scholarly journals Quadrotor UAV Control for Transportation of Cable Suspended Payload

2019 ◽  
Vol 26 (2) ◽  
pp. 77-84 ◽  
Author(s):  
Tom Kusznir ◽  
Jarosław Smoczek
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Wide Range ◽  
Time Required ◽  
Interest In Research ◽  
Emergency Equipment ◽  
Pendulum Dynamics ◽  
4 Degrees Of Freedom

Abstract Payload transportation with UAV’s (Unmanned Aerial Vehicles) has become a topic of interest in research with possibilities for a wide range of applications such as transporting emergency equipment to otherwise inaccessible areas. In general, the problem of transporting cable suspended loads lies in the under actuation, which causes oscillations during horizontal transport of the payload. Excessive oscillations increase both the time required to accurately position the payload and may be detrimental to the objects in the workspace or the payload itself. In this article, we present a method to control a quadrotor with a cable suspended payload. While the quadrotor itself is a nonlinear system, the problem of payload transportation with a quadrotor adds additional complexities due to both input coupling and additional under actuation of the system. For simplicity, we fix the quadrotor to a planar motion, giving it a total of 4 degrees of freedom. The quadrotor with the cable suspended payload is modelled using the Euler-Lagrange equations of motion and then partitioned into translation and attitude dynamics. The design methodology is based on simplifying the system by using a variable transformation to decouple the inputs, after which sliding mode control is used for the translational and pendulum dynamics while a feedback linearizing controller is used for the rotational dynamics of the quadrotor. The sliding mode parameters are chosen so stability is guaranteed within a certain region of attraction. Lastly, the results of the numerical simulations created in MATLAB/Simulink are presented to verify the effectiveness of the proposed control strategy.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

Comparison between Analytical and Vectorial Methods of the Synthesis of Equations of Motion

1983 ◽  
Vol 197 (4) ◽  
pp. 265-274
Author(s):  
Z J Goraj
Keyword(s):  
Angular Momentum ◽  
Analytical Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discrete Systems ◽  
Momentum Equation ◽  
Lagrange Equations ◽  
Weak Points ◽  
Complicated Geometry ◽  
Boltzmann Hamel Equations

In this paper the advantages and weak points of the analytical and vectorial methods of the derivation of equations of motion for discrete systems are considered. The analytical method is discussed especially with respect to Boltzmann-Hamel equations, as generalized Lagrange equations. The vectorial method is analysed with respect to the momentum equation and to the generalized angular momentum equation about an arbitrary reference point, moving in an arbitrary manner. It is concluded that, for the systems with complicated geometry of motion and a large number of degrees of freedom, the vectorial method can be more effective than the analytical method. The combination of the analytical and vectorial methods helps to verify the equations of motion and to avoid errors, especially in the case of systems with rather complicated geometry.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

Second-Order Sliding Mode Control of a Perturbed-Crane

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Carlos Vázquez ◽  
Leonid Fridman ◽  
Joaquin Collado ◽  
Ismael Castillo
Keyword(s):  
Lyapunov Functions ◽  
Pid Controller ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Second Order ◽  
Convergence Time ◽  
Model Description ◽  
External Perturbations ◽  
Wide Range ◽  
Second Order Sliding Mode

A five degrees-of-freedom overhead crane system affected by external perturbations is the topic of study. Existing methods just handle the unperturbed case or, in addition, the analysis is limited to three or two degrees-of-freedom. A wide range of processes cannot be restricted to these scenarios and this paper goes a step forward proposing a control solution for a five degrees-of-freedom system under the presence of matched and unmatched disturbances. The contribution includes a model description and a second-order sliding mode (SOSM) control design ensuring the precise trajectory tracking for the actuated variables and at the same time the regulation of the unactuated variables. Furthermore, the proposed approach is supported by the design of strong Lyapunov functions providing an estimation of the convergence time. Simulations and experiments, including a comparison with a proportional-integral-derivative (PID) controller, verified the advantages of the methodology.

scholarly journals Dynamical analysis of a 2-degrees of freedom spatial pendulum

2018 ◽  
Vol 184 ◽  
pp. 01003 ◽  
Author(s):  
Stelian Alaci ◽  
Florina-Carmen Ciornei ◽  
Sorinel-Toderas Siretean ◽  
Mariana-Catalina Ciornei ◽  
Gabriel Andrei Ţibu
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dynamical Analysis ◽  
Analysis Software ◽  
Lagrange Equations ◽  
Moments Of Inertia ◽  
Dynamical Simulation ◽  
Principal Moments Of Inertia

A spatial pendulum with the vertical immobile axis and horizontal mobile axis is studied and the differential equations of motion are obtained applying the method of Lagrange equations. The equations of motion were obtained for the general case; the only simplifying hypothesis consists in neglecting the principal moments of inertia about the axes normal to the oscillation axes. The system of nonlinear differential equations was numerically integrated. The correctness of the obtained solutions was corroborated to the dynamical simulation of the motion via dynamical analysis software. The perfect concordance between the two solutions proves the rightness of the equations obtained.

scholarly journals Minimization of dynamic joint reaction forces of the 2-DOF serial manipulators based on interpolating polynomials and counterweights

