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.

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.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

A new technique to control brushless motor for blood pump application

This article presents a back-electromotive force (BEMF)-based technique of detection for sensorless brushless direct current motor (BLDCM) drivers. The BLDCM has been chosen as the energy converter in rotary or pulsatile blood pumps that use electrical motors for pumping. However, in order to operate properly, the BLDCM driver needs to know the shaft position. Usually, that information is obtained through a set of Hall sensors assembled close to the rotor and connected to the electronic controller by wires. Sometimes, a large distance between the motor and controller makes the system susceptible to interference on the sensor signal because of winding current switching. Thus, the goal of the sensorless technique presented in this study is to avoid this problem. First, the operation of BLDCM was evaluated on the electronic simulator PSpice. Then, a BEMF detector circuitry was assembled in our laboratories. For the tests, a sensor-dependent system was assembled where the direct comparison between the Hall sensors signals and the detected signals was performed. The obtained results showed that the output sensorless detector signals are very similar to the Hall signals at speeds of more than 2500 rpm. Therefore, the sensorless technique is recommended as a responsible or redundant system to be used in rotary blood pumps.

Biogeochemical cycles of nutrients in tropical Eucalyptus plantations Main features shown by intensive monitoring in Congo and Brazil

The sustainability of fast-growing tropical Eucalyptus plantations is of concern in a context of rising fertilizer costs, since large amounts of nutrients are removed with biomass every 6-7 years from highly weathered soils. A better understanding of the dynamics of tree requirements is required to match fertilization regimes to the availability of each nutrient in the soil. The nutrition of Eucalyptus plantations has been intensively investigated and many studies have focused on specific fluxes in the biogeochemical cycles of nutrients. However, studies dealing with complete cycles are scarce for the Tropics. The objective of this paper was to compare these cycles for Eucalyptus plantations in Congo and Brazil, with contrasting climates, soil properties, and management practices. The main features were similar in the two situations. Most nutrient fluxes were driven by crown establishment the two first years after planting and total biomass production thereafter. These forests were characterized by huge nutrient requirements: 155, 10, 52, 55 and 23 kg ha(-1) of N, P, K, Ca and Mg the first year after planting at the Brazilian study site, respectively. High growth rates the first months after planting were essential to take advantage of the large amounts of nutrients released into the soil solutions by organic matter mineralization after harvesting. This study highlighted the predominant role of biological and biochemical cycles over the geochemical cycle of nutrients in tropical Eucalyptus plantations and indicated the prime importance of carefully managing organic matter in these soils. Limited nutrient losses through deep drainage after clear-cutting in the sandy soils of the two study sites showed the remarkable efficiency of Eucalyptus trees in keeping limited nutrient pools within the ecosystem, even after major disturbances. Nutrient input-output budgets suggested that Eucalyptus plantations take advantage of soil fertility inherited from previous land uses and that long-term sustainability will require an increase in the inputs of certain nutrients. (C) 2009 Elsevier B.V. All rights reserved.

Private valuation of carbon sequestration in forest plantations

Approval of the Clean Development Mechanism, provided for in the Kyoto Protocol, enables countries with afforested land to trade in carbon emissions reduction certificates related to carbon dioxide equivalent quantities (CO(2-e)) stored within a certain forest area. Potential CO(2-e) above base line sequestration was determined for two forest sites on commercial eucalyptus plantations in northern Brazil (Bahia). Compensation values for silvicultural regimes involving rotation lengths greater than economically optimal were computed using the Faustmann formula. Mean values obtained were US$8.16 (MgCO(2-e))(-1) and US $7.19 (MgCO(2-e))(-1) for average and high site indexes, respectively. Results show that carbon supply is more cost-efficient in highly productive sites. Annuities of US$18.8 Mg C(-1) and US$35.1 Mg C(-1) and yearly payments of US$4.4 m(-3) and US$8.2 m(-3) due for each marginal cubic meter produced were computed for high and average sites, respectively. The estimated value of the tonne of carbon defines minimum values to be paid to forest owners, in order to induce a change in silvicultural management regimes. A reduction of carbon supply could be expected as a result of an increase in wood prices, although it would not respond in a regular manner. For both sites, price elasticity of supply was found to be inelastic and increased as rotation length moved further away from economically optimal: 0.24 and 0.27 for age 11 years in average- and high-productivity sites, respectively. This would be due to biomass production potential as a limiting factor; beyond a certain threshold value. an increase in price does not sustain a proportional change in carbon storage supply. The environmental service valuation model proposed might be adequate for assessing potential supply in plantation forestry, from a private landowner perspective, with an economic opportunity cost. The model is not applicable to low commercial value forest plantations. (C) 2009 Elsevier B.V. All rights reserved.

