Small Vicinity Research Articles

Composite active disturbance rejection robust control for a prototype of an active damping artificial ankle prosthesis

AbstractThe problem of robust control applied to adjust the configuration of an ankle prosthesis based on disturbance estimation has been addressed in this study. Active disturbance rejection control was the paradigm used for controlling the robotic prosthesis by means of a direct active estimation. Based on this active estimation, the robust controller implemented the disturbance cancellation providing a fast converge to the origin of the tracking error. The uncertainties affecting the prosthesis dynamics were identified by a high‐order extended state high gain observer. This identification was used to force the tracking between the actual position and force needed in the ankle prosthesis and some reference values obtained by a biomechanical gait cycle analysis. Therefore, the estimated states were used to implement a robust output feedback controller that was effective to reject actively the perturbations. This rejection implemented within the controller forced the trajectory tracking to a small vicinity of the origin. A strategy based on composite Lyapunov function served to prove that tracking problem for the prosthesis was successfully solved despite the switching nature of the gait cycle. The controller was implemented in numerical simulations for showing the convergence of the tracking error. The convergence of this tracking error to the region around the origin was obtained within the first second of simulation.

Equilibrium states of thermodynamic systems in a small vicinity of the equilibrium values of parameters: Bifurcation, stability and sensitivity analyses

The dynamic behavior of thermodynamic systems described by a single order parameter and several control parameters is studied in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameters in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameters (bifurcation diagrams). Relations between the infinitesimal quantities of order parameters and the control of dynamical systems are given, and the formulae for the order parameter sensitivity are presented depending on the variations in the control parameters. In addition, we carried out specific calculations with respect to the thermodynamic systems described by one order parameter and several control parameters in the Landau-type kinetic potential. The peculiarities of the anomalous generation and extinction phenomenon of crystal nuclei at very low temperatures in non-equilibrium supercooled liquids are also presented.

Existence of elusive Kordylewsky cosmic dust clouds

Detection of areas of increased density of cosmic dust in near-Earth space is important from both theoretical and practical points of view. To continue our explication of the phenomenon of appearance-disappearance of the Kodylewski dust clouds, we consider dynamics of charged dust particles in the small vicinity of Lagrange libration point. The masses of particles are comparable to the masses of protons and electrons. These particles induce a self-consistent electric as well as a self-consistent gravitational fields. As a result, we obtain an existence of periodically changing stable configuration of an ensemble of the charged particles. It should be taken into account when planning space missions.

Complementary sliding mode control with adaptive switching gain for PMSM

Since the control system in a permanent magnet synchronous motor (PMSM) has uncertainties and disturbances, the switching gain is a key factor in effecting chattering in sliding mode control. An adaptive switching gain is proposed for complementary sliding mode control (CSMC) to regulate the PMSM velocity. The proposed switching gain is designed according to system uncertainties. When the value of the sliding modulus is outside the boundary layer, it is positive, resulting in an increase in the switching gain. Conversely, when it is negative, the gain is decreasing. Further, the proposed law considers an arbitrary small vicinity of the sliding manifold, in which the derivatives of the adaptive switching gains are inversely proportional to the sliding modulus to speed up the gain adjustment process. The proposed gain for complementary sliding mode control is applied to regulate the PMSM velocity; comparisons of experimental results show that the proposed gain has a faster gain adjustment process than CSMC and alleviates chattering, resulting in a greater velocity accuracy.

On the Number of Limit Cycles Bifurcated from Some Non-Polynomial Hamiltonian Systems

This paper studies the limit cycles produced by small perturbations of certain planar Hamiltonian systems. The limit cycles under consideration correspond to critical levels of the Hamiltonian, that is they are located in a small vicinity of a separatrix contour or a critical point. Two most interesting facts in the paper are that the Hamiltonian function is not a polynomial and that the system under consideration comes from a model of oscillator with a pair of irrational nonlinearities, which implies the transition from smooth to discontinuous dynamics. This model has been proposed recently by Han et al. in a paper published in 2012.

