Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Effects of levels of potassium and nitrogen on yields and post-harvest conservation of onions in winter

Potassium and nitrogen are the elements present in the highest percentage in the onion dry matter. The objective of this experiment was to evaluate yield and post-harvest conservation of Vale Ouro IPA-11 onion cultivar regarding to nitrogen and potassium levels. The experiment was carried out in Petrolina-PE, Brazil, from June to September 2009. The experimental design was a completely randomized block in a 4 x 3 factorial design, composed of four nitrogen levels (0, 60, 120 and 180 kg ha-1) and three potassium levels (0, 90 and 180 kg ha-1) with three replications. The highest yield of commercial bulbs was achieved at an estimated N level of 172.6 kg ha-1. The lowest yield of noncommercial bulbs was estimated at N level of 147.0 kg ha-1. Lower percentage of smaller bulbs (class 2) were obtained by increasing levels of N x K, with a quadratic effect at the dose of 90 kg ha-1 K2O and minimum production point with 127.6 kg N ha-1 (20.3%). Regarding larger caliber bulbs (class 4), linear effects were found both in the absence and for the level of 90 kg ha-1 of K2O as levels of N were increased. When the highest level of 180 kg ha-1 K2O was applied, the level of 92.8 kg ha-1 of N was estimated as the one that would promote the highest bulb yield of this class (35.4%), and 5.3% was found in the lack of potassium fertilization.

Application of GA3 and girdling of branches on the production of extemporaneous fruits of 'Tahiti' acid lime

The objective of this study was to evaluate the effect of girdling of branches and the application of GA3, still in the main crop flowering on the formation of reproductive structures, the fruit set of the following extemporaneous flowering of 'Tahiti' acid lime. This work used a randomized block design with five replications in a 4x3 factorial design. The first factor was the foliar application of GA3, 88 days before extemporaneous flowering at five concentrations (0, 7, 14 and 21 mg.L-1). The second factor was the girdling times, 108 days before flowering onset (A108AF), 78 days before flowering (A78AF) plus no-girdling control (NG). In extemporaneous flowering, the proportion of buds, flowers and fruits that abscised was 38.75, 31.25 and 18.64% respectively and 11.34% of all reproductive structures formed were collected. GA3 did not affect fruit set. Girdling increased fruit set by 229 and 256% at A108DAF and A78DAF respectively, in relation to NG plants. The GA3 reduced the formation of floral structures, which resulted in a quadratic increase in field production by reducing the competition for photoassimilates among fruits. The concentration of 21 mg.L-1 was the most productive, with 15.97 fruit.plant-1.

Detection of incipient left ventricular hypertrophy in mild to moderate arterial hypertension with normal electrocardiogram and echocardiogram: a new use for signal-averaged electrocardiography

OBJECTIVE: To assess signal-averaged electrocardiogram (SAECG) for diagnosing incipient left ventricular hypertrophy (LVH). METHODS: A study with 115 individuals was carried out. The individuals were divided as follows: GI - 38 healthy individuals; GII - 47 individuals with mild to moderate hypertension and normal findings on echocardiogram and ECG; and GIII - 30 individuals with hypertension and documented LVH. The magnitude vector of the SAECG was analyzed with the high-pass cutoff frequency of 40 Hz through the bidirectional four-pole Butterworth high-pass digital filter. The mean quadratic root of the total QRS voltage (RMST) and the two-dimensional integral of the QRS area of the spectro-temporal map were analyzed between 0 and 30 Hz for the frequency domain (Int FD), and between 40 and 250 Hz for the time domain (Int TD). The electrocardiographic criterion for LVH was based on the Cornell Product. Left ventricular mass was calculated with the Devereux formula. RESULTS: All parameters analyzed increased from GI to GIII, except for Int FD (GII vs GIII) and RMST log (GII vs GIII). Int TD showed greater accuracy for detecting LVH with an appropriate cutoff > 8 (sensitivity of 55%, specificity of 81%). Positive values (> 8) were found in 56.5% of the G II patients and in 18.4% of the GI patients (p< 0.0005). CONCLUSION: SAECG can be used in the early diagnosis of LVH in hypertensive patients with normal ECG and echocardiogram.

