Form Of Dynamic Equations Research Articles

Dynamic modeling of closed-chain robotic manipulators in the presence of frictional dynamic forces: A planar case

In this paper, the phenomenon of impact-contact in a closed-loop robotic chain has been dynamically modeled. The motion of this system, which comprises rigid links and ideal joints, has two phases. In the flight phase, the system is suspended in the air and moves only under the effect of Earth’s gravity. And in the impact phase, the mentioned robotic mechanism collides with a rough surface. We first present the direct form of dynamic equations for an open chain robotic system in the suspension phase. Then by applying the constraints that originate from the closed topology of the examined kinematic chain, the differential equations of the closed-loop system are obtained for the flight phase. In the impact phase, the contact force model is employed for modeling the impact-contact phenomenon. Although this method of impact modeling is more realistic, it leads to the stiffening of motion equations. In order to solve these equations, a special computational algorithm has been developed in this paper. To achieve more realistic results, the force of friction has also been considered in the collision of system joints with the ground. The dynamic formulations of friction have been used to obtain the friction force. In these models, an additional state variable is added to system variables in order to simulate some of the existing friction phenomena. Another objective of this paper is to present a criterion for selecting the most suitable model for simulating the motion of closed-loop robotic systems in the presence of friction. In this regard, the four dynamic friction force models of Dahl, reset integrator, LuGre, and elasto-plastic have been compared with the two static models of Coulomb and Bengisu & Akay. Although the developed algorithm is able to simulate any closed-loop robotic system that comes into contact with an uneven surface, the simulation of a 5-rigid-link closed-loop mechanism in collision with a rough surface of sinusoidal profile has been presented in this paper.

Study of the hexapod dynamics using equations in redundant coordinates

The dynamics of hexapods (Stewart platforms) has been extensively studied for several decades. In this problem, the equations of motion are usually constructed using the basic theorems of mechanics. Lagrange equations of the second kind are often constructed for the same purpose. In the present paper, a new form of dynamic equations is considered. These equations are a special form of equations of motion of a system of rigid bodies (equations of dynamics in redundant coordinates). This approach is used to obtain the differential equations of motion of a hexapod in redundant coordinates. In this case, the loaded Stewart platform is considered as a rigid body, whose position is determined by setting the radius vector of the center of mass and the unit vectors of the body-axes system. From the vector form of the Lagrange equations of the first kind scalar differential equations of motion of the mechanical system under consideration are obtained. The obtained equations for some standard motions of the hexapod are numerically integrated. It is noted that the stable motion of the mechanical system under consideration can be obtained only with the introduction of feedbacks.

Electromagnetic effects on the stability of anisotropic cylinder

This paper is devoted to analyzing the stability of charged anisotropic cylinder using the radial perturbation scheme. For this purpose, we consider the non-static cylindrically symmetric self-gravitating system and apply both Eulerian as well as Lagrangian approaches to establish a linearized perturbed form of dynamical equations. The conservation of baryon number is used to evaluate perturbed radial pressure in terms of an adiabatic index. A variational principle is developed to find a characteristic frequency which helps to examine the combined effect of charge and anisotropy on the stability of gaseous star. It is found that dynamical instability can be prevented until the radius of cylinder exceeds the limit [Formula: see text] and anisotropy increases the instability up to the limiting value of [Formula: see text]. Finally, we conclude that the system becomes more stable by increasing the definite amount of charge gradually.

On a cotangent form of a nonholonomic lagrangian dynamics

A Lagrangian form of dynamic equations for nonlinear nonholonomic constraints was studied by the first author in a previous paper. The aim of this paper is to put these equations in a cotangent form, according to some regularity conditions. It is particularized as an example to a decelerated motion of a free particle, when some dual simple equations are obtained.

Dynamical instability of anisotropic homogeneous cylinder

In this paper, we consider a non-static cylindrically symmetric self-gravitating system with anisotropic matter configuration and investigate its stability regions by using a homogenous model. We establish perturbed form of dynamical equations by using Eulerian and Lagrangian approaches. The conservation of baryon number is applied to obtain adiabatic index as well as perturbed pressure. A variational principle is used to find characteristic frequency which helps to compute the instability criteria. It is found that dynamical instability can be prevented till the radius of a cylinder exceeds the limit R[Formula: see text]18. We conclude that the system becomes unstable against radial oscillations as the radial pressure increases relative to tangential pressure.

Reverse-engineering ecological theory from data.

Ecologists have long sought to understand the dynamics of populations and communities by deriving mathematical theory from first principles. Theoretical models often take the form of dynamical equations that comprise the ecological processes (e.g. competition, predation) believed to govern system dynamics. The inverse of this approach-inferring which processes and ecological interactions drive observed dynamics-remains an open problem in ecology. Here, we propose a way to attack this problem using a machine learning method known as symbolic regression, which seeks to discover relationships in time-series data and to express those relationships using dynamical equations. We found that this method could rapidly discover models that explained most of the variance in three classic demographic time series. More importantly, it reverse-engineered the models previously proposed by theoretical ecologists to describe these time series, capturing the core ecological processes these models describe and their functional forms. Our findings suggest a potentially powerful new way to merge theory development and data analysis.

