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.

Population Dynamics Modeling of Arapaima gigas

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males’ parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region.

Aspectos relacionados à utilização da equação logística quadrática em processos eletroquímicos

The concepts of dissipation and feedback are contained in the behavior of many natural dynamical systems. They have been used to predict the evolution of populations leading to the formulation of the quadratic logistic equation (QLE). More recently, the QLE has been used to provide a better understanding of physicochemical systems with promising results. Many physical, chemical and biological dynamic phenomena can be understood on the basis of the QLE and this work describes the main aspects of this equation and some recent applications, with emphasis on electrochemical systems. Also, it is illustrated the concept of potential energy as a convenient way of describing the stability of the fixed points of the QLE.

Lagrangian multipliers for coast-arcs of optimum space trajectories

Some properties of generalized canonical systems - special dynamical systems described by a Hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. A complete closed-form solution for Lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. Classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. For circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Network connectance and autonomy analyses of the photosynthetic apparatus in tropical tree species from different successional groups under contrasting irradiance conditions

Biological systems are complex dynamical systems whose relationships with environment have strong implications on their regulation and survival. From the interactions between plant and environment can emerge a quite complex network of plant responses rarely observed through classical analytical approaches. The objective of this current study was to test the hypothesis that photosynthetic responses of different tree species to increasing irradiance are related to changes in network connectances of gas exchange and photochemical apparatus, and alterations in plant autonomy in relation to the environment. The heat dissipative capacity through daily changes in leaf temperature was also evaluated. It indicated that the early successional species (Citharexylum myrianthum Cham. and Rhamnidium elaeocarpum Reiss.) were more efficient as dissipative structures than the late successional one (Cariniana legalis (Mart.) Kuntze), suggesting that the parameter deltaT (T ºCair - T ºCleaf) could be a simple tool in order to help the classification of successional classes of tropical trees. Our results indicated a pattern of network responses and autonomy changes under high irradiance. Considering the maintenance of daily CO2 assimilation, the tolerant species (C. myrianthum and R. elaeocarpum) to high irradiance trended to maintain stable the level of gas exchange network connectance and to increase the autonomy in relation to the environment. On the other hand, the late successional species (C. legalis) trended to lose autonomy, decreasing the network connectance of gas exchange. All species showed lower autonomy and higher network connectance of the photochemical apparatus under high irradiance.

Using passive techniques for vibration damping in mechanical systems

This paper examines two passive techniques for vibration reduction in mechanical systems: the first one is based on dynamic vibration absorbers (DVAs) and the second uses resonant circuit shunted (RCS) piezoceramics. Genetic algorithms are used to determine the optimal design parameters with respect to performance indexes, which are associated with the dynamical behavior of the system over selected frequency bands. The calculation of the frequency response functions (FRFs) of the composite structure (primary system + DVAs) is performed through a substructure coupling technique. A modal technique is used to determine the frequency response function of the structure containing shunted piezoceramics which are bonded to the primary structure. The use of both techniques simultaneously on the same structure is investigated. The methodology developed is illustrated by numerical applications in which the primary structure is represented by simple Euler-Bernoulli beams. However, the design aspects of vibration control devices presented in this paper can be extended to more complex structures.

Understanding the complexity in low dimensional systems

Complex System is any system that presents involved behavior, and is hard to be modeled by using the reductionist approach of successive subdivision, searching for ''elementary'' constituents. Nature provides us with plenty of examples of these systems, in fields as diverse as biology, chemistry, geology, physics, and fluid mechanics, and engineering. What happens, in general, is that for these systems we have a situation where a large number of both attracting and unstable chaotic sets coexist. As a result, we can have a rich and varied dynamical behavior, where many competing behaviors coexist. In this work, we present and discuss simple mechanical systems that are nice paradigms of Complex System, when they are subjected to random external noise. We argue that systems with few degrees of freedom can present the same complex behavior under quite general conditions.