Estudo sôbre as temperaturas médias em Campinas

This paper deals with the study by orthogonal polynomials of trends in the mean annual and mean monthly temperatures (in degrees Centigrade) in Campinas (State of São Paulo, Brasil), from 1890 up to 1956. Only 4 months were studied (January, April, July and October) taken as typical of their respective season. For the annual averages both linear and quadratic components were significant, the regression equation being y = 19.95 - 0.0219 x + 0.00057 x², where y is the temperature (in degrees Centigrade) and x is the number of years after 1889. Thus 1890 corresponds to x = 1, 1891, to x = 2, etc. The equation shows a minimum for the year 1908, with a calculated mean y = 19.74. The expected means by the regression equation are given below. Anual temperature means for Campinas (SP, Brasil) calculated by the regression equation Year Annual mean (Degrees Centigrade) 1890 19.93 1900 10.78 1908 19.74 (minimum) 1010 19.75 1920 19.82 1930 20.01 1940 20.32 1950 20.74 1956 21.05 The mean for 67 years was 20.08°C with standard error of the mean 0.08°G. For January the regression equation was y = 23.08 - 0.0661 x + 0.00122 x², with a minimum of 22.19°C for 1916. The average for 67 years was 22.70°C, with standard error 0.12°C. For April no component of regression was significant. The average was 20.42°C, with standard error 0.13°C. For July the regression equation was of first degree, y = 16.01 + 0.0140X. The average for 67 years was 16.49°C, with standard error of the mean 0.14°C. Finally, for October the regression equation was y = 20.55 - 0.0362x + 0.00078x², with a minimum of 20.13°C for 1912. The average was 20.52°C, with standard error of the mean equal to 0.14°C.

Studies of membrane fluidity and heart contractile force in Trypanosoma cruzi infected mice

In Chagas disease serious cardiac dysfunction can appear. We specifically studied the cardiac function by evaluating: ventricle contractile force and norepinephrine response, affinity and density of beta-adrenergic receptors, dynamic properties of myocardial membranes, and electrocardiography. Albino swiss mice (n = 250) were infected with 55 trypomastigotes, Tulahuen strain and studied at 35, 75, and 180 days post-infection, that correspond to the acute, indeterminate, and chronic phase respectively. Cardiac beta-adrenergic receptors' affinity, myocardial contractility, and norepinephrine response progressively decreased from the acute to the chronic phase of the disease (p < 0.01). The density (expressed as fmol/mg.prot) of the receptors was similar to non-infected mice (71.96 ± 0.36) in both the acute (78.24 ± 1.67) and indeterminate phases (77.28 ± 0.91), but lower in the chronic disease (53.32 ± 0.71). Electrocardiographic abnormalities began in the acute phase and were found in 65% of the infected-mice during the indeterminate and chronic phases. Membrane contents of triglycerides, cholesterol, and anisotropy were similar in all groups. A quadratic correlation between the affinity to beta-adrenergic receptors and cardiac contractile force was obtained. In conclusion the changes in cardiac beta-adrenergic receptors suggests a correlation between the modified beta-adrenergic receptors affinity and the cardiac contractile force.

Flooded rice yield as affected by levels of water salinity in different stages of its cycle

Losses of productivity of flooded rice in the State of Rio Grande do Sul, Brazil, may occur in the Coastal Plains and in the Southern region due to the use of saline water from coastal rivers, ponds and the Laguna dos Patos lagoon, and the sensibility of the plants are variable according to its stage of development. The purpose of this research was to evaluate the production of rice grains and its components, spikelet sterility and the phenological development of rice at different levels of salinity in different periods of its cycle. The experiment was conducted in a greenhouse, in pots filled with 11 dm³ of an Albaqualf. The levels of salinity were 0.3 (control), 0.75, 1.5, 3.0 and 4.5 dS m-1 kept in the water layer by adding a salt solution of sodium chloride, except for the control, in different periods of rice development: tillering initiation to panicle initiation; tillering initiation to full flowering; tillering initiation to physiological maturity; panicle initiation to full flowering; panicle initiation to physiological maturity and full flowering to physiological maturity. The number of panicles per pot, the number of spikelets per panicle, the 1,000-kernel weight, the spikelet sterility, the grain yield and phenology were evaluated. All characteristics were negatively affected, in a quadratic manner, with increased salinity in all periods of rice development. Among the yield components evaluated, the one most closely related to grain yields of rice was the spikelet sterility.