Dynamic Modeling of a Six Degree-of-Freedom Flight Simulator Motion Base

This paper presents a closed-form solution for the direct dynamic model of a flight simulator motion base. The motion base consists of a six degree-of-freedom (6DOF) Stewart platform robotic manipulator driven by electromechanical actuators. The dynamic model is derived using the Newton–Euler method. Our derivation is closed to that of Dasgupta and Mruthyunjaya (1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012), however, we give some insights into the structure and properties of those equations, i.e., a kinematic model of the universal joint, inclusion of electromechanical actuator dynamics and the full dynamic equations in matrix form in terms of Euler angles and platform position vector. These expressions are interesting for control, simulation, and design of flight simulators motion bases. Development of a inverse dynamic control law by using coefficients matrices of dynamic equation and real aircraft trajectories are implemented and simulation results are also presented.

On the magnetorotational instability and elastic buckling.

This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almost-critical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Both the magnetic and elastic systems reduce to a simple one-dimensional wave equation with a non-local nonlinear feedback. Under transformation, the equation comprises a large number of mean-field interacting Duffing oscillators. This system was the first proven example of a strange attractor in a partial differential equation. Finding the same reduced equation in two natural applications suggests the model might result from other applications and could fall into a universal class based on symmetry.

Intelligent Model-Reference Method to Control of Industrial Robot Arm

Computed torque controller (CTC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness. In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty in computed torque controller.

Design High Precision Intelligent Nonlinear-Based Controller

Computed torque controller (CTC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness. In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty in computed torque controller.

Design Stable Robust Intelligent Nonlinear Controller for 6- DOF Serial Links Robot Manipulator

In this research parallel Proportional-Derivative (PD) fuzzy logic theory plus Integral part (I) is used to compensate the system dynamic uncertainty controller according to highly nonlinear control theory sliding mode controller. Sliding mode controller (SMC) is an important considerable robust nonlinear controller. In presence of uncertainties, this controller is used to control of highly nonlinear systems especially for multi degrees of freedom (DOF) serial links robot manipulator. In opposition, sliding mode controller is an effective controller but chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameters are two significant drawbacks. To reduce these challenges, new stable intelligent controller is introduce.

Design Modified Fuzzy PD Gravity Controller with Application to Continuum Robot

Refer to this research, a position modified parallel error-based fuzzy Proportional Derivative (PD) gravity controller is proposed for continuum robot manipulator. The main problem of the pure conventional nonlinear controller was equivalent dynamic formulation in uncertain systems. The main challenge of linear controllers is linearization techniques and the quality of performance. The nonlinear equivalent dynamic problem in uncertain system is solved by applied fuzzy logic theory to modified PD gravity. To estimate the continuum robot manipulator system's dynamic, proportional plus modified derivative with 7 rules Mamdani inference system is design and applied to modified PD gravity methodology. The proportional coefficient of controller is tuned by new methodology in limitation uncertainties. The results demonstrate that the proposed controller is a partly model-free controllers which works well in certain and partly uncertain system.

Design Modified Sliding Mode Controller with Parallel Fuzzy Inference System Compensator to Control of Spherical Motor

The increasing demand for multi-degree-of- freedom (DOF) actuators in a number of industries has motivated a flurry of research in the development of non-conventional actuators, spherical motor. This motor is capable of providing smooth and isotropic three- dimensional motion in a single joint. Not only can the spherical motor combine 3-DOF motion in a single joint, it has a large range of motion with no singularities in its workspace. The spherical motor, however, exhibits coupled, nonlinear and very complex dynamics that make the design and implementation of feedback controllers very challenging. The orientation- varying torque generated by the spherical motor also contributes to the challenges in controller design. This paper contributes to the on-going research effort by exploring alternate methods for nonlinear and robust controlling the motor. The robust sliding mode controller proposed in this paper is used to further demonstrate the appealing features exhibited by the spherical motor. In opposition, sliding mode controller is used in many applications especially to control of highly uncertain systems; it has two significant drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem and chattering phenomenon in uncertain system (e.g., spherical motor) can be solved by using artificial intelligence theorem and applied a modified linear controller to switching part of sliding mode controller. Using Lyapunov-type stability arguments, a robust modified linear fuzzy sliding mode controller is designed to achieve this objective. The controller developed in this paper is designed in a robust stabilizing torque is designed for the nominal spherical motor dynamics derived using the constrained Lagrangian formulation. The eventual stability of the controller depends on the torque generating capabilities of the spherical motor.

