Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature. (C) 2011 Elsevier Ltd. All rights reserved.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

MPC for tracking zone regions

This paper deals with the problem of tracking target sets using a model predictive control (MPC) law. Some MPC applications require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some other variables - possibly including input variables - are steered to fixed target or set-point. In real applications, this problem is often overcome by including and excluding an appropriate penalization for the output errors in the control cost function. In this way, throughout the continuous operation of the process, the control system keeps switching from one controller to another, and even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. From a theoretical point of view, the control objective of this kind of problem can be seen as a target set (in the output space) instead of a target point, since inside the zones there are no preferences between one point or another. In this work, a stable MPC formulation for constrained linear systems, with several practical properties is developed for this scenario. The concept of distance from a point to a set is exploited to propose an additional cost term, which ensures both, recursive feasibility and local optimality. The performance of the proposed strategy is illustrated by simulation of an ill-conditioned distillation column. (C) 2010 Elsevier Ltd. All rights reserved.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. Here, a stable M PC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system. (C) 2008 Elsevier Ltd. All rights reserved.

Closed-loop model re-identification of processes under MPC with zone control

This work deals with a procedure for model re-identification of a process in closed loop with ail already existing commercial MPC. The controller considered here has a two-layer structure where the upper layer performs a target calculation based on a simplified steady-state optimization of the process. Here, it is proposed a methodology where a test signal is introduced in a tuning parameter of the target calculation layer. When the outputs are controlled by zones instead of at fixed set points, the approach allows the continuous operation of the process without an excessive disruption of the operating objectives as process constraints and product specifications remain satisfied during the identification test. The application of the method is illustrated through the simulation of two processes of the oil refining industry. (c) 2008 Elsevier Ltd. All rights reserved.

Distributed MPC for Thermal Comfort and Load Allocation with Energy Auction

This paper presents a distributed predictive control methodology for indoor thermal comfort that optimizes the consumption of a limited shared energy resource using an integrated demand-side management approach that involves a power price auction and an appliance loads allocation scheme. The control objective for each subsystem (house or building) aims to minimize the energy cost while maintaining the indoor temperature inside comfort limits. In a distributed coordinated multi-agent ecosystem, each house or building control agent achieves its objectives while sharing, among them, the available energy through the introduction of particular coupling constraints in their underlying optimization problem. Coordination is maintained by a daily green energy auction bring in a demand-side management approach. Also the implemented distributed MPC algorithm is described and validated with simulation studies.

Monetary policy under the Labour government 1997- 2010: the first 13 years of the MPC

This paper examines the performance of monetary policy under the new framework established in 1997 up to the end of the Labour government in May 2010. Performance was relatively good in the years before the crisis, but much weaker from 2008. The new framework largely neglected open economy issues, while the Treasury’s EMU assessment in 2003 can be interpreted in different ways. inflation targeting in the UK and elsewhere may have contributed in some way to the eruption and depth of the financial crisis from 2008, but UK monetary policy responded in a bold and innovative way. Overall, the design and operation of monetary policy were much better than in earlier periods, but there remains scope for significant further evolution.

Computationally reliable approaches of contractive MPC for discrete-time systems

La tesis pretende explorar acercamientos computacionalmente confiables y eficientes de contractivo MPC para sistemas de tiempo discreto. Dos tipos de contractivo MPC han sido estudiados: MPC con coacción contractiva obligatoria y MPC con una secuencia contractiva de conjuntos controlables. Las técnicas basadas en optimización convexa y análisis de intervalos son aplicadas para tratar MPC contractivo lineal y no lineal, respectivamente. El análisis de intervalos clásicos es ampliado a zonotopes en la geometría para diseñar un conjunto invariante de control terminal para el modo dual de MPC. También es ampliado a intervalos modales para tener en cuenta la modalidad al calcula de conjuntos controlables robustos con una interpretación semántica clara. Los instrumentos de optimización convexa y análisis de intervalos han sido combinados para mejorar la eficacia de contractive MPC para varias clases de sistemas de tiempo discreto inciertos no lineales limitados. Finalmente, los dos tipos dirigidos de contractivo MPC han sido aplicados para controlar un Torneo de Fútbol de Copa Mundial de Micro Robot (MiroSot) y un Tanque-Reactor de Mezcla Continua (CSTR), respectivamente.

Input constraints handling in an MPC/feedback linearization scheme

The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.

Real-Time Control Of Floods Along The Demer River, Belgium, By Means Of MPC In Combination With GA And A Fast Conceptual River Model

Climate model projections show that climate change will further increase the risk of flooding in many regions of the world. There is a need for climate adaptation, but building new infrastructure or additional retention basins has its limits, especially in densely populated areas where open spaces are limited. Another solution is the more efficient use of the existing infrastructure. This research investigates a method for real-time flood control by means of existing gated weirs and retention basins. The method was tested for the specific study area of the Demer basin in Belgium but is generally applicable. Today, retention basins along the Demer River are controlled by means of adjustable gated weirs based on fixed logic rules. However, because of the high complexity of the system, only suboptimal results are achieved by these rules. By making use of precipitation forecasts and combined hydrological-hydraulic river models, the state of the river network can be predicted. To fasten the calculation speed, a conceptual river model was used. The conceptual model was combined with a Model Predictive Control (MPC) algorithm and a Genetic Algorithm (GA). The MPC algorithm predicts the state of the river network depending on the positions of the adjustable weirs in the basin. The GA generates these positions in a semi-random way. Cost functions, based on water levels, were introduced to evaluate the efficiency of each generation, based on flood damage minimization. In the final phase of this research the influence of the most important MPC and GA parameters was investigated by means of a sensitivity study. The results show that the MPC-GA algorithm manages to reduce the total flood volume during the historical event of September 1998 by 46% in comparison with the current regulation. Based on the MPC-GA results, some recommendations could be formulated to improve the logic rules.

