measurements, the proposed controller can be interpreted as a multi-model nonlinear predictive control (MMPC). The performance of the MMPC strategy is illustrated by simulation experiments on a problem that involves reactant concentration control of a tubular reactor with recycle.This work has been also partially founded by the Spanish Ministry of Science and Innovation (SMART-QC, AGL2008-05267-C03-01), the FP7 CAFE project (KBBE-2007-1-212754), the Project PTDC/EQU-ESI/73458/2006 from the Portuguese Foundation for Science and Technology and PI grant 07/IN.1/I1838 by Science Foundation Ireland. Also, the authors acknowledge financial support received by a collaborative grant GRICES-CSIC.Peer reviewe
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
A robust multi-model predictive controller for distributed parameter systems
12 páginas, 6 figurasIn this work a robust nonlinear model predictive controller for nonlinear convection–diffusion-reaction systems is presented. The controller makes use of a collection of reduced order approximations of the plant (models) reconstructed on-line by projection methods on proper orthogonal decomposition (POD) basis functions. The model selection and model update step is based on a sufficient condition that determines the maximum allowable process-model mismatch to guarantee stable control performance despite process uncertainty and disturbances. Proofs on the existence of a sequence of feasible approximations and control stability are given.
Since plant approximations are built on-line based on actual measurements, the proposed controller can be interpreted as a multi-model nonlinear predictive control (MMPC). The performance of the MMPC strategy is illustrated by simulation experiments on a problem that involves reactant concentration control of a tubular reactor with recycle.This work has been also partially founded by the Spanish Ministry of Science and Innovation (SMART-QC, AGL2008-05267-C03-01), the FP7 CAFE project (KBBE-2007-1-212754), the Project PTDC/EQU-ESI/73458/2006 from the Portuguese Foundation for Science and Technology and PI grant 07/IN.1/I1838 by Science Foundation Ireland. Also, the authors acknowledge financial support received by a collaborative grant GRICES-CSIC.Peer reviewe
Comparison of discrete dynamic pipeline models for operational optimization of District Heating Networks
Optimal operation of District Heating Networks (DHNs) is a very challenging task. One of the main challenges for DHNs optimization tool designers is the choice of an adequate dynamic thermal pipeline model which gives a good tradeoff between accurately modeling the physics of the thermodynamic processes and simultaneously yielding a numerically efficient model. To address this, the paper states the main Partial Differential Equation (PDE) which is used to describe the convection of hot water throughout the literature, together with reasonable assumptions that lead to minor deviations from measurements. Then, different approaches are described which can be used to solve the respective PDE. More specifically, the very common Node Method (NM), approximations of the NM, the lagrangian approach and different Finite Difference (FD) approaches are presented. The main aim of this work is to provide a qualitative and quantitative comparison of these modeling approaches in the context of optimal DHN operation. Our quantitative results show, that by comparing the different approaches to measurement data, the NM yields the smallest modeling errors for most of the temporal discretization sizes. The qualitative comparison identifies that the lagrangian method lacks the differentiability necessary for the implementation in optimization tools. The advantages of the FD approaches include guaranteeing a fixed number of variables, a constant information depth of the temperature distribution along the pipeline and the simplicity of implementation into optimization tools. The approximations of the NM bring benefits when varying mass flow directions need to be considered, which is a crucial aspect in 4t h generation DHNs
Stability Analysis of Piecewise Affine Systems with Multi-model Model Predictive Control
Constrained model predictive control (MPC) is a widely used control strategy,
which employs moving horizon-based on-line optimisation to compute the optimum
path of the manipulated variables. Nonlinear MPC can utilize detailed models
but it is computationally expensive; on the other hand linear MPC may not be
adequate. Piecewise affine (PWA) models can describe the underlying nonlinear
dynamics more accurately, therefore they can provide a viable trade-off through
their use in multi-model linear MPC configurations, which avoid integer
programming. However, such schemes may introduce uncertainty affecting the
closed loop stability. In this work, we propose an input to output stability
analysis for closed loop systems, consisting of PWA models, where an observer
and multi-model linear MPC are applied together, under unstructured
uncertainty. Integral quadratic constraints (IQCs) are employed to assess the
robustness of MPC under uncertainty. We create a model pool, by performing
linearisation on selected transient points. All the possible uncertainties and
nonlinearities (including the controller) can be introduced in the framework,
assuming that they admit the appropriate IQCs, whilst the dissipation
inequality can provide necessary conditions incorporating IQCs. We demonstrate
the existence of static multipliers, which can reduce the conservatism of the
stability analysis significantly. The proposed methodology is demonstrated
through two engineering case studies.Comment: 28 pages 9 figure
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