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.

Biomass equations for forest regrowth in the eastern Amazon using randomized branch sampling

Forest regrowth occupies an extensive and increasing area in the Amazon basin, but accurate assessment of the impact of regrowth on carbon and nutrient cycles has been hampered by a paucity of available allometric equations. We develop pooled and species-specific equations for total aboveground biomass for a study site in the eastern Amazon that had been abandoned for 15 years. Field work was conducted using randomized branch sampling, a rapid technique that has seen little use in tropical forests. High consistency of sample paths in randomized branch sampling, as measured by the standard error of individual paths (14%), suggests the method may provide substantial efficiencies when compared to traditional procedures. The best fitting equations in this study used the traditional form Y=a×DBHb, where Y is biomass, DBH is diameter at breast height, and a and b are both species-specific parameters. Species-specific equations of the form Y=a(BA×H), where Y is biomass, BA is tree basal area, H is tree height, and a is a species-specific parameter, fit almost as well. Comparison with previously published equations indicated errors from -33% to +29% would have occurred using off-site relationships. We also present equations for stemwood, twigs, and foliage as biomass components.

Sex-Specific Equations to Estimate Maximum Oxygen Uptake in Cycle Ergometry

AbstractBackground:Aerobic fitness, assessed by measuring VO2max in maximum cardiopulmonary exercise testing (CPX) or by estimating VO2max through the use of equations in exercise testing, is a predictor of mortality. However, the error resulting from this estimate in a given individual can be high, affecting clinical decisions.Objective:To determine the error of estimate of VO2max in cycle ergometry in a population attending clinical exercise testing laboratories, and to propose sex-specific equations to minimize that error.Methods:This study assessed 1715 adults (18 to 91 years, 68% men) undertaking maximum CPX in a lower limbs cycle ergometer (LLCE) with ramp protocol. The percentage error (E%) between measured VO2max and that estimated from the modified ACSM equation (Lang et al. MSSE, 1992) was calculated. Then, estimation equations were developed: 1) for all the population tested (C-GENERAL); and 2) separately by sex (C-MEN and C-WOMEN).Results:Measured VO2max was higher in men than in WOMEN: -29.4 ± 10.5 and 24.2 ± 9.2 mL.(kg.min)-1 (p < 0.01). The equations for estimating VO2max [in mL.(kg.min)-1] were: C-GENERAL = [final workload (W)/body weight (kg)] x 10.483 + 7; C-MEN = [final workload (W)/body weight (kg)] x 10.791 + 7; and C-WOMEN = [final workload (W)/body weight (kg)] x 9.820 + 7. The E% for MEN was: -3.4 ± 13.4% (modified ACSM); 1.2 ± 13.2% (C-GENERAL); and -0.9 ± 13.4% (C-MEN) (p < 0.01). For WOMEN: -14.7 ± 17.4% (modified ACSM); -6.3 ± 16.5% (C-GENERAL); and -1.7 ± 16.2% (C-WOMEN) (p < 0.01).Conclusion:The error of estimate of VO2max by use of sex-specific equations was reduced, but not eliminated, in exercise tests on LLCE.

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Heavy rainfall equations for Santa Catarina, Brazil

Knowledge of intensity-duration-frequency (IDF) relationships of rainfall events is extremely important to determine the dimensions of surface drainage structures and soil erosion control. The purpose of this study was to obtain IDF equations of 13 rain gauge stations in the state of Santa Catarina in Brazil: Chapecó, Urussanga, Campos Novos, Florianópolis, Lages, Caçador, Itajaí, Itá, Ponte Serrada, Porto União, Videira, Laguna and São Joaquim. The daily rainfall data charts of each station were digitized and then the annual maximum rainfall series were determined for durations ranging from 5 to 1440 min. Based on these, with the Gumbel-Chow distribution, the maximum rainfall was estimated for durations ranging from 5 min to 24 h, considering return periods of 2, 5, 10, 20, 25, 50, and 100 years,. Data agreement with the Gumbel-Chow model was verified by the Kolmogorov-Smirnov test, at 5 % significance level. For each rain gauge station, two IDF equations of rainfall events were adjusted, one for durations from 5 to 120 min and the other from 120 to 1440 min. The results show a high variability in maximum intensity of rainfall events among the studied stations. Highest values of coefficients of variation in the annual maximum series of rainfall were observed for durations of over 600 min at the stations of the coastal region of Santa Catarina.

Estimating the value of the metal-ligand bond dissociation enthalpy<D> (M-L) for adducts using empirical equations supported by TG data

In this work is presented and tested (for 106 adducts, mainly of the zinc group halides) two empirical equations supported in TG data to estimate the value of the metal-ligand bond dissociation enthalpy for adducts: <D> (M-O) = t i / g if t i < 420 K and <D> (M-O) = (t i / g ) - 7,75 . 10-2 . t i if t i > 420 K. In this empirical equations, t i is the thermodynamic temperature of the beginning of the thermal decomposition of the adduct, as determined by thermogravimetry, andg is a constant factor that is function of the metal halide considered and of the number of ligands, but is not dependant of the ligand itself. To half of the tested adducts the difference between experimental and calculated values was less than 5%. To about 80% of the tested adducts, the difference between the experimental (calorimetric) and the calculated (using the proposed equations) values are less than 15%.

Low-flow estimates in regions of extrapolation of the regionalization equations: a new concept

ABSTRACT Knowledge of natural water availability, which is characterized by low flows, is essential for planning and management of water resources. One of the most widely used hydrological techniques to determine streamflow is regionalization, but the extrapolation of regionalization equations beyond the limits of sample data is not recommended. This paper proposes a new method for reducing overestimation errors associated with the extrapolation of regionalization equations for low flows. The method is based on the use of a threshold value for the maximum specific low flow discharge estimated at the gauging sites that are used in the regionalization. When a specific low flow, which has been estimated using the regionalization equation, exceeds the threshold value, the low flow can be obtained by multiplying the drainage area by the threshold value. This restriction imposes a physical limit to the low flow, which reduces the error of overestimating flows in regions of extrapolation. A case study was done in the Urucuia river basin, in Brazil, and the results showed the regionalization equation to perform positively in reducing the risk of extrapolation.

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.

Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

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.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.