The connected graph method in mathematical modeling of system dynamics for systems with distributed link masses

It is well known that the traditional modeling theories adopt the Cartesian coordinates to establish the dynamic equation of solar array system. The order of this equation is often very high, which is inconvenient for controller design. The Cartesian coordinates are difficult to be measured in practice. In this paper, the joint coordinates are used as generalized variables to establish the dynamic equation of the solar array system. The single direction recursive construction method and the Jourdain’s velocity variation principle are used in modeling the system. The order of the established equation is lower, and the joint coordinates are easily measured in practice. Besides the dynamics modeling, joint friction and control design are extensively studied in this paper too. A three-dimensional revolute joint model is introduced, and the contribution of joint friction to the dynamic equation of the system is deduced. A fuzzy PD controller is designed to eliminate the drift of spacecraft caused by the deployment of solar array. In the end of this paper, numerical simulations are carried out to analyze the deployment dynamics and control effect of the solar array system with friction.

Многомоментные потоковые модели производственной линии (Multi-Movements Flow Model Production Line)

Mathematical modeling and nonlinear vibration analysis of a coupled hydro-generator shaft-foundation system

The intelligent control problem of space-based manipulator system with bounded control torques and uncertain parameters is studied. According to the system's momentum conservation and Lagrange's equation, the system's dynamics equation is established. An adaptive control based on saturated velocity filter for space-based manipulator system with bounded control torques and uncertain payload parameters is developed. The proposed control scheme overcomes the influence of the uncertain parameters on the control accuracy by using adaptive controller; limits the control torques by using hyperbolic functions, which lets the control more realistic. And in the control process, it doesn't need to measure and feed back the system's velocity signal by using the velocity filter, which makes the control simpler. The simulation validates the effectiveness of the proposed control scheme.

A semi-autonomous unmanned underwater vehicle (UUV), named LAURS, is being developed at the Laboratory of Sensors and Actuators at the University of Sao Paulo. The vehicle has been designed to provide inspection and intervention capabilities in specific missions of deep water oil fields. In this work, a method of modeling and identification of yaw motion dynamic system model of an open-frame underwater vehicle is presented. Using an on-board low cost magnetic compass sensor the method is based on the utilization of an uncoupled 1-DOF (degree of freedom) dynamic system equation and the application of the integral method which is the classical least squares algorithm applied to the integral form of the dynamic system equations. Experimental trials with the actual vehicle have been performed in a test tank and diving pool. During these experiments, thrusters responsible for yaw motion are driven by sinusoidal voltage signal profiles. An assessment of the feasibility of the method reveals that estimated dynamic system models are more reliable when considering slow and small sinusoidal voltage signal profiles, i.e. with larger periods and with relatively small amplitude and offset.

This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a second-order linear hyperbolic equation with variable coefficients. Solutions to this equation are constructed using Euler–Darboux transformations. This allows us to find new exact solutions of the equations of acoustics and gas dynamics, depending on two arbitrary functions.

Two classes of models for describing production flow lines are analyzed. The use of models of these classes for the design of highly efficient control systems of production lines, the technological route of which consists of a large number of technological operations, is analyzed. The division of the technological route into a large number of operations is caused by the development trend of modern production lines. Synchronization of production line equipment performance is provided by an accumulating buffer. A formalized description of the production line was used as a foundation for constructing equations for each models class. The common features of using each models class in the description of production systems, as well as the conditions for their application, are shown. The form of the system dynamics model and PDE model equations is substantiated. The assumption about a deterministic rate of processing parts and the absence of a time delay and feedback between the parameters of technological operations was made when deriving the equations. The use of generalized technological operations in the system dynamics model as a way to reduce the number of model equations is discussed. Two limiting transitions from the PDE model equations to the system dynamics equations are demonstrated. It is shown that the system dynamics equations are a special case of the PDE model equations, the result of the aggregation of production line parameters within the technological operation. The method for constructing level equations for the system dynamics model is substantiated. For production lines with a different number of operations, the solution to the problem of processing parts along a production line is presented. The comparative analysis of the solutions obtained using the system dynamics and PDE model equations is obtained

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.

We present a first-order recursive approach to sensitivity analysis based on the application of the direct differentiation method to the inverse Lagrangian dynamics of rigid multibody systems. Our method is simple and efficient and is characterized by the following features. Firstly, it describes the kinematics of multibody systems using branch connectivity graphs and joint-branch connectivity matrices. For most mechanical systems with an open-tree kinematic structure, this method turns out to be more efficient compared to other kinematic descriptions employing joint or link connectivity graphs. Secondly, a recursive sensitivity analysis is presented for a dynamic system with an open-tree kinematic structure and inverse dynamic equations described in terms of the Lagrangian formalism. Thirdly, known approaches to recursive inverse dynamic and sensitivity analyses are modified to include dynamic systems with external forces and torques acting simultaneously at all joints. Finally, the proposed method for sensitivity analysis is easy to implement and computationally efficient. It can be utilized to evaluate the derivatives of the dynamic equations of multibody systems in gradient-based optimization algorithms. It also allows less experienced users to perform sensitivity analyses using the power of high-level programming languages such as MATLAB. To illustrate the method, simulation results for a human body model are discussed. The shortcomings of the method and possible directions for future work are outlined.