Fractional PD-IλDμ Error Manifolds for Robust Tracking Control of Robotic Manipulators

Linear proportional-integral-derivative (PID) controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders λ and μ, there has been studied the fractional-order PIλDμ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as, a more flexible structure and a preciser performance. In addition, proportional and derivative (PD) and PID error manifolds have been classically proposed; however, there remains the question on how FPID-like error manifolds perform for the control of nonlinear plants, such as robots. In this paper, this problem is addressed by proposing a PD-IλDμ error manifold for novel vector saturated control. The stability analysis shows convergence into a small vicinity of the origin, wherein, such hybrid combination of integer- and fractional-order error manifolds provides further insights into the closed-loop response of the nonlinear plant. Simulations studies are carried out to illustrate the feasibility of the proposed scheme.

Hydrodynamic bifurcation in electro-osmotically driven periodic flows

In this paper we report a novel inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially-periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability though a supercritical bifurcation. Surprisingly, the new flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20-30, and we discuss its potential applications in microfluidic devices.

Equations of an elliptic boundary layer in shells of revolution under shock normal edge loading

The asymptotic equations describing an elliptic boundary layer in shells of revolution at shock normal edge loading are obtained. The considered type of a boundary layer is concentrated in the small vicinity of Rayleigh front. Asymptotic methods in combinations with a symbolical method of Lurye are used. The elliptical equations describing behavior of a boundary layer on thickness for this boundary layer and the hyperbolic equations describing boundary conditions on faces are received.

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Focusing the Cherenkov radiation using dielectric concentrator: simulations and comparison with theory

We proceed with investigation of specific dielectric target that effectively concentrates Cherenkov radiation from a charged particle bunch into a small vicinity of the focus point located at the symmetry axis of the target. The case of “non-ideal concentration” where the charge velocity differs from the designed one was considered theoretically in our previous paper. In particular, we have noted that geometrical rays form caustics in this case, and areas of radiation concentration are shifted with respect to the designed focus point. Since the direction of this shift relates to the sign of the charge velocity deviation, this effect can be used for diagnostics of bunch velocity. Here we perform numerical simulations in COMSOL using frequency domain solver and compare simulated results with theoretical ones. In particular, we show that simulated focus area is indeed shifted with change in charge velocity and the position of this area correlate very well with analytical predictions.

Effects of phase singularity in the interference of two laser fields with a wide spectrum

The interference of laser beams with a wide spectrum is studied theoretically and numerically. It is shown that in the cross section of such intersecting beams in a small vicinity of zero of the complex mutual coherence function, the change in the argument of the slow amplitude of this function corresponds to the phase singularity. An approximate analytical representation of the mutual coherence function in the vicinity of the singularity point is given. It is found that an average ‘funnel’ diameter of the modulus of the mutual coherence function that arises in the singularity region does not depend on the intensity of the light beams and remains constant when the longitudinal coordinate changes. The emergence of phase dislocations in the interference pattern is established.

Bouncing solutions from generalized EoS

We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a generalized equation of state (GEoS) of the form p(rho )=Arho +Brho ^{lambda }, where A, B and lambda are constants. In our solution A=-1/3, lambda =1/2, and B<0 is kept as a free parameter. For particular values of the initial conditions, we find that our solution obeys the null energy condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, phi , with a positive kinetic energy and a potential V(phi ). We numerically compute the scalar field as a function of time as well as its potential V(phi ), and we find an analytical function for the potential that fits very accurately with the numerical data obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence there is no spontaneous symmetry minimum of V(phi ). We show numerically that the bouncing scenario is structurally stable in a small vicinity of the value A=-1/3. We also include the study of the evolution of the linear fluctuations due to linear perturbations in the metric. These perturbations show an oscillatory behavior near the bouncing and approach a constant at large scales.

