Basic Dynamic Systems Research Articles

PEMODELAN SISTEM DINAMIK DAN IMPLEMENTASI SIMULINK PENGENDALIAN KESTABILAN UNMANNED AERIAL VEHICLE MULTIROTOR HEXACOPTER CARGO

The rapid growth of Unmanned Aerial Vehicle (UAV) technology, or drone, has shown its popularity and has been significantly applied to various purposes today. Nevertheless, with all the sophistication of drones, many related topics are still attractive, especially when a drone is designed to carry out a cargo mission. Thus, in this research, the dynamic model of a Hexacopter drone to deliver goods belongs to PT Aero Terra Scan is being developed. This dynamic modeling aims to further the drone's development by modeling it in 2 cases: no-payload and with a payload of 5 kg cases. The dynamic model of this Hexacopter is based on flight dynamics, a field of science studied in Aeronautical Engineering, and is implemented using Simulink. Through the results of this research, several conclusions have been withdrawn: (1) The drone's unstable nature characteristic inherently, even though it is analyzed from the initial hover condition. Thus, the drone and its system as a whole can never be separated with the feedback control that made it can maneuver adequately. (2) Several technical parameters of this Hexacopter, including the geometry, mass, the moment of inertia, until the estimation of motor throttle is required to achieve its hover conditions, both in the no-payload case and with-payload of 5 kg case. (3) The Hexacopter basic dynamic system model is based on the flight dynamics until its motion system control tuning through root locus map analysis using Simulink.

Dynamical aspects of a restricted three-vortex problem

Abstract Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects of the restricted three-vortex problem when one of the point vortices is assumed to be fixed at a location in the plane. The motion of the passive tracer is explored from a rotating frame of reference within which the free vortex with non-zero circulation remains stationary. By using basic dynamical system theory, it is shown that the vortex motion is always bounded, and any configuration of the three vortices must go through at least one collinear state. The present analysis reveals that any non-relative equilibrium solution of the vortex system either has periodic inter-vortex distances or it will asymptotically converge to a relative equilibrium configuration. The initial conditions required for different types of motion are explained in detail by exploiting the Hamiltonian structure of the problem. The underlying effects of a fixed vortex on the motion of vortices are also explored.

Central Limit Theorem in View of Subspace Convex-Cyclic Operators

In our work we have defined an operator called subspace convex-cyclic operator. The property of this newly defined operator relates eigenvalues which have eigenvectors of modulus one with kernels of the operator. We have also illustrated the effect of the subspace convex-cyclic operator when we let it function in linear dynamics and joining it with functional analysis. The work is done on infinite dimensional spaces which may make linear operators have dense orbits. Its property of measure preserving puts together probability space with measurable dynamics and widens the subject to ergodic theory. We have also applied Birkhoff’s Ergodic Theorem to give a modified version of subspace convex-cyclic operator. To work on a separable infinite Hilbert space, it is important to have Gaussian invariant measure from which we use eigenvectors of modulus one to get what we need to have. One of the important results that we have got from this paper is the study of Central Limit Theorem. We have shown that providing Gaussian measure, Central Limit Theorem holds under the certain conditions that are given to the defined operator. In general our work is theoretically new and is combining three basic concepts dynamical system, operator theory and ergodic theory under the measure and statistics theory.

When underwater degraded images meet logical stochastic resonance

Owing to light attenuation and high background noise, underwater images are significantly degraded, which hiders the development of underwater exploration. However, noise itself can be used to counter noise. In this paper, we apply logical stochastic resonance (LSR) to help detect weak objects from low-quality underwater images. On the basis of analysis of the physical character of underwater images, three models, namely basic dynamical system driven by Gaussian noise, basic dynamical system driven by Ornstein–Uhlenbeck (OU) noise, and dynamical system with extra delay loop, are chosen to study the performance of LSR-based object detection. The main workflow of LSR-based object detection is introduced. To analyze the performance of LSR, we perform explicit experiments and systematically discuss the interplay of additional noise with the system parameters. LSR is proven to be helpful in detecting weak objects from low-quality underwater images. Both OU noise and extra delay loop will help the whole system to maintain stability in a higher noisy background.