2015 ◽  
Vol 42 (4) ◽  
pp. 249-260 ◽  
Author(s):  
Slavisa Salinic ◽  
Marina Boskovic ◽  
Radovan Bulatovic
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Symbolic Form ◽  
Serial Manipulators ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Inertia Forces ◽  
Joint Reaction ◽  
Selection Of

This paper presents two ways for the minimization of joint reaction forces due to inertia forces (dynamic joint reaction forces) in a two degrees of freedom (2-DOF) planar serial manipulator. The first way is based on the optimal selection of the angular rotations laws of the manipulator links and the second one is by attaching counterweights to the manipulator links. The influence of the payload carrying by the manipulator on the dynamic joint reaction forces is also considered. The expressions for the joint reaction forces are obtained in a symbolic form by means of the Lagrange equations of motion. The inertial properties of the manipulator links are represented by dynamical equivalent systems of two point masses. The weighted sum of the root mean squares of the magnitudes of the dynamic joint reactions is used as an objective function. The effectiveness of the two ways mentioned is discussed.

VIBRATION SUPPRESSION OF A ROTATING HUB-BEAM SYSTEM WITH A FLEXIBLE SUPPORT USING FRACTIONAL ORDER SLIDING MODE CONTROL

2017 ◽  
Vol 41 (4) ◽  
pp. 627-643 ◽  
Author(s):  
Mohsen Vakilzadeh ◽  
Mohammad Eghtesad ◽  
Mohammad Rahim Nami ◽  
Ghasem Khajepour
Keyword(s):  
Fractional Order ◽  
Vibration Suppression ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Angular Position ◽  
Industrial Applications ◽  
Superior Performance ◽  
Sensors And Actuators ◽  
Flexible Support ◽  
Wide Range

In this paper, a rotating hub-blade system with a flexible support which represents a wide range of industrial applications is considered for modelling and control. The flexible blade is assumed as an Euler–Bernoulli beam. In addition, three piezoelectric layers are mounted on the blade as sensors and actuators to reduce vibrations of the blade attached to the hub. For modelling, the Lagrange’s method is utilized to obtain the equations of motion of the system. In order to simultaneously suppress vibrations of the system and track the desired angular position of the hub, designing an appropriate controller is carried out. In this regard, a fractional order sliding mode (FOSM) controller is proposed to fulfil these objectives and then the comparison between FOSM controller and the classical sliding mode controller is presented in order to investigate the effectiveness of the proposed controller. The simulation results indicate the superior performance of the fractional order controller in compare to the integer order sliding.

Effects of Temperature and Cross Section Variations on the Vibrational Behavior of Finished Wire Blocks

2014 ◽  
Vol 622-623 ◽  
pp. 95-102
Author(s):  
Mohammadzaman Savari ◽  
Paul Josef Mauk ◽  
Oberrat Bernhardt Weyh
Keyword(s):  
Product Quality ◽  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Equation System ◽  
Rolling Process ◽  
Essential Elements ◽  
Lagrange Equations ◽  
Cross Sectional ◽  
Coupled Equations

Because of the great speed range in a finishing block of a wire rod mill, the reduction of torsional vibrations makes it possible to achieve closer rolling tolerances. The components transmitting the torque like gear box, coupling etc. can generate non-smooth or alternating torques which affect the product quality. To study the influences of torsion vibrations on the product quality, the dynamic interactions of the block and rolling process are simultaneously analyzed by a simulation model. As an example, a three stand arrangement is considered. The real transmission system is idealized as a structurally discrete torsional vibration model. The generalized rotational coordinates with a large number of rotational degrees of freedom can be reduced among others constants by means of gear ratios. Euler-Lagrange equations are applied to create the coupled equations of motion, which together constitute an ordinary differential equation of order 28. The rolling and main drive torques are defined as excitation for vibration on the right side of the equation system. A DC motor is selected as main drive and the voltage circuit equation of motor is integrated into the system of differential equations. The armature current and its interaction are consequently simulated. The rotational speed of rolls and motor, as well as roll torques, longitudinal stresses in rod and section widths are shown in diagrams as the result and thereby the torsional vibration of the essential elements of the system are studied for different temperatures and cross-sectional variations.

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

Dynamic Modeling and Analysis for a Planar Three Degrees-of-Freedom Manipulator Under Prescribed Mount Motion

2019 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Moving Frame ◽  
Parallel Plates ◽  
Modeling And Analysis ◽  
Three Degrees Of Freedom

Abstract This paper presents dynamic modeling of a planar, three degrees-of-freedom manipulator consisting of two parallel plates, referred to as top and base plates, which are connected by three actuated legs. When a sensitive equipment is carried by a moving robot or vehicle, it becomes necessary to mount the equipment on a platform which achieves precise positioning for stabilization. The objectives of this paper are to derive analytical equations of motion and apply them to control simulations on the stabilizing planar manipulator. In the derivation of analytical equations of motion, the moving frame method is utilized to describe the kinematics of the two-dimensional multibody system. For the manipulator system comprised of jointed bodies, a graph tree is utilized, which visually illustrates how the constituent bodies are connected to each other. For kinetics, the principle of virtual work is employed to derive the analytical equations of motion for the manipulator system. The resulting equations of motion are used to numerically assess the performance of a sliding mode controller (SMC) to stabilize the top plate from the motion of the translating and rotating base plate. In the numerical simulation, the SMC is compared with a simple PID controller to evaluate both the tracking performance and robustness.

Sign in / Sign up

Export Citation Format

Share Document