Dynamic Modeling and Simulation of Parallel Mechanisms Using the Virtual Spring Approach

2000 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin ◽  
Li Cheng
Keyword(s):  
Closed Loop ◽  
Differential Algebraic Equations ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
New Approach ◽  
Flexible Links ◽  
Simulation Results ◽  
Loop Constraints ◽  
Virtual Springs ◽  
Good Agreement

Abstract A new approach for the dynamic simulation of parallel mechanisms or mechanical systems is presented in this paper. This approach uses virtual springs and dampers to include the closed-loop constraints thereby avoiding the solution of differential-algebraic equations. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the 6-dof Gough-Stewart platform. Simulation results are given for the four-bar linkages and the 6-dof manipulator. The results achieve a good agreement with the results obtained from other conventional approaches.

Closed Loop Resonator Based Compact UWB Antenna with Single Notched Band Varying between WLAN and X-band for UWB Applications

Frequenz ◽  
2020 ◽  
Vol 74 (5-6) ◽  
pp. 201-209
Author(s):  
Mohammad Ahmad Salamin ◽  
Sudipta Das ◽  
Asmaa Zugari
Keyword(s):  
Closed Loop ◽  
Ground Plane ◽  
Frequency Range ◽  
Uwb Antenna ◽  
Notched Band ◽  
X Band ◽  
Compact Size ◽  
Simulation Results ◽  
Uwb Applications ◽  
Good Agreement

AbstractIn this paper, a novel compact UWB antenna with variable notched band characteristics for UWB applications is presented. The designed antenna primarily consists of an adjusted elliptical shaped metallic patch and a partial ground plane. The proposed antenna has a compact size of only 17 × 17 mm2. The suggested antenna covers the frequency range from 3.1 GHz to 12 GHz. A single notched band has been achieved at 7.4 GHz with the aid of integrating a novel closed loop resonator at the back plane of the antenna. This notched band can be utilized to alleviate the interference impact with the downlink X-band applications. Besides, a square slot was cut in the loop in order to obtain a variable notched band. With the absence and the existence of this slot, the notched band can be varied to mitigate interference of the upper WLAN band (5.72–5.82 GHz) and X-band (7.25–7.75 GHz) with UWB applications. A good agreement between measurement and simulation results was achieved, which affirms the appropriateness of this antenna for UWB applications.

scholarly journals Modeling and PDC fuzzy control of planar parallel robot

2017 ◽  
Vol 14 (1) ◽  
pp. 172988141668711
Author(s):  
Benyamine Allouche ◽  
Antoine Dequidt ◽  
Laurent Vermeiren ◽  
Michel Dambrine
Keyword(s):  
Structural Characteristics ◽  
Differential Algebraic Equations ◽  
Parallel Robots ◽  
Linear Matrix ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Trajectory Tracking Control ◽  
Model Based ◽  
Takagi Sugeno

Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential–algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential–algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

scholarly journals An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

2022 ◽  
Vol 12 (2) ◽  
pp. 890
Author(s):  
Paweł Dra̧g
Keyword(s):  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Differential Algebraic Equations ◽  
Multiple Shooting ◽  
Small Range ◽  
Algebraic Equations ◽  
New Approach ◽  
Highly Nonlinear ◽  
Special Cases ◽  
Wide Range

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

scholarly journals A Generalized State-Space Aeroservoelastic Model Based on Tangential Interpolation

Aerospace ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 9 ◽  
Author(s):  
David Quero ◽  
Pierre Vuillemin ◽  
Charles Poussot-Vassal
Keyword(s):  
State Space ◽  
Reference Model ◽  
Differential Algebraic Equations ◽  
Summation Method ◽  
Algebraic Equations ◽  
Minimal Order ◽  
New Approach ◽  
Model Based ◽  
Generalized State Space ◽  
Generalized State

In this work, a new approach for the generation of a generalized state-space aeroservoelastic model based on tangential interpolation is presented. The resulting system of differential algebraic equations (DAE) is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). The new approach is applied first for the generation of an aerodynamic model for the bidimensional unsteady incompressible flow in the time domain. Next, an application on the generation of an aeroservoelastic model for loads evaluation of the flutter reduced order assessment (FERMAT) model under atmospheric disturbances is done, showing an excellent agreement with the reference model in the frequency domain. The proposed aeroservoelastic model of minimal order is suited for loads analysis and multivariable control design, and an application to a gust loads alleviation (GLA) strategy is shown.

Variational Analysis of a Two Link Slider-Crank Mechanism Using Polynomial Chaos Theory

2017 ◽  
Author(s):  
Paul S. Ryan ◽  
Sarah C. Baxter ◽  
Philip A. Voglewede
Keyword(s):  
Chaos Theory ◽  
Closed Loop ◽  
Polynomial Chaos ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Advantages And Disadvantages ◽  
Multi Body ◽  
Polynomial Chaos Theory ◽  
Body Dynamic ◽  
Crank Mechanism

Variation occurs in many closed loop multi-body dynamic (MBD) systems in the geometry, mass, or forces. Understanding how MBD systems respond to variation is imperative for the design of a robust system. However, simulation of how variation propagates into the solution is complicated as most MBD systems cannot be simplified into to a system of ordinary differential equations (ODE). This paper investigates polynomial chaos theory (PCT) as a means of quantifying the effects of uncertainty in a closed loop MBD system governed by differential algebraic equations (DAE). To demonstrate how PCT could be used, the motion of a two link slider-crank mechanism is simulated with variation in the link lengths. To validate and show the advantages and disadvantages of PCT in closed loop MBD systems, the PCT approach is compared to Monte Carlo simulations.