On Santilli's methods in Birkhoffian inverse problem

In this paper, we mainly study the simplification and improvement of Santilli's methods in Birkhoffian system, which is a more general type of basic dynamic system. The theories and methods of Birkhoffian dynamics have been used in hadron physics, quantum physics, rotational relativity theory, and fractional dynamics. As is well known, Lagrangian inverse problem, Hamiltonian inverse problem, and Birkhoffian inverse problem are the main objects of the dynamic inverse problems. The results given by Douglas (Douglas J 1941 Trans. Amer. Math. Soc. 50 71) and Havas[Havas P 1957 Nuovo Cimento Suppl. Ser. X5 363] show that only the self-adjoint Newtonian systems can be represented by Lagrange's equations, so the Lagrangian inverse problem is not universal for a holonomic constrained mechanical system. Furthermore, from the equivalence between Lagrange's equation and Hamilton's equation, Hamiltonian inverse problem is not universal. A natural question is then raised:whether there exists a self-adjoint dynamical model whose inverse problem is universal for holonomic constrained mechanical systems, in the field of analytical mechanics.An in-depth study of this issue in the 1980s by R. M. Santilli shows that a universal self-adjoint model exists for a holonomic constrained mechanic system that satisfies the basic conditions of locality, analyticity, and formality. The Birkhoff's equation is a natural extension of the Hamilton's equation, which shows the geometric properties of a nonconservative system as a general symplectic structure. This more general symplectic structure provides the geometry for the study of the non-conservative system preserving structure algorithms. Therefore, it is particularly important to study the problem of the Birkhoffian representation for the holonomic constrained system.For the inverse problem of Birkhoff's dynamics, studied mainly are the condition under which the mechanical systems can be represented by Birkhoff's equations and the construction method of Birkhoff's functions. However, due to the extensiveness and complexity of the holonomic nonconservative system, Birkhoff's dynamical functions do not have so simple construction method as Lagrange function and Hamilton function. The research results of this issue are very few. The existing construction methods are mainly for three constructions proposed by Santilli[Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York:Springer-Verlag) pp25-28], and there are still many technical problems to be solved in the applications of these methods.In order to solve these problems, this article mainly focuses on the following content. First, according to the existence theorem of Cauchy-Kovalevskaya type equations, we prove that the autonomous system always has an autonomous Birkhoffian representation. Second, a more concise method is given to prove that Santilli's second method can be simplified. An equivalent relationship implied in Santilli's third method is found, an improved Santilli's third method is proposed, and the MATLAB programmatic calculation of the method is studied. Finally, the full text is summarized and the results are discussed.

A torsional vibration damper based on a serial viscoelastic coupling of its seismic mass

The design of dynamic torsional vibration dampers of piston internal combustion engines is generally based on the principle of a dynamic damper with one degree of freedom in which the coupling of the seismic mass of the damper to the basic dynamic system is realized by a two-parameter parallel rheological model. With known realizations of this principle, it is usually difficult to achieve the optimum value of the respective damper parameters determined from the computational models, which is particularly true for optimal damping values. A dynamic torsional damper, based on the series arrangement principle of the elastic and damping element, offers better design options to achieve the optimum parameters of both the elastic and damping elements.

An unconventional rubber torsional vibration damper with two degrees of freedom

Rubber torsional dampers with one degree of freedom are a long-time proven tool for vibration damping in crank mechanisms, especially for passenger cars. Their advantages include, in particular, a relatively simple design and low production costs. The viscoelastic coupling of the damper ring with the basic dynamic system is realized by a rubber spring made of natural or synthetic rubber. The disadvantages of rubber dampers are, in particular, insufficient damping properties of the rubber spring compared with the optimal values resulting from the respective calculation models. This limits the application of rubber dampers to larger power units, such as diesel engines for tractors and trucks. The article deals with the design and optimization of the parameters of an unconventional rubber torsional damper with two degrees of freedom, which even with limited damping parameters of the rubber springs shows a significantly higher damping effect compared to the common design of rubber dampers with one degree of freedom.

Two kinds of generalized gradient representations for generalized Birkhoff system

Brikhoff system is a kind of basic dynamical system. The theory and method of Brikhoff system dynamics have been applied to the hadron physics, quantum physics, relativity and rotational relativistic system. The properties of gradient system not only play an important role in revealing the internal structure of dynamical system, but also help to explore the dynamical behavior of the system. In this paper, two kinds of generalized gradient representations for generalized Birkhoff system are studied. First, two kinds of generalized gradient systems, i. e., the generalized skew gradient system and the generalized gradient system with symmetric negative definite matrix, are proposed and the characteristics of the systems are studied. Second, the relations of stability between these two kinds of gradient system and the dynamical system are discussed. Third, the condition under which a generalized Birkhoff system can be considered as one of the two generalized gradient systems is obtained. Fourth, the gradient discrimination method of stability of the generalized Brikhoff system is given, and the characteristics of the generalized gradient systems can be used to study the stability of the generalized Birkhoff system. Finally, some examples are given to illustrate the application of the result. Therefore, once the mechanical system is expressed as the generalized gradient system, the stability and the asymptotic stability can be conveniently studied by using the properties of generalized gradient system. The difficulty in constructing Lyapunov functions is avoided, and a convenient method of analyzing the stability of mechanical system is provided.