Otimização do processo de síntese do aluminato de cobalto via método de polimerização de complexos (MPC) através do planejamento fatorial fracionado

In the ceramics industry are becoming more predominantly inorganic nature pigments. Studies in this area allow you to develop pigments with more advanced properties and qualities to be used in the industrial context. Studies on synthesis and characterization of cobalt aluminate has been widely researched, cobalt aluminate behavior at different temperatures of calcinations, highlighting especially the temperatures of 700, 800 and 900° C that served as a basis in the development of this study, using the method of polymerization of complex (CPM), economic, and this method applied in ceramic pigment synthesis. The procedure was developed from a fractional factorial design 2 (5-2) in order to optimize the process of realization of the cobalt aluminate (CoAl2O4), having as response surfaces the batch analysis data of Uv-vis spectroscopy conducted from the statistic software 7.0, for this were chosen five factors as input variables: citric acid (stoichiometric manner), puff or pyrolysis time (h), temperature (° C), and calcinations (° C/min), at levels determined for this study. By applying statistics in the process of obtaining the CoAl2O4 is possible the study of these factors and which may have greater influence in getting the synthesis. The pigments characterized TG/DSC analyses, and x-ray diffraction (XRD) and scanning electron microscope (SEM/EDS) in order to establish the structural and morphological aspects of pigment CoAl2O4, among the factors studied it were found to statically with increasing calcinations temperature 700°< 800 <900 °C, the bands of Uv-vis decrease with increasing intensity of absorbance and that with increasing time of puff or pyrolysis (h) there is an increase in bands of Uv-vis proportionally, the generated model set for the conditions proposed in this study because the coefficient of determination can explain about 99.9% of the variance (R²), response surfaces generated were satisfactory, so it s possible applicability in the ceramics industry of pigments

SN 2005at - A neglected type Ic supernova at 10 Mpc

We present a photometric and spectroscopic study of a reddened type Ic supernova (SN) 2005at. We report our results based on the available data of SN 2005at, including late-time observations from the Spitzer Space Telescope and the Hubble Space Telescope. In particular, late-time mid-infrared observations are something rare for type Ib/c SNe. In our study we find SN 2005at to be very similar photometrically and spectroscopically to another nearby type Ic SN 2007gr, underlining the prototypical nature of this well-followed type Ic event. The spectroscopy of both events shows similar narrow spectral line features. The radio observations of SN 2005at are consistent with fast evolution and low luminosity at radio wavelengths. The late-time Spitzer data suggest the presence of an unresolved light echo from interstellar dust and dust formation in the ejecta, both of which are unique observations for a type Ic SN. The late-time Hubble observations reveal a faint point source coincident with SN 2005at, which is very likely either a declining light echo of the SN or a compact cluster. For completeness we study ground-based pre-explosion archival images of the explosion site of SN 2005at, however this only yielded very shallow upper limits for the SN progenitor star. We derive a host galaxy extinction of A_V ∼ 1.9 mag for SN 2005at, which is relatively high for a SN in a normal spiral galaxy not viewed edge-on.

Otimização do processo de síntese do aluminato de cobalto via método de polimerização de complexos (MPC) através do planejamento fatorial fracionado

In the ceramics industry are becoming more predominantly inorganic nature pigments. Studies in this area allow you to develop pigments with more advanced properties and qualities to be used in the industrial context. Studies on synthesis and characterization of cobalt aluminate has been widely researched, cobalt aluminate behavior at different temperatures of calcinations, highlighting especially the temperatures of 700, 800 and 900° C that served as a basis in the development of this study, using the method of polymerization of complex (CPM), economic, and this method applied in ceramic pigment synthesis. The procedure was developed from a fractional factorial design 2 (5-2) in order to optimize the process of realization of the cobalt aluminate (CoAl2O4), having as response surfaces the batch analysis data of Uv-vis spectroscopy conducted from the statistic software 7.0, for this were chosen five factors as input variables: citric acid (stoichiometric manner), puff or pyrolysis time (h), temperature (° C), and calcinations (° C/min), at levels determined for this study. By applying statistics in the process of obtaining the CoAl2O4 is possible the study of these factors and which may have greater influence in getting the synthesis. The pigments characterized TG/DSC analyses, and x-ray diffraction (XRD) and scanning electron microscope (SEM/EDS) in order to establish the structural and morphological aspects of pigment CoAl2O4, among the factors studied it were found to statically with increasing calcinations temperature 700°< 800 <900 °C, the bands of Uv-vis decrease with increasing intensity of absorbance and that with increasing time of puff or pyrolysis (h) there is an increase in bands of Uv-vis proportionally, the generated model set for the conditions proposed in this study because the coefficient of determination can explain about 99.9% of the variance (R²), response surfaces generated were satisfactory, so it s possible applicability in the ceramics industry of pigments