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Journal articles on the topic 'Double pendulums'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Bendersky, S., and B. Sandler. "Investigation of a spatial double pendulum: an engineering approach." Discrete Dynamics in Nature and Society 2006 (2006): 1–22. http://dx.doi.org/10.1155/ddns/2006/25193.

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The behavior of a spatial double pendulum (SDP), comprising two pendulums that swing in different planes, was investigated. Movement equations (i.e., mathematical model) were derived for this SDP, and oscillations of the system were computed and compared with experimental results. Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. Solutions for free oscillations of the pendulums and graphic descriptions of changes in the frequency spectra were used for the dynamic investigation of the pendulums for different initial conditions of motion. The value of the friction constant was estimated experimentally and incorporated into the equations of motion of the pendulums. This step facilitated the comparison between the computed and measured oscillations.

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2

Oiwa, Shunya, and Takahiro Yajima. "Jacobi stability analysis and chaotic behavior of nonlinear double pendulum." International Journal of Geometric Methods in Modern Physics 14, no. 12 (2017): 1750176. http://dx.doi.org/10.1142/s0219887817501766.

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In this paper, we study the Jacobi stability on the nonlinear double pendulum by the Kosambi–Cartan–Chern (KCC) theory. We assume that the mass and length of rods of two kinds of pendulums are equal, respectively. Moreover, we consider the case that initial angles of the double pendulum are equal. Under these conditions, we obtain the boundary between Jacobi stable and unstable trajectories for initial angles. It is shown that the condition of Jacobi stable or unstable depends only on deflection angles of the nonlinear double pendulum. Then, we discuss relationships between Jacobi stability, physical parameters and other concepts of stability such as Lyapunov stability and chaos. We suggest that the ratio of length of rods and the mass ratio of pendulums of the double pendulum do not affect the Jacobi stability. It is suggested that the equilibrium points in the Jacobi stable region and in the Jacobi unstable region are Lyapunov stable and Lyapunov unstable, respectively, and that the motions in the Jacobi unstable region are related to the onset of chaotic behavior.

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3

Arouna, Traor´e G. Y., M. Dosso, and J. C. Koua Brou. "Application of a Rank-One Perturbation to Pendulum Systems." Journal of Mathematics Research 12, no. 5 (2020): 47. http://dx.doi.org/10.5539/jmr.v12n5p47.

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From a perturbation theory proposed by Mehl, et al., a study of the rank-one perturbation of the problems governed by pendulum systems is presented. Thus, a study of motion of the simple pendulum, double and triple pendulums with oscillating support, not coupled as coupled by a spring and double pendulum with fixed support is proposed. Finally (strong) stability and instability zones are calculated for each studied system.

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4

Medrano-Cerda, G. A., E. E. Eldukhri, and M. Cetin. "Balancing and Attitude Control of Double and Triple Inverted Pendulums." Transactions of the Institute of Measurement and Control 17, no. 3 (1995): 143–54. http://dx.doi.org/10.1177/014233129501700306.

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The design of robust computer control systems for balancing and attitude control of double and triple inverted pendulums is considered in this paper. For the double inverted pendulum, a DC motor mounted at the upper hinge is used to balance and control attitude of the upper link. For the triple inverted pendulum a DC motor mounted at the middle hinge is used to control the middle link, whereas proportional position control applied to a motor at the upper hinge is utilised to maintain the upper link in alignment with the middle link. In both cases the lower hinge is left free to rotate. The controller designs are based on linearised discrete-time models of the inverted pendulums. Each controller utilises state feedback implemented via reduced-order state observers. The relative stability properties of the control systems are evaluated using Nyquist plots of suitably defined functions. The controllers are designed using Matlab and implemented in a PC using C language. Experimental results showed satisfactory performance.

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5

Liu, Y., H. Yu, and S. Cang. "Modelling and motion control of a double-pendulum driven cart." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226, no. 2 (2011): 175–87. http://dx.doi.org/10.1177/0959651811414507.

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The significant advantage of ground mobile robots (GMRs) is their accessibility to areas that are inaccessible for humans. One difficulty of current GMR technology is that the external driving mechanisms, such as wheel, track, and leg, restrict its applications. In order to solve this limitation, the present paper proposes a novel driving mechanism using a novel GMR called the double-pendulum driven cart (DPDC). The DPDC, which employs only internal thrust and static friction, is capable of steering by two parallel pendulums mounted on the cart, and is able to implement planar elemental motions by designing the pendulum trajectory properly. The paper first studies the dynamic modelling and the motion control issues of the DPDC. A closed-loop controller using the partial feedback linearization technique is then designed for the tracking control of the parallel pendulums to guarantee accurate motion of the cart. Extensive simulation results verify the proposed model and the efficiency of the motion control strategy.