Near-Optimal Hybrid Processing for Massive MIMO Systems via Matrix Decomposition

For the practical implementation of massive multiple-input multiple-output (MIMO) systems, the hybrid processing (precoding/combining) structure is promising to reduce the high cost rendered by large number of RF chains of the traditional processing structure. The hybrid processing is performed through low-dimensional digital baseband processing combined with analog RF processing enabled by phase shifters. We propose to design hybrid RF and baseband precoders/combiners for multi-stream transmission in point-to-point massive MIMO systems, by directly decomposing the pre-designed unconstrained digital precoder/combiner of a large dimension. The constant amplitude constraint of analog RF processing results in the matrix decomposition problem non-convex. Based on an alternate optimization technique, the non-convex matrix decomposition problem can be decoupled into a series of convex sub-problems and effectively solved by restricting the phase increment of each entry in the RF precoder/combiner within a small vicinity of its preceding iterate. A singular value decomposition based technique is proposed to secure an initial point sufficiently close to the global solution of the original non-convex problem. Through simulation, the convergence of the alternate optimization for such a matrix decomposition based hybrid processing (MD-HP) scheme is examined, and the performance of the MD-HP scheme is demonstrated to be near-optimal.

Hidden attractors localization in Chua circuit via the describing function method

In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.

Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure

The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors’ opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.

Organization of uniform dispersal for group of small satellites after their separation and acceptable spread at stages of their further approaches

Mutual-relative motion of satellites constellation after their placing into initial orbit is characterized the satellites reiterated approaches to minimal distances. Determined separation conditions for each satellite pair in constellation, which realization leads to minimal satellites approaches. It was sustained, that distances between satellites can reach extreme minimal values due to minor angular deviations of orbit planes and always occurring flight altitudes long-period oscillations. Received analytical relations for estimation of angular deviations and distances between satellites orbit planes at the phases of periodical approaches. It was approved that in some vicinity of orbit numbers can occur following almost simultaneously: small differences of angular distances from the equator for any satellite pair in constellation; minimal angular deviations of satellites orbit planes (in general they have different precession after separation of different directions and with various velocities). Analytical relationships were numerically confirmed with using software for satellites movement prediction at the phases of their approaches to the minimum distances. The area of satellites separation parameters was built, with its implementation in a small vicinity of flight orbits the satellites approach to distances less than 100 m. The minimum distance in the specified area according to the single calculations is ~10 m.

Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control

ABSTRACTThis paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.

Effector profiles distinguish formae speciales of Fusarium oxysporum

Formae speciales (ff.spp.) of the fungus Fusarium oxysporum are often polyphyletic within the species complex, making it impossible to identify them on the basis of conserved genes. However, sequences that determine host-specific pathogenicity may be expected to be similar between strains within the same forma specialis. Whole genome sequencing was performed on strains from five different ff.spp. (cucumerinum, niveum, melonis, radicis-cucumerinum and lycopersici). In each genome, genes for putative effectors were identified based on small size, secretion signal, and vicinity to a "miniature impala" transposable element. The candidate effector genes of all genomes were collected and the presence/absence patterns in each individual genome were clustered. Members of the same forma specialis turned out to group together, with cucurbit-infecting strains forming a supercluster separate from other ff.spp. Moreover, strains from different clonal lineages within the same forma specialis harbour identical effector gene sequences, supporting horizontal transfer of genetic material. These data offer new insight into the genetic basis of host specificity in the F. oxysporum species complex and show that (putative) effectors can be used to predict host specificity in F. oxysporum.

A New Adaptive Sliding-Mode Control Scheme for Application to Robot Manipulators

This paper presents a new adaptive sliding-mode control (ASMC) scheme that uses the time-delay estimation (TDE) technique, then applies the scheme to robot manipulators. The proposed ASMC uses a new adaptive law to achieve good tracking performance with small chattering effect. The new adaptive law considers an arbitrarily small vicinity of the sliding manifold, in which the derivatives of the adaptive gains are inversely proportional to the sliding variables. Such an adaptive law provides remarkably fast adaptation and chattering reduction near the sliding manifold. To yield the desirable closed-loop poles and simplify a complicated system model by adapting feedback compensation, the proposed ASMC scheme works together with a pole-placement control (PPC) and a TDE technique. It is shown that the tracking errors of the proposed ASMC scheme are guaranteed to be uniformly ultimately bounded (UUB) with arbitrarily small bound. The practical effectiveness and the fast adaptation of the proposed ASMC are illustrated in simulations and experiments with robot manipulators, and compared with those of an existing ASMC.

Robust disturbance rejection control of a biped robotic system using high-order extended state observer

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy.