Fast experimental identification of suspension models for control design

This paper presents both the theoretical and the experimental approaches of the development of a mathematical model to be used in multi-variable control system designs of an active suspension for a sport utility vehicle (SUV), in this case a light pickup truck. A complete seven-degree-of-freedom model is successfully quickly identified, with very satisfactory results in simulations and in real experiments conducted with the pickup truth. The novelty of the proposed methodology is the use of commercial software in the early stages of the identification to speed up the process and to minimize the need for a large number of costly experiments. The paper also presents major contributions to the identification of uncertainties in vehicle suspension models and in the development of identification methods using the sequential quadratic programming, where an innovation regarding the calculation of the objective function is proposed and implemented. Results from simulations of and practical experiments with the real SUV are presented, analysed, and compared, showing the potential of the method.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 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.

Optimizing model predictive control of an industrial distillation column

The main scope of this work is the implementation of an MPC that integrates the control and the economic optimization of the system. The two problems are solved simultaneously through the modification of the control cost function that includes an additional term related to the economic objective. The optimizing MPC is based on a quadratic program (QP) as the conventional MPC and can be solved with the available QP solvers. The method was implemented in an industrial distillation system, and the results show that the approach is efficient and can be used, in several practical cases. (C) 2011 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.

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.

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.

Tabasco pepper production with CO(2) application using drip irrigation

Tabasco pepper production with CO(2) application using drip irrigation. Application of CO(2) through water reduces the soil solution pH, causing variations in nutrient mobility and consequent effects on the absorption. The objective of this study was to analyze the effects of carbon dioxide rates supplied by drip irrigation in the production of Capsicum frutescens L. crop. A randomized block design with four treatments and eight replications was used. The treatments were four rates of CO(2): 0 (T1), 451.95 (T2); 677.93 (T3) and 903.92 (T4) kg ha(-1). The fruits were counted and weighed; the length and the diameter were obtained from an average of 20 fruits per plant, randomly taken, from each treatment in the plot. The quadratic effect (p < 0.01) occurred for CO(2) on the yield and there was quadratic effect (p < 0.05) of the rates on the number of fruits. There were no effects of CO(2) rates on the green matter, dry matter and fruit length and diameter. The T2 treatment provided greater yield and higher number of fruits per plant with an increase of 16 and 26%, respectively in relation to T1 (without CO(2)). CO(2) application favored the increase in the yield because of the greater number of fruits per plant in the Tabasco pepper crop.

Meat Quality of Lambs Fed on Palm Kernel Meal, a By-product of Biodiesel Production

This study aimed to establish the optimum level of palm kernel meal in the diet of Santa Ines lambs based on the sensorial characteristics and fatty acid profile of the meat. We used 32 lambs with a starting age of 4 to 6 months and mean weight of 22 2.75 kg, kept in individual stalls. The animals were fed with Tifton-85 hay and a concentrate mixed with 0.0, 6.5, 13.0 or 19.5% of palm kernel meal based on the dry mass of the complete diet. These levels formed the treatments. Confinement lasted 80 days and on the last day the animals were fasted and slaughtered. After slaughter, carcasses were weighed and sectioned longitudinally, along the median line, into two antimeres. Half-carcasses were then sliced between the 12th and 13th ribs to collect the loin (longissimus dorsi), which was used to determine the sensorial characteristics and fatty acid profile of the meat. For sensorial evaluation, samples of meat were given to 54 judges who evaluated the tenderness, juiciness, appearance, aroma and flavor of the meat using a hedonic scale. Fatty acids were determined by gas chromatography. The addition of palm kernel meal to the diet had no effect on the sensorial characteristics of meat juiciness, appearance, aroma or flavor. However, tenderness showed a quadratic relationship with the addition of the meal to the diet. The concentration of fatty acids C12:0, C14:0 and C16:0 increased with the addition of palm kernel meal, as did the sum of medium-chain fatty acids and the atherogenicity index. Up to of 19.5% of the diet of Santa Ines lambs can be made up of palm kernel meal without causing significant changes in sensorial characteristics. However, the fatty acid profile of the meat was altered.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

Milk yield, milk composition, eating behavior, and lamb performance of ewes fed diets containing soybean hulls replacing coastcross (Cynodon species) hay