Selenocentric reference coordinates net in the dynamic system

In this work, the selenocentric dynamic reference net was developed for the first time in the field of selendesy in order to address problems with space navigation. Three tasks were addressed in this research: a) the analysis of the mathematical model of the orthogonal coordinate transformation accuracy; b) the identification of the basic dynamic reference system objects with ones that are contained in reducing catalogues; and c) the extension of the base points net of the basic dynamic reference system. The result was a dynamic coordinate system summary that contains 1162 objects. The correlation analysis of this net was carried out and was found to coincide with modern dynamic coordinate systems that have been obtained. This selenocentric reference catalogue covers the full visible area of the Moon.

Windowed phase unwrapping using a first-order dynamic system following iso-phase contours

In this work, we show a windowed phase-unwrapping technique that uses a first-order dynamic system and scans the phase following its iso-phase contours. In previous works, we have shown that low-pass first-order dynamic systems are very robust and useful in phase-unwrapping problems. However, it is well known that all phase-unwrapping methods have a minimum signal-to-noise ratio that they tolerate. This paper shows that scanning the phase within local windows and using a path following strategy, the first-order unwrapping method increases its tolerance to noise. In this way, using the improved approach, we can unwrap phase maps where the basic dynamic phase-unwrapping system fails. Tests and results are given, as well as the source code in order to show the performance of the proposed method.

Design of Reset Control Systems: The PI + CI Compensator

Reset compensation has been used to overcome limitations of linear and time invariant (LTI) compensation. In this work, a new reset compensator, referred to as proportional and integral (PI) + CI (Clegg integrator), is introduced. It basically consists of adding a Clegg integrator to a PI compensator, with the goal of improving the closed loop response by using the nonlinear characteristic of this element. It turns out that by resetting a percentage of the integral term in a PI compensator, a significant improvement can be obtained over a well-tuned PI compensator in some relevant practical cases, such as systems with dominant lag and integrating systems. The work is devoted to the development of PI + CI tuning rules for basic dynamic systems in a wide range of applications, including first and higher order plus dead time systems.

AN INTRODUCTION TO QUANTITATIVE POINCARÉ RECURRENCE IN DYNAMICAL SYSTEMS

We present some recurrence results in the context of ergodic theory and dynamical systems. The main focus will be on smooth dynamical systems, in particular, those with some chaotic/hyperbolic behavior. The aim is to compute recurrence rates, limiting distributions of return times, and short returns. We choose to give the full proofs of the results directly related to recurrence, avoiding as much as possible to hide the ideas behind technical details. This drove us to consider as our basic dynamical system a one-dimensional expanding map of the interval. We note, however, that most of the arguments still apply to higher dimensional or less uniform situations, so that most of the statements continue to hold. Some basic notions from the thermodynamic formalism and the dimension theory of dynamical systems will be recalled.

Discussion of Dr. Judy Pickles's Paper: The Perspective of Nonlinear Open Systems Theory

Nonlinear dynamic systems theory originally began as an attempt to understand interactions in both living and nonliving systems such as ecosystems and cloud formations. Because it is a field and systems theory, dynamic systems concepts offer a rich source of patented applications to the psychoanalytic situation. This article first briefly reviews some basic dynamic systems principles. The clinical material presented by Dr. Pickles is then discussed with an effort to apply dynamic systems concepts. In particular, the notions of introducing novelty and the need for measured perturbation as part of the process of analytic change are emphasized.

New solvable many-body problems in the plane

We revisit an integrable (indeed, superintegrable and solvable) many-body model introduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model (or rather the more basic dynamical system that underlies its solvable character, and other avatars of it) can be conveniently reinterpreted as (rotation-invariant) models in the plane; and we thereby present several new (solvable, isochronous and rotation-invariant) many-body problems in the plane.