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6

Wang, Hong Qi. "Dynamics Modeling of the Planar Double Inverted Pendulum." Applied Mechanics and Materials 195-196 (August 2012): 17–22. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.17.

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planar double inverted pendulum is a strong coupling, uncertain and complex nonlinear system, and the dynamics model of which is the basis of control, simulation and analysis. In the paper coordinate systems of the planar double inverted pendulum were first defined, and then the dynamics model of which was built up based on screw theory and the Lagrange principle. The modeling method used being systematic and standardized, it is easy to extend to dynamics modeling of higher order planar inverted pendulums or other multi-body systems.

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7

Kishida, Yoshiyuki, Sigeru Omatu, and Michifumi Yoshioka. "Self-Tuning Neuro-PID for Stabilization of Double Inverted Pendulum." Journal of Robotics and Mechatronics 10, no. 5 (1998): 439–44. http://dx.doi.org/10.20965/jrm.1998.p0439.

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This paper covers a new self-tuning neuro-PID control architecture and its application to stabilization of single and double inverted pendulums. Single-Input multioutput controls the inverted pendulum using the PID controller. PID gains are tuned using two types of neural networks. Simulation results demonstrate the effectiveness of the proposed approach.

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8

Hassanzadeh, I., A. Nejadfard, and M. Zadi. "A Multivariable Adaptive Control Approach for Stabilization of a Cart-Type Double Inverted Pendulum." Mathematical Problems in Engineering 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/970786.

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This paper considers the design and practical implementation of linear-based controllers for a cart-type double inverted pendulum (DIPC). A constitution of two linked pendulums placed on a sliding cart, presenting a three Degrees of Freedom and single controlling input structure. The controller objective is to keep both pendulums in an up-up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted nonlinear model is linearized around up-up position. First, the LQR method is used to stabilize DIPC by a feedback gain matrix in order to minimize a quadratic cost function. Without using an observer to estimate the unmeasured states, in the next step we make use of LQG controller which combines the Kalman-Bucy filter estimation and LQR feedback control to obtain a better steady-state performance, but poor robustness. Eventually, to overcome the unknown nonlinear model parameters, an adaptive controller is designed. This controller is based on Model Reference Adaptive System (MRAS) method, which uses the Lyapunov function to eliminate the defined state error. This controller improves both the steady-state and disturbance responses.

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9

Rasouli, Fatemeh, and Kyle B. Reed. "Identical Limb Dynamics for Unilateral Impairments through Biomechanical Equivalence." Symmetry 13, no. 4 (2021): 705. http://dx.doi.org/10.3390/sym13040705.

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Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a limb or an assistive device. This study develops a mathematical model of dissimilar double pendulums that mimics human walking with unilateral gait impairment and establishes identical dynamics between asymmetric limbs. It introduces new coefficients that create biomechanical equivalence between two sides of an asymmetric gait. The numerical solution demonstrates that dissimilar double pendulums can have symmetric kinematic and kinetic outcomes. Parallel solutions with different physical parameters but similar biomechanical coefficients enable interchangeable designs that could be incorporated into gait rehabilitation treatments or alternative prosthetic and ambulatory assistive devices.

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10

Fradkov, Alexander, Boris Andrievsky, and Kirill Boykov. "Control of the coupled double pendulums system." Mechatronics 15, no. 10 (2005): 1289–303. http://dx.doi.org/10.1016/j.mechatronics.2005.03.008.

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11

Ramezanifard, Mehdi. "Design of Intelligent Controllers for Double Inverted Pendulum." Ciência e Natura 37 (December 19, 2015): 406. http://dx.doi.org/10.5902/2179460x20802.

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In this paper, first a fuzzy controller is proposed for systems comprising two inverted pendulums placed in the same plane, where one pendulum moves along the X-axis and the other moves along the Y-axis; rules of a Fuzzy-Mamdani controller is improved by considering the behavior of an operator and a the developed expert system and by trial and error in the observation of the system’s behavior. Simulation results obtained in MATLAB are proposed and then two other intelligent methods are presented. In the second proposed method, a TSK controller is designed with Anfis training approach and its simulation results are presented. Finally, a non-fuzzy controller (linearization feedback) is used as the supervisor fuzzy controller and the simulation results are presented. At last, performance of the three controllers is compared and the results are demonstrated.

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12

Kim, Chyon Hae, Hiroshi Tsujino, and Shigeki Sugano. "Rapid Short-Time Path Planning for Phase Space." Journal of Robotics and Mechatronics 23, no. 2 (2011): 271–80. http://dx.doi.org/10.20965/jrm.2011.p0271.