The objective of this experiment was to evaluate the effects of replacing coastcross hay NDF by soybean hull (SH) NDF on the lactation performance and eating behavior of ewes and also on the performance of their lambs. Fifty-six Santa Ines lactating ewes (56.1 +/- 6.8 kg of initial BW; mean +/- SD) were penned individually and used in a randomized complete block design with 14 blocks and 4 treatments. Diets were formulated to provide similar concentrations of NDF (56%) and CP (16%). The SH NDF replaced 33 (SH33), 67 (SH67), or 100% (SH100) of the NDF contributed by coastcross hay in a 70% forage-based diet (SH0), resulting in SH inclusion rates of 0, 25, 54, and 85% of the dietary DM. Once a week, from the second to the eighth week of lactation (weaning time), ewes were separated from their lambs, stimulated by a 6-IU i.v. oxytocin injection, and hand milked to empty the udder. After 3 h, milk production was obtained after the same procedure. Quadratic effect for milk production (142.4, 179.8, 212.6, and 202.9 g/3 h) and cubic effect for DMI (2.27, 2.69, 3.25, and 3.00 kg/d) were observed as SH inclusion increased from 0 to 85% of the dietary DM. Milk fat (7.59, 7.86, 7.59, and 7.74%), protein (4.53, 4.43, 4.40, and 4.55%), and total solids (18.24, 18.54, 18.39, and 18.64%) did not differ among the 70% forage-based diet and diets with SH NDF replacing 33, 67, or 100% of the NDF. A linear increase in lactose concentration was observed with SH inclusion. Ewe BW gain during the trial showed a cubic response (0.37, 0.03, 4.80, and 2.80 kg) with SH inclusion. The preweaning ADG of lambs increased linearly, and ADG of lambs after weaning decreased linearly with SH inclusion. Final BW of lambs (2 wk after weaning) did not differ among treatments. Eating behavior observations were conducted with 44 ewes. The same facilities, experimental design, dietary treatments, and feeding management were used. Observations were visually recorded every 5 min for a 24-h period when ewes were 46 +/- 6.8 d in milk. Eating time (min/d, min/g of DMI, and min/g of NDF intake) and time expended in rumination and chewing activities (min/g of DMI and min/g of NDF intake) decreased linearly with the addition of SH in the diets. The inclusion of SH improved DMI and milk production, also reflecting on the BW of lambs at weaning. Milk performance was not affected when SH NDF replaced 100% of hay NDF.

Potassium Soil Test Calibration for Lowland Rice on an Inceptisol

Potassium (K) plays an important role in many physiological and biochemical processes in plants and its adequate use is an important issue for sustainable economic crop production. Soil test-based K fertilizer recommendations are very limited for lowland rice (Oryza sativa L.) grown on Inceptisols. The objective of this study was to calibrate K soil testing for the response of lowland rice (cv. Ipagri 109) to added K. A field experiment was conducted in the farmers` field in the municipality of Lagoa da Confusao, State of Tocantins, central Brazil. The K rates used were 0, 125, 250, 375, 500, and 625 kg K ha-1 applied as broadcast and incorporated during sowing of the first rice crop. Rice responded significantly to K fertilization during 2 years of experimentation. Maximum grain yield of about 6,000 kg ha-1 was obtained with 57 mg K kg-1 soil in the first year and with 30 mg K kg-1 in the second year. This indicated that at low levels of K in the soil, nonexchangeable K was available for plant growth. Potassium use efficiency designated as agronomic efficiency (kg grain produced/kg K applied) decreased significantly in a quadratic fashion with increasing K level in the soil. Agronomic efficiency had a significantly linear association with grain yield. Hence, improving agronomic efficiency with management practices can improve rice yield.

Optimization of Pothomorphe umbellata (L.) Miquel topical formulations using experimental design

Pothomorphe umbellata is a native plant widely employed in the Brazilian popular medicine. This plant has been shown to exert a potent antioxidant activity on the skin and to delay the onset and reduce the incidence of UVB-induced skin damage and photoaging. The aim of this work was to optimize the appearance, the centrifuge stability and the permeation of emulsions containing R umbellata (0. 1% 4-nerolidylchatecol). Experimental design was used to study ternary mixtures models with constraints and graphical representation by phase diagrams. The constraints reduce the possible experimental domain, and for this reason, this methodology offers the maximum information while requiring the minimum investment. The results showed that the appearance follows a linear model, and that the aqueous phase was the principal factor affecting the appearance; the centrifuge stability parameter followed a mathernatic quadratic model and the interactions between factors produced the most stable emulsions; skin permeation was improved by the oil phase, following a linear model generated by data analysis. We propose as optimized P. umbellata formulation: 68.4% aqueous phase, 26.6% oil phase and 5.0% of self-emulsifying phase. This formulation displayed an acceptable compromise between factors and responses investigated. (c) 2007 Elsevier B.V. All rights reserved.

Influence of ammonium chloride feeding time and light intensity on the cultivation of Spirulina (Arthrospira) platensis

This study dealt with the influence of both the feeding time and light intensity on the fed-batch culture of the cyanobacterium Spirulina (Arthrospira) platensis using ammonium chloride as a nitrogen source. For this purpose, a 2 2 plus star central composite experimental design combined with response surface methodology was employed, and the maximum cell concentration (X-m), the cell productivity (P-X), and the yield of biomass on nitrogen (Y-X/N) were selected as the response variables. The optimum values of X-m (1,833 mgL(-1)) and Y-X/N (5.9 gg(-1)) estimated by the model at light intensity of 13 klux and feeding time of 17.2 days were very close to those obtained experimentally under these conditions (X-m = 1,771 +/- 41 mg L-1; Y-X/N = 5.7 +/- 0.17 gg(-1)). The cell productivity was a decreasing function of the ammonium chloride feeding time and a quadratic function of the light intensity. The protein and lipid contents of dry biomass collected at the end of cultivations were shown to decrease with increasing light intensity.