A coupled dynamics model for a noncontact piezo-electric motor modulated by electromagnetic force is presented in this paper. Coupled dynamic equations of the motor system are derived. From the equations, the natural frequency, and modal function equations of the motor system are provided. Considering the nonlinear constitutive relation of a piezo-electric stack, nonlinear coupled dynamic equations of the motor system are established, and the nonlinear vibration frequency equation of the motor system is obtained. The linear and nonlinear coupled natural frequencies, modal shapes, and forced responses of the motor system are studied using the obtained equations. Modal shapes of the motor system are then classified, and the deviation between the nonlinear vibration frequency and linear natural frequency of the motor system and its variation with system parameters are analyzed. The research provides a useful reference for design and analysis of the dynamic behavior of the motor system.

A simplified approach to solving the equations of population dynamics (Lotka–Volterra equations), which is a nonlinear multidimensional system of ordinary differential equations of the first order, describing the competitive interaction of universities included in some world university ranking, is proposed. The phase variables in these equations are the values of the integral indicator of the university ranking, which is called Overall or Total Score. The simplification consists in reducing this system to a system of independent Verhulst equations with analytic solutions in exponents of time and passing from them to stationary solutions when time tends to infinity. It is shown that with this approach and a given growth rate Overall (Total) Score, it is possible to find symmetric coefficients of interuniversity competition for no more than three competing universities. When finding such coefficients for the first three universities in the THE ranking, numerical solutions of the original system of population dynamics equations were obtained using the Runge–Kutta method in MatLab. It is shown that the development of this approach, based on the equations of population dynamics, can consist in turning to the concept of competitive – cooperative university interactions. The system of differential equations describes the process of changing the integral indicator during the period between two ratings. Using the found values of the coefficients of interuniversity competition, the system is solved sequentially for all stages of the ranking, and the decisions at the previous stage are used as the initial conditions for the next one.

Dynamic response of shear-deformable axisymmetric orthotropic circular plate structures solved by the DQEM and EDQ based time integration schemes

Paper presents two models for gravity instability simulations using compressible gas formulations, and especially, using regularised gas dynamic equations, or, in other words, the quasi-gas dynamic (QGD) equation system. The first part of the paper describes the layer flow for a single-component gas and the second one is one-fluid approximation for a gas mixture. Here a density equation for a mixture is split in two equations for each gas species. Momentum and energy equations are presented for a mixture with unified velocity and temperature and aggregated density and pressure. Examples of numerical calculations of Rayleigh-Taylor instability for different Atwood numbers are shown. The obtained results correspond to the well-known behaviour features of the Rayleigh-Taylor instability.

The effects of flexible joints on the dynamic response and control of robot are studied in this paper. Firstly, the spatial robot model consisting of $n$ flexible joints and $n$ flexible links is built, and the dynamic equations of the robot system are derived via the Lagrangian's equations. The tensile deformation, bending deformation, torsional deformation, and nonlinear coupling deformation of the flexible link are considered. Furthermore, the effects of the flexible joint are also considered in order to provide an important theoretical basis for the research of the vibration suppression and control of robots. The flexible joint is simplified as a linear torsion spring with damping, and the mass effect of the flexible joint is also considered in the model. Secondly, the dynamic simulations of the spatial manipulators are done to explore the effects of the joint stiffness and damping on the dynamic response of the robot system. The results show that as the stiffness coefficient increases, the amplitude of dynamic response of the flexible robot decreases, and the vibration frequency of the system becomes larger. As the damping coefficient increases, the dynamic response of the flexible robot decreases, and the dynamic response decays faster. The vibration of the flexible robot can be suppressed by adjusting the values of the stiffness and damping of the flexible joint. Finally, in order to study the effects of the flexibility of the joint on the control system, the rigid-joint manipulator and flexible-joint manipulator are made to move under the same circular motion. Then the joint torques of the two system are obtained respectively by solving the inverse dynamics equations, and the influence of the flexibility of the joint on the dynamics control is studied. The results show that the actuating torques required in the flexible-joint system are reduced compared to that required in the rigid-joint system.

Dynamic modeling and control for dual-flexible servo system considering two-dimensional deformation based on neural network compensation