Structural quality of a no-tillage red latosol 50 months after gypsum aplication

Gypsum application may enhance the soil quality for plants in terms of soil chemical and physical properties. The objective of this study was to evaluate the effects of gypsum application on the structural quality of a no-tillage Red Latosol. The experiment was initiated in September 2005 in Guarapuava-PR, with gypsum applications of 0; 4; 8; and 12 Mg ha-1 on the soil surface. In November 2009, two soil blocks were sampled from the 0-0.3 m layer for visual evaluation of the soil structure quality (Sq) and to determine the aggregate-tensile strength (ATS). Soil penetration resistance (PR) and gravimetric moisture (H%) of the 0-0.300 m layer were evaluated, and soil cores were collected (layers 0.000-0.075 and 0.075-0.150 m), to determine soil bulk density (BD), total soil porosity (TP), microporosity (Mi), and macroporosity (Ma). Data were subjected to analysis of regression at 5 %. No significant effects of gypsum application on ATS and H % of aggregates were observed, but for Sq, a quadratic effect (0.000-0.075 m) and linear increase (0.075-0.150 and 0.150-0.300 m) were stated, indicating soil quality decrease, although Sq remained mostly below 3.0, with good to intermediate soil quality. Soil PR increased with gypsum, but also remained below critical levels. No effect was observed for soil H % at the moment of PR determination on the field. The gypsum applications decreased BD in the 0.075-0.150 m layer, and increased PT and Ma, while in 0.000-0.075 m some Ma was converted to Mi, without affecting PT and BD. These last results indicate a gain in soil structural quality by gypsum applications, but the higher scores of soil structure and values of soil penetration resistance, though still below thresholds, should be monitored to prevent limitations to soil use in the future.

Brachiaria sp yield and nutrient contents after nitrogen and sulphur fertilization

Among the production factors, adequate fertilization is an important tool to raise the productivity of pastoral systems and consequently increase the share of Brazil in the supply chain of primary agricultural products at the global level. The objective of this study was to evaluate the interaction of nitrogen and sulfur fertilization in BRACHIARIA DECUMBENS: Stapf. The experiment in pots with Dystrophic Oxisol was evaluated in a completely randomized design with four replications in a 5 x 3 factorial arrangement, involving five N doses (0, 100, 200, 400, and 800 mg dm-3) in the form of ammonium nitrate and three S doses (0, 20 and 80 mg dm-3) in the form of calcium sulfate, with a total of 15 treatments. In the treatments with low S dose, calcium was provided as calcium chloride, to ensure a homogeneous Ca supply in all treatments. The results showed that the tiller production and dry weight of green leaves and of stems + sheaths and total dry weight were favored by the combination of N and S fertilizer, while the proportion of dry leaves was reduced. Nitrogen fertilization raised the N contents in green leaves and stems + sheaths and reduced K contents in fresh and dry leaves. The response to S rates in the N content of green leaves was quadratic.

Soil fertility, nutrition and yield of maize and barley with gypsum application on soil surface in no-till

Annual crop yield and nutrition have shown differentiated responses to modifications in soil chemical properties brought about by gypsum application. The aim of this study was to evaluate the effect of gypsum application rates on the chemical properties of a Latossolo Bruno (Clayey Oxisol), as well as on the nutrition and yield of a maize-barley succession under no-till. The experiment was set up in November 2009 in Guarapuava, Parana, Brazil, applying gypsum rates of 0.0, 1.5, 3.0, 4.5, and 6.0 Mg ha-1 to the soil surface upon sowing maize, with crop succession of barley. Gypsum application decreased the levels of Al3+ and Mg2+ in the 0.0-0.1 m layer and increased soil pH in the layers from 0.2-0.6 m depth. Gypsum application has increased the levels of Ca2+ in all soil layers up to 0.6 m, and the levels of S-SO4(2-) up to 0.8 m. In both crops, the leaf concentrations of Ca and S were increased while Mg concentrations have decreased as a function of gypsum rates. There was also an effect of gypsum rates on grain yield, with a quadratic response of maize and a linear increase for barley. Yield increases were up to 11 and 12 % in relation to control for the maximum technical efficiency (MTE) rates of 3.8 and 6.0 Mg ha-1 of gypsum, respectively. Gypsum application improved soil fertility in the profile, especially in the subsurface, as well as plant nutrition, increasing the yields of maize and barley.