Radial variation of the wood anatomical structure of Gmelina arborea trees from different climatic and management conditions in Costa Rica

The evaluations of the effect of the climatic conditions and of the intensity of forest management in the trunk of the Gmelina arborea Linn. Roxb. trees are restricted to its physical-mechanical properties and use. The present work has as objective to study the radial variations of the wood anatomy of the gmelina trees sampled in plantations of 30 sites in Costa Rica, characterized by two climatic conditions (tropical dry and humid) and three intensities of forest management (intensive, moderate and without management). The results of the analyses demonstrated the existence of radial variation of the different anatomical parameters, except for the fiber lumen diameter and multiple vessels in the wood of the gmelina trees. For the wood anatomical elements, fibers (width, lumen diameter, and length), vessels (multiple vessels, diameter and frequency) and radial parenchyma (height) relationships were observed with the climate (tropical humid and dry). The radial variations of the wood anatomical elements were, also, influenced by the management regimes of the gmelina trees.

Diet-dependent life history, feeding preference and thermal requirements of the predatory mite Neoseiulus baraki (Acari: Phytoseiidae)

Neoseiulus baraki Athias-Henriot (Acari: Phytoseiidae) has been reported from the Americas, Africa and Asia, often in association with Aceria guerreronis Keifer (Acari: Eriophyidae), one of the most important pests of coconut (Cocos nucifera L.) in diVerent parts of the world. That phytoseiid has been considered one of the most common predators associated with A. guerreronis in Brazil. The objective of this study was to evaluate the feeding preference and the eVect of food items commonly present on coconut fruits and several temperature regimes on the life history of a Brazilian population of N. baraki. Completion of immature development was possible when N. baraki was fed A. guerreronis, Steneotarsonemus concavuscutum Lofego and Gondim Jr., and Tyrophagus putrescentiae (Schrank). Fecundity was highest on T. putrescentiae (39.4 eggs), followed by A. guerreronis (24.8 eggs). In choice tests, irrespective of the food on which N. baraki was reared, a larger number of adults of this predator chose leaf discs containing A. guerreronis than discs containing other food items, demonstrating a preference of the former for the latter as food. Egg to adult thermal developmental time was calculated as 84.2 degree-days, above a threshold of 15.8 degrees C. This lower developmental threshold is higher than previously published for phytoseiid species from higher latitudes. Neoseiulus baraki was shown to have higher biotic potential at 30 degrees C (r(m) 0.29). The results suggest N. baraki to be a promising biological control agent of A. guerreronis, well adapted to survive and develop in areas with relatively high temperatures, where that pest prevails.

The effect of host plants on Tetranychus evansi, Tetranychus urticae (Acari: Tetranychidae) and on their fungal pathogen Neozygites floridana (Entomophthorales: Neozygitaceae)

