Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Time-lag in biological responses to landscape changes in a highly dynamic Atlantic forest region

Time-lagged responses of biological variables to landscape modifications are widely recognized, but rarely considered in ecological studies. In order to test for the existence of time-lags in the response of trees, small mammals, birds and frogs to changes in fragment area and connectivity, we studied a fragmented and highly dynamic landscape in the Atlantic forest region. We also investigated the biological correlates associated with differential responses among taxonomic groups. Species richness and abundance for four taxonomic groups were measured in 21 secondary forest fragments during the same period (2000-2002), following a standardized protocol. Data analyses were based on power regressions and model selection procedures. The model inputs included present (2000) and past (1962, 1981) fragment areas and connectivity, as well as observed changes in these parameters. Although past landscape structure was particularly relevant for trees, all taxonomic groups (except small mammals) were affected by landscape dynamics, exhibiting a time-lagged response. Furthermore, fragment area was more important for species groups with lower dispersal capacity, while species with higher dispersal ability had stronger responses to connectivity measures. Although these secondary forest fragments still maintain a large fraction of their original biodiversity, the delay in biological response combined with high rates of deforestation and fast forest regeneration imply in a reduction in the average age of the forest. This also indicates that future species losses are likely, especially those that are more strictly-forest dwellers. Conservation actions should be implemented to reduce species extinction, to maintain old-growth forests and to favour the regeneration process. Our results demonstrate that landscape history can strongly affect the present distribution pattern of species in fragmented landscapes, and should be considered in conservation planning. (C) 2009 Elsevier Ltd. All rights reserved.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Atenolol blunts blood pressure increase during dynamic resistance exercise in hypertensives

center dot Dynamic resistance exercise promotes a sizeable increase in blood pressure during its execution in non medicated hypertensives. WHAT THIS STUDY ADDS center dot Atenolol not only decreases blood pressure level but also mitigates the increase of blood pressure during dynamic resistance exercise in hypertensive patients. An increase in blood pressure during resistance exercise might be at least in part attributed to an increase in cardiac output. AIMS This study was conducted to determine whether atenolol was able to decrease BP level and mitigate BP increase during dynamic resistance exercise performed at three different intensities in hypertensives. METHODS Ten essential hypertensives (systolic/diastolic BP between 140/90 and 160/105 mmHg) were blindly studied after 6 weeks of placebo and atenolol. In each phase, volunteers executed, in a random order, three protocols of knee-extension exercises to fatigue: (i) one set at 100% of 1 RM; (ii) three sets at 80% of 1 RM; and (iii) three sets at 40% of 1 RM. Intra-arterial radial blood pressure was measured throughout the protocols. RESULTS Atenolol decreased systolic BP maximum values achieved during the three exercise protocols (100% = 186 +/- 4 vs. 215 +/- 7, 80% = 224 +/- 7 vs. 247 +/- 9 and 40% = 223 +/- 7 vs. 252 +/- 16 mmHg, P < 0.05). Atenolol also mitigated an increase in systolic BP in the first set of exercises (100% = +38 +/- 5 vs. +54 +/- 9; 80% = +68 +/- 11 vs. +84 +/- 13 and 40% = +69 +/- 7 vs. +84 +/- 14, mmHg, P < 0.05). Atenolol decreased diastolic BP values and mitigated its increase during exercise performed at 100% of 1 RM (126 +/- 6 vs. 145 +/- 6 and +41 +/- 6 vs. +52 +/- 6, mmHg, P < 0.05), but not at the other exercise intensities. CONCLUSIONS Atenolol was effective in both reducing systolic BP maximum values and mitigating BP increase during resistance exercise performed at different intensities in hypertensive subjects.

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Measuring Dynamic Oscillations of a Small Span Cable-Stayed Footbridge: Case Study Using L1 GPS Receivers

Highly redundant or statically undetermined structures, such as a cable-stayed bridge, have been of particular concern to the engineering community nowadays because of the complex parameters that must be taken into account for healthy monitoring. The purpose of this study was to verify the reliability and practicability of using GPS to characterize dynamic oscillations of small span bridges. The test was carried out on a cable-stayed wood footbridge at Escola de Engenharia de Sao Carlos-Universidade de Sao Paulo, Brazil. Initially a static load trial was carried out to get an idea of the deck amplitude and oscillation frequency. After that, a calibration trial was carried out by applying a well known oscillation on the rover antenna to check the environment detectable limits for the method used. Finally, a dynamic load trial was carried out by using GPS and a displacement transducer to measure the deck oscillation. The displacement transducer was used just to confirm the results obtained by the GPS. The results have shown that the frequencies and amplitude displacements obtained by the GPS are in good agreement with the displacement transducer responses. GPS can be used as a reliable tool to characterize the dynamic behavior of large structures such as cable-stayed footbridges undergoing dynamic loads.