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This paper addresses optimal motion for general machines. Approximation for optimal motion requires a global path planning algorithm that precisely calculates the whole dynamics of a machine in a brief calculation. We propose a path planning algorithm that consists of path searching and pruning algorithms. The pruning algorithmis based on our analysis of state resemblance in general phase space. To confirm precision, calculation cost, optimality and applicability of the proposed algorithm, we conducted several shortest time path planning experiments for the dynamic models of double inverted pendulums. Precision to reach the goal states of the pendulums was better than other algorithms. Calculation cost was 58 times faster at least. We could tune optimality of proposed algorithm via resolution parameters. A positive correlation between optimality and resolutions was confirmed. Applicability was confirmed in a torque based position and velocity feedback control simulation. As a result of this simulation, the double inverted pendulums tracked planned motion under noise while keeping within torque limitations.

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13

Sonobe, Motomichi, Takahiro Kondou, Kenichiro Matsuzaki, Nobuyuki Sowa, and Junichi Hino. "C08 Vibration Control of Pendulums Based on Jacobian Elliptic Functions : Application to a Serial Double Pendulum System." Proceedings of the Symposium on the Motion and Vibration Control 2009.11 (2009): 148–51. http://dx.doi.org/10.1299/jsmemovic.2009.11.148.

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14

Li, Tieshan, Wei Li, and Renxiang Bu. "A novel decentralised adaptive NN tracking control for double inverted pendulums." International Journal of Modelling, Identification and Control 13, no. 4 (2011): 269. http://dx.doi.org/10.1504/ijmic.2011.041782.

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15

Kharola, Ashwani, and Pravin P. Patil. "A Comparative Study for Position Regulation and Anti-Swing Control of Highly Non-Linear Double Inverted Pendulum (DIP) System Using Different Soft Com." International Journal of Fuzzy System Applications 6, no. 2 (2017): 59–81. http://dx.doi.org/10.4018/ijfsa.2017040104.

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This paper presents a comparative analysis for stabilization and control of highly non-linear, complex and multi-variable Double Inverted Pendulum on cart. A Matlab-Simulink model of DIP has been built using governing mathematical equations. The objective is to control both the pendulums at vertical position while cart is free to move in horizontal direction. The control of DIP was achieved using three different soft-computing techniques namely Fuzzy logic reasoning, Neural networks (NN's) and Adaptive neuro fuzzy inference system (ANFIS). The results show that the ANFIS controller is more effective as compared to other two controllers in terms of settling time (sec), maximum overshoot (degree) and steady state error. The regression (R) and mean square error (MSE) values obtained after training of Neural network were adequate and the training error obtained in ANFIS was also optimum. All the three controllers were able to stabilize the DIP system but ANFIS control provides better results as illustrated with the help of graphs and tables.

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16

Cadoni, Mariano, Roberto De Leo, and Giuseppe Gaeta. "Solitons in a double pendulums chain model, and DNA roto-torsional dynamics." Journal of Nonlinear Mathematical Physics 14, no. 1 (2007): 128–46. http://dx.doi.org/10.2991/jnmp.2007.14.1.10.

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17

Motallebzadeh, Farzaneh, Sadjaad Ozgoli, and Hamid Reza Momeni. "Multilevel Adaptive Control of Interconnected Nonlinear Systems: Application to Double Coupled Inverted Pendulums." IFAC Proceedings Volumes 43, no. 8 (2010): 418–23. http://dx.doi.org/10.3182/20100712-3-fr-2020.00069.

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18

Cadoni, Mariano, Roberto De Leo, and Giuseppe Gaeta. "Sine-Gordon solitons, auxiliary fields and singular limit of a double pendulums chain." Journal of Physics A: Mathematical and Theoretical 40, no. 43 (2007): 12917–29. http://dx.doi.org/10.1088/1751-8113/40/43/006.

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19

Mouhamadou, Dosso, Traore G. Y. Arouna, and Jean-Claude Koua Brou. "Rank-k perturbation of Hamiltonian Systems with Periodic Coefficients and Applications." European Journal of Pure and Applied Mathematics 12, no. 4 (2019): 1744–70. http://dx.doi.org/10.29020/nybg.ejpam.v12i4.3574.

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Jordan canonical forms of a rank-k perturbation of symplectic matrices and the fundamental solutions of Hamiltonian systems are presented on the basis of work done by C. Mehl et, al.. Small rank-k perturbations of Mathieu systems are analyzed. More precisely, it is shown that the rank-k perturbations of coupled or non-coupled double pendulums and the motion of an ion through a quadrupole analyzer slightly perturb the behavior of their spectra and their stabilities.