In a series of tritrophic-level interaction experiments, the effect of selected host plants of the spider mites, Tetranychus evansi and Tetranychus urticae, on Neozygites floridana was studied by evaluating the attachment of capilliconidia, presence of hyphal bodies in the infected mites, mortality from fungal infection, mummification and sporulation from fungus-killed mite cadavers. Host plants tested for T. evansi were tomato, cherry tomato, eggplant, nightshade, and pepper while host plants tested for T. urticae were strawberry, jack bean, cotton and Gerbera. Oviposition rate of the mites on each plant was determined to infer host plant suitability while host-switching determined antibiosis effect on fungal activity. T. evansi had a high oviposition on eggplant, tomato and nightshade but not on cherry tomato and pepper. T. urticae on jack bean resulted in a higher oviposition than on strawberry, cotton and Gerbera. Attachment of capilliconidia to the T. evansi body, presence of hyphal bodies in infected T. evansi and mortality from fungal infection were significantly higher on pepper, nightshade and tomato. The highest level of T. evansi mummification was observed on tomato. T. evansi cadavers from tomato and eggplant produced more primary conidia than those from cherry tomato, nightshade and pepper. Switching N. floridana infected T. evansi from one of five Solanaceous host plants to tomato had no prominent effect on N. floridana performance. For T. urticae, strawberry and jack bean provided the best N. floridana performance when considering all measured parameters. Strawberry also had the highest primary conidia production. This study shows that performance of N. floridana can vary with host plants and may be an important factor for the development of N. floridana epizootics. (C) 2011 Elsevier Inc. All rights reserved.

Acquired tolerance of tomato (Lycopersicon esculentum cv. Micro-Tom) plants to cadmium-induced stress

The effects of varying concentrations of cadmium (Cd) on the development of Lycopersicon esculentum cv. Micro-Tom (MT) plants were investigated after 40 days (vegetative growth) and 95 days (fruit production), corresponding to 20 days and 75 days of exposure to CdCl(2), respectively. Inhibition of growth was clearly observed in the leaves after 20 days and was greater after 75 days of growth in 1 mM CdCl(2), whereas the fruits exhibited reduced growth following the exposure to a concentration as low as 0.1 mM CdCl(2). Cd was shown to accumulate in the roots after 75 days of growth but was mainly translocated to the upper parts of the plants accumulating to high concentrations in the fruits. Lipid peroxidation was more pronounced in the roots even at 0.05 mM CdCl(2) after 75 days, whereas in leaves, there was a major increase after 20 days of exposure to 1 mM CdCl(2), but the fruit only exhibited a slight significant increase in lipid peroxidation in plants subjected to 1 mM CdCl(2) when compared with the control. Oxidative stress was also investigated by the analysis of four key antioxidant enzymes, which exhibited changes in response to the increasing concentrations of Cd tested. Catalase (EC 1.11.1.6) activity was shown to increase after 75 days of Cd treatment, but the major increases were observed at 0.1 and 0.2 mM CdCl(2), whereas guaiacol peroxidase (EC 1.11.1.7) did not vary significantly from the control in leaves and roots apart from specific changes at 0.5 and 1 mM CdCl(2). The other two enzymes tested, glutathione reductase (EC 1.6.4.2) and superoxide dismutase (SOD, EC 1.15.1.1), did not exhibit any significant changes in activity, apart from a slight decrease in SOD activity at concentrations above 0.2 mM CdCl(2). However, the most striking results were obtained when an extra treatment was used in which a set of plants was subjected to a stepwise increase in CdCl(2) from 0.05 to 1 mM, leading to tolerance of the Cd applied even at the final highest concentration of 1 mM. This apparent adaptation to the toxic effect of Cd was confirmed by biomass values being similar to the control, indicating a tolerance to Cd acquired by the MT plants.

Deciphering the weathering processes using environmental mineralogy and geochemistry: Towards an integrated model of laterite and podzol genesis in the Upper Amazon Basin

This article reports major results from collaborative research between France and Brazil on soil and water systems, carried out in the Upper Amazon Basin. It reveals the weathering processes acting in the partly inundated, low elevation plateaus of the Basin, mostly covered by evergreen forest. Our findings are based on geochemical data and mineral spectroscopy that probe the crystal chemistry of Fe and Al in mineral phases (mainly kaolinite, Al- and Fe-(hydr)oxides) of tropical soils (laterites). These techniques reveal crystal alterations in mineral populations of different ages and changes of metal speciation associated with mineral or organic phases. These results provide an integrated model of soil formation and changes (from laterites to podzols) in distinct hydrological compartments of the Amazon landscapes and under altered water regimes. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.