Do Rates and Splitting of Phosphogypsum Applications Influence the Soil and Annual Crops in a No-Tillage System?

ABSTRACT Applications of phosphogypsum (PG) provide nutrients to the soil and reduce Al3+ activity, favoring soil fertility and root growth, but allow Mg2+ mobilization through the soil profile, resulting in variations in the PG rate required to achieve the optimum crop yield. This study evaluated the effect of application rates and splitting of PG on soil fertility of a Typic Hapludox, as well as the influence on annual crops under no-tillage. Using a (4 × 3) + 1 factorial structure, the treatments consisted of four PG rates (3, 6, 9, and 12 Mg ha-1) and three split applications (P1 = 100 % in 2009; P2 = 50+50 % in 2009 and 2010; P3 = 33+33+33 % in 2009, 2010 and 2011), plus a control without PG. The soil was sampled six months after the last PG application, in stratified layers to a depth of 0.8 m. Corn, wheat and soybean were sown between November 2011 and December 2012, and leaf samples were collected for analysis when at least 50 % of the plants showed reproductive structures. The application of PG increased Ca2+ concentrations in all sampled soil layers and the soil pH between 0.2 and 0.8 m, and reduced the concentrations of Al3+ in all layers and of Mg2+ to a depth of 0.6 m, without any effect of splitting the applications. The soil Ca/Mg ratio increased linearly to a depth of 0.6 m with the rates and were found to be higher in the 0.0-0.1 m layer of the P2 and P3 treatments than without splitting (P1). Sulfur concentrations increased linearly by application rates to a depth of 0.8 m, decreasing in the order P3>P2>P1 to a depth of 0.4 m and were higher in the treatments P3 and P2 than P1 between 0.4-0.6 m, whereas no differences were observed in the 0.6-0.8 m layer. No effect was recorded for K, P and potential acidity (H+Al). The leaf Ca and S concentration increased, while Mg decreased for all crops treated with PG, and there was no effect of splitting the application. The yield response of corn to PG rates was quadratic, with the maximum technical efficiency achieved at 6.38 Mg ha-1 of PG, while wheat yield increased linearly in a growing season with a drought period. Soybean yield was not affected by the PG rate, and splitting had no effect on the yield of any of the crops. Phosphogypsum improved soil fertility in the profile, however, Mg2+ migrated downwards, regardless of application splitting. Splitting the PG application induced a higher Ca/Mg ratio in the 0.0-0.1 m layer and less S leaching, but did not affect the crop yield. The application rates had no effect on soybean yield, but were beneficial for corn and, especially, for wheat, which was affected by a drought period during growth.

Relationship between potassium fertilization and panicle blast severity in upland rice

The influence of K2O (0, 40, 80, 120 kg ha-1) at varying rates of N application (0, 30, 60 kg ha-1) at planting, on panicle blast (Pyricularia grisea (Cooke) Sacc.) was studied in a field experiment conducted during three consecutive years with the upland rice cultivar Douradão. Panicle blast severity decreased with increasing rates of potassium in the absence of nitrogen (N0). The relationship between panicle blast and K rates was quadratic at 30 kg ha-1 of nitrogen. Significant response to K fertilization was not obtained at 60 kg ha-1 of nitrogen in relation to panicle blast severity.

Effect of soil-water tension on herbaceous cotton yield

A field experiment was conducted during two years, 1990/91, in an alluvial soil, in the State of Paraíba, Brazil, to study the effect of the levels of soil-water tension, 50, 100, 200, 300, 400 and 600 kPa, at 20 cm depth, on upland cotton (Gossypium hirsutum L.r. latifolium Hutch, cv. CNPA-6H) yield. The experimental design was a complete randomized block with six treatments and four repetitions. There was an effect of the treatments on plant height, leaf area index and cotton yield, but the precocity index was not modified. Water should be applied when the soil-water tension, measured at 20 cm depth, reaches values around 200 kPa. There was a quadratic (R² = 0.893**) response of cotton yields to soil water tension, with the maximum when water was applied at 52% of soil water depletion.