Design Parallel Fuzzy Partly Inverse Dynamic Method plus Gravity Control for Highly Nonlinear Continuum Robot

Refer to this research, a position parallel error-based fuzzy inverse dynamic plus gravity controller is proposed for continuum robot manipulator. The main problem of the pure inverse dynamic controller was equivalent dynamic formulation in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using fuzzy logic theory. To estimate the continuum robot manipulator system's dynamic, 49 rules Mamdani inference system is design and applied to inverse dynamic plus gravity methodology. This methodology is based on applied fuzzy logic in equivalent nonlinear dynamic part to estimate unknown parameters. The results demonstrate that the error-based parallel fuzzy inverse dynamic plus gravity controller is a partly model-free controllers which works well in certain and partly uncertain system.

Design Sliding Mode Controller of with Parallel Fuzzy Inference System Compensator to Control of Robot Manipulator

Sliding mode controller (SMC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon, and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem and chattering phenomenon in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness. In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty.

Model-Free Adaptive Fuzzy Sliding Mode Controller Optimized by Particle Swarm for Robot Manipulator

The main purpose of this paper is to design a suitable control scheme that confronts the uncertainties in a robot. Sliding mode controller (SMC) is one of the most important and powerful nonlinear robust controllers which has been applied to many non-linear systems. However, this controller has some intrinsic drawbacks, namely, the chattering phenomenon, equivalent dynamic formulation, and sensitivity to the noise. This paper focuses on applying artificial intelligence integrated with the sliding mode control theory. Proposed adaptive fuzzy sliding mode controller optimized by Particle swarm algorithm (AFSMC-PSO) is a Mamdani's error based fuzzy logic controller (FLS) with 7 rules integrated with sliding mode framework to provide the adaptation in order to eliminate the high frequency oscillation (chattering) and adjust the linear sliding surface slope in presence of many different disturbances and the best coefficients for the sliding surface were found by offline tuning Particle Swarm Optimization (PSO). Utilizing another fuzzy logic controller as an impressive manner to replace it with the equivalent dynamic part is the main goal to make the model free controller which compensate the unknown system dynamics parameters and obtain the desired control performance without exact information about the mathematical formulation of model.

Performance-Based Adaptive Gradient Descent Optimal Coefficient Fuzzy Sliding Mode Methodology

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is the main challenge in this paper. This paper focuses on the design and analysis of a chattering free Mamdani's fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller for highly nonlinear dynamic six degrees of freedom robot manipulator, in presence of uncertainties. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani's performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. Pure sliding mode controller and error-based fuzzy sliding mode controller have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain. Since the sliding surface gain is adjusted by gradient descent optimization method. Fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning gradient descent optimal fuzzy sliding mode controller based on switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).

Axial Vibration Analysis of Buried Pipeline under Earthquake Interaction

The model of buried pipeline is adopted as Euler-Bernoulli beam, which is acted by inner fluid and outer constrained soil. The differential equation of axial vibration is deduced, applying the Hamilton principle. The differential equation of axial vibration is changed into basic form of dynamics equations, considering earthquake excitation as random wave. Utilizing the method of the elasticity time-travel analysis to programming, the responses of the displacement and acceleration at the pipe midpoint obtained, moreover the pipe elements are analyzed. The soil parameter, pipe parameter, earthquake dynamic parameter are considered as the influence elements of pipe response. The characteristic of the soil has an influence on response of velocity and acceleration. Along with soil from soft to hard, the response of acceleration becomes smaller and smaller. In the same soil, the earthquake damage rate of the piping increases along with earthquake intensity increasing.

Transverse Vibration Analysis of Buried Pipeline under Earthquake Interaction

The vibration of buried pipeline is influenced by inner fluid and outer constrained soil. Euler-Bernoulli beam is analyzed in the vibration model of buried pipeline, using the Hamilton principle. In addition, the differential equations of transverse vibration of buried pipeline deduced by the mechanical model are transformed into basic form of dynamics equations, considering earthquake excitation as random wave. Using the method of the elasticity time-travel analysis to programming, the pipe element, the soil parameter and the earthquake dynamic parameter are analyzed in the Matlab software. With soil from soft to hard, the response of piping displacement becomes smaller and smaller. In the same soil, the earthquake damage rate of the piping becomes increaser and increaser with earthquake intensity increasing.

The d’Alembert–Lagrange equation exploited on a Riemannian manifold

In this paper, we present a geometric exploitation of the d’Alembert–Lagrange equation (or alternatively, Lagrange form of the d’Alembert’s principle) on a Riemannian manifold. We develop the d’Alembert–Lagrange equation in a geometric form, as well as an explicit analytic form with respect to an arbitrary frame in a coordinate neighborhood on the configuration manifold. We provide a procedure to determine the governing dynamic equations of motion. Examples are given to illustrate the new formulation of dynamic equations and their relations to alternative ones. The objective is to provide a generalized perspective of governing equations of motion and its suitability for studying complex dynamic systems subject to nonholonomic constraints.