Symbolic Linearized Equations for Nonholonomic Multibody Systems With Closed-Loop Kinematics

2018 ◽  
Author(s):  
Márton Kuslits ◽  
Dieter Bestle
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Linearized Equations ◽  
Nonlinear Equations Of Motion ◽  
Loop Constraints

Multibody systems and associated equations of motion may be distinguished in many ways: holonomic and nonholonomic, linear and nonlinear, tree-structured and closed-loop kinematics, symbolic and numeric equations of motion. The present paper deals with a symbolic derivation of nonlinear equations of motion for nonholonomic multibody systems with closed-loop kinematics, where any generalized coordinates and velocities may be used for describing their kinematics. Loop constraints are taken into account by algebraic equations and Lagrange multipliers. The paper then focuses on the derivation of the corresponding linear equations of motion by eliminating the Lagrange multipliers and applying a computationally efficient symbolic linearization procedure. As demonstration example, a vehicle model with differential steering is used where validity of the approach is shown by comparing the behavior of the linearized equations with their nonlinear counterpart via simulations.

Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism

1990 ◽  
Vol 112 (4) ◽  
pp. 640-645 ◽  
Author(s):  
H. McClamroch ◽  
D. Wang
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Control Design ◽  
Algebraic Model ◽  
Differential Algebraic Equations ◽  
Linear Feedback ◽  
Control Law ◽  
Algebraic Equations ◽  
Constraint Force ◽  
Constrained System

A feedback control problem for a constrained mechanism is formulated and solved. The mechanism is controlled by forces applied to the mechanism which are to be adjusted according to a linear control law, based on feedback of the positions and velocities of the mechanism and feedback of the constraint force on the mechanism. The control objective is to achieve accurate and robust local regulation of the motion of the mechanism and of the constraint force on the mechanism. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic model of the constrained system and by the nonlinear characteristics of the model. The control design approach involves use of a certain nonlinear transformation which leads to a set of decoupled differential-algebraic equations; classical control design methodology can be applied to these latter equations. An example of a planar mechanism is studied in some detail, for two different regulation objectives. Specific control laws are developed using the described methodology. Comparisons are made with a closed loop system, where the control law is derived without proper consideration of the constraint force. Computer simulations are presented to demonstrate the several closed-loop properties.

scholarly journals Analysis of the growth kinetics of Fe2B layers by the integral method

2018 ◽  
Vol 54 (3) ◽  
pp. 361-367 ◽  
Author(s):  
M. Keddam ◽  
M. Kulka
Keyword(s):  
Diffusion Coefficients ◽  
Integral Method ◽  
Present Model ◽  
Armco Iron ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Boron Diffusion ◽  
Alternative Approach ◽  
Kinetics Of ◽  
Good Agreement

In this study, an alternative approach based on the integral method was proposed to estimate the values of boron diffusion coefficients in the Fe2B layers grown at the surface of Armco iron. The set of differential algebraic equations (DAE) system was obtained to estimate the value of activation energy for boron diffusion when pack-boriding of Armco iron in the range of 1123 to 1273 K taking into account the boride incubation time. The present model has been validated by making a comparison between the experimental value of Fe2B layer thickness obtained at 1253 K for 5 h and the predicted results by using two different approaches. A good agreement was observed between these two set of data.

Modeling, Realization, and Simulation of Thermo-Fluid Coupled Systems Using Singularly Perturbed Sliding Manifolds

2000 ◽  
Author(s):  
Brandon W. Gordon ◽  
Harry Asada
Keyword(s):  
State Space ◽  
Time Scale ◽  
Differential Algebraic Equations ◽  
Coupled Systems ◽  
Control Methods ◽  
Algebraic Equations ◽  
Singular Perturbation Method ◽  
New Approach ◽  
Sliding Control ◽  
Fluid Systems

Abstract A new approach based on sliding control is presented for modeling and simulation of thermo-fluid systems described by differential-algebraic equations (DAEs). The dynamics of thermo-fluid systems are often complicated by momentum interactions that occur on a time scale that is orders of magnitude faster than the time scale of interest. To address this problem the momentum equation is often modeled using algebraic steady state approximations. This will, in general, result in a model described by nonlinear DAEs for which few control methods are currently applicable. In this paper, the modeling problem is addressed using an approach that systematically constructs an explicit state space approximation of the DAEs. The state space model can in turn be used with existing control methods. This procedure, known as realization, is achieved by solving an associated nonlinear control problem by combining boundary layer sliding control with the singular perturbation method. The necessary criteria for key properties such as convergence are established. Further, the new approach is illustrated using a vapor compression cycle example. This demonstrates significant advantages over directly modeling momentum interactions.

Controlling a Dynamic System With Open and Closed Loops: Application to Ladder Climbing

1997 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas ◽  
Norman I. Badler
Keyword(s):  
Dynamic System ◽  
Closed Loop ◽  
Step Length ◽  
Initial Position ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Step Frequency ◽  
Joint Torques ◽  
Closed Loops ◽  
Baumgarte Stabilization

Abstract We develop a method for animating systems with open and closed loops and in particular ladder climbing for virtual world applications. Ladder climbing requires the modeling of dynamic open and closed-loop chains. We model the stance phase and the associated closed-loop dynamics, through the use of the Lagrange multiplier method which results in a system of differential algebraic equations (DAE). We use the Lagrange method for the dynamic formulation of the swing phase. The input to the algorithm is a given forward velocity, step length, step frequency and a chosen gait. The algorithm then determines the initial and final positions for each phase of ladder climbing. We use the Newton-Ralphson method to find the vector of joint torques that drives the dynamic system from the initial position to the final position. We use the Baumgarte stabilization method to achieve stability of the numerical integration. We present a series of real-time animations involving ladder climbing.

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