The integrity of dynamical systems

This paper opens a discussion on what are the basic properties, contents and concept of integrity of dynamical systems. The main research problem for the study of the integrity of dynamical systems is to recover measures of integrity of dynamical system structures and dynamical system processes by which we can conclude that system dynamics is stable, whether the system possesses integrity or whether that system loses integrity. By using two examples of free and forced transversal vibrations of the elastically connected double-plate systems and corresponding system with a discontinuity in elastical connection, we show some basic properties of the integrity of basic dynamical system. The integrity of corresponding dynamical processes in the behaviour of the whole system and its subsystems or in component processes and in response of the whole system with respect to corresponding system with discontinuity have been studied by using methods of Bernoulli's particular integral and Lagrange's method of constants variation. It is shown that one-frequency regimes change into multi-frequency regimes induced by discontinuity in the system, which represents the loss of integrity of the system and marks the appearance of the loss of integrity of corresponding processes.

On time reparametrizations and isomorphisms of impulsive dynamical systems

We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined

Asymmetrical chattering arc in vertical plane flight

The asymmetrical chattering arc of a winged space vehicle in the vertical plane reentry flight has been studied. With the use of dimensionless variables, we need only two parameters to specify the aerodynamic characteristics of the vehicle, one is the ballistic coefficient and the other is the maximum lift-to-drag ratio. The control variable is the normalized lift coefficient (NLC), the ratio of the lift coefficient and the lift coefficient at the maximum lift-to-drag ratio. The chattering flight happens when the NLC switches rapidly between its maximum and minimum values. We use the chattering control on the NLC to obtain maximum drag, or say, maximum deceleration. The asymmetrical chattering arc will be existing when the maximum and minimum NLCs have different absolute values. We started the study of the asymmetrical chattering from an example of basic dynamical system. It is found that a singular arc can be replaced by either a symmetrical or an asymmetrical chattering arc. The net effects on the lift and drag will be the weighted sums of the first and second orders of the maximum and minimum NLCs, respectively. The weighting factor is the percentage of acting time. A typical asymmetrical chattering reentry flight has the characteristics of maximum deceleration and phugoid oscillation.

Basic Stochastic Dynamic Systems of Growth and Trade

Uncertainties are intrinsic features of dynamic economic systems, and this paper considers the dynamic implications of factor endowment (labor, capital) uncertainties for a small growing trading economy. The stochastic growth models presented extend the open neoclassical two‐sector growth model (Deardorff) to a stochastic environment in continuous time, and extend the diffusion dynamics of one‐sector growth models (Merton; Bourguignon) to a trading two‐sector economy. It is demonstrated that the basic propositions of deterministic steady‐state growth and endogenous growth theory, under some specifications and certain parametric restrictions, are preserved within a stochastic framework.

Response of coupled one-dimensional dynamic systems

In a recent paper a formalism was developed for accounting for “The response of coupled basic one-dimensional dynamic systems”. In the present paper the formalism is extended in several ways. The most significant and fundamental of these is that the dynamic systems need not be basic. The propagator matrices, the blocked drive vectors, the specifically assigned response vectors, and the impedances of the dynamic systems at the stems of the junctions all assume new forms. In addition, it appears that one may incorporate in the impedance matrix of a junction not only the new forms of the impedances of the dynamic systems that relate to this junction, but also parallel impedance elements that describe interactions between non-adjacent series impedance elements. These new forms and interactions admit to direct incorporation in the formalism previously developed and, therefore, there is no need to repeat the development here. The reader, however, needs to become acquainted with the previous development if he wishes to benefit from an extension to the formalism afforded by the material presented herein.

Response of coupled basic one-dimensional dynamic systems

In a recent paper a formalism was developed by the authors for accounting for the “response of multiple coupled dynamic systems”. The dynamic systems were considered basic and one-dimensional; the impedances were assumed to be uniform over the spatial extents of the dynamic systems and the propagation mode in each dynamic system was assumed to be simple and defined by a single speed. In this paper the formalism is slightly extended to accommodate external drives that are applied within the coupling junctions that separate dynamic systems and to ascertain the response within these junctions were the need to arise. A junction is considered to be a boundary at which a number of dynamic systems may terminate. A boundary in turn may be composed of a number of elementary structural components which are stacked in a prescribed manner. The analytical procedure adopted for the extension is based on the concept of blocking the interfaces between a boundary and the dynamic systems that it terminates. The coupling across a boundary is then accounted for by assigning appropriately determined response velocities on these interfaces. In determining these response velocities the external drive components within the boundary are accommodated and the response components within the boundary are yielded as by-products.