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

BED NUCLEUS OF THE STRIA TERMINALIS alpha(1)- AND alpha(2)-ADRENOCEPTORS DIFFERENTIALLY MODULATE THE CARDIOVASCULAR RESPONSES TO EXERCISE IN RATS

Dynamic exercise evokes sustained blood pressure and heart rate (HR) increases. Although it is well accepted that there is a CNS mediation of cardiovascular adjustments during dynamic exercise, information on the role of specific CNS structures is still limited. The bed nucleus of the stria terminalis (BST) is involved in exercise-evoked cardiovascular responses in rats. However, the specific neurotransmitter involved in BST-related modulation of cardiovascular responses to dynamic exercise is still unclear. In the present study, we investigated the role of local BST adrenoceptors in the cardiovascular responses evoked when rats are submitted to an acute bout of exercise on a rodent treadmill. We observed that bilateral microinjection of the selective alpha 1-adrenoceptor antagonist WB4101 into the BST enhanced the HR increase evoked by dynamic exercise without affecting the mean arterial pressure (MAP) increase. Bilateral microinjection of the selective alpha 2-adrenoceptor antagonist RX821002 reduced exercise-evoked pressor response without changing the tachycardiac response. BST pretreatment with the nonselective beta-adrenoceptor antagonist propranolol did not affect exercise-related cardiovascular responses. BST treatment with either WB4101 or RX821002 did not affect motor performance in the open-field test, which indicates that effects of BST adrenoceptor antagonism in exercise-evoked cardiovascular responses were not due to changes in motor activity. The present findings are the first evidence showing the involvement of CNS adrenoceptors in cardiovascular responses during dynamic exercise. Our results indicate an inhibitory influence of BST alpha 1-adrenoceptor on the exercise-evoked HR response. Data also point to a facilitatory role played by the activation of BST alpha 2-adrenoceptor on the pressor response to dynamic exercise. (C) 2011 IBRO. Published by Elsevier Ltd. All rights reserved.

The bed nucleus of the stria terminalis modulates exercise-evoked cardiovascular responses in rats

Dynamic exercise evokes sustained cardiovascular changes, which are characterized by blood pressure and heart rate (HR) increases. Although it is well accepted that there is a central nervous system (CNS) mediation of cardiovascular adjustments during dynamic exercise, information on the role of specific CNS structures is limited. The bed nucleus of the stria terminalis (BST) is a forebrain structure known to be involved in central cardiovascular control. Based on this, we tested the hypothesis that BST modulates HR and mean arterial pressure (MAP) responses evoked when rats are submitted to dynamic exercise. Male Wistar rats were tested at three levels of exercise (0.4, 0.8 and 1 km h-1) on a rodent treadmill before and after BST treatment with CoCl(2), a non-selective neurotransmission blocker. Bilateral microinjection of CoCl(2) (1 nmol in 100 nl artificial cerebrospinal fluid) into the BST reduced the pressor response to exercise at 0.4 km h-1 as well as the tachycardic responses evoked by exercise at 0.4, 0.8 and 1 km h-1. The BST treatment with CoCl(2) did not affect baseline MAP or HR, suggesting a lack of tonic BST influence on cardiovascular parameters at rest. Moreover, BST treatment with CoCl(2) did not affect motor performance in the open-field test, which indicates that effects of BST inhibition on cardiovascular responses to dynamic exercise are not due to changes in motor activity. The present results suggest that local neurotransmission in the BST modulates exercise-related cardiovascular adjustments. Data indicate that BST facilitates pressor and tachycardic responses evoked by dynamic exercise in rats.

Dynamic picture of the inner asteroid belt: implications for the density, size and taxonomic distributions of real objects

In this paper, we construct a dynamic portrait of the inner asteroidal belt. We use information about the distribution of test particles, which were initially placed on a perfectly rectangular grid of initial conditions, after 4.2 Myr of gravitational interactions with the Sun and five planets, from Mars to Neptune. Using the spectral analysis method introduced by Michtchenko et al., the asteroidal behaviour is illustrated in detail on the dynamical, averaged and frequency maps. On the averaged and frequency maps, we superpose information on the proper elements and proper frequencies of real objects, extracted from the data base, AstDyS, constructed by Milani and Knezevic. A comparison of the maps with the distribution of real objects allows us to detect possible dynamical mechanisms acting in the domain under study; these mechanisms are related to mean-motion and secular resonances. We note that the two- and three-body mean-motion resonances and the secular resonances (strong linear and weaker non-linear) have an important role in the diffusive transportation of the objects. Their long-lasting action, overlaid with the Yarkovsky effect, may explain many observed features of the density, size and taxonomic distributions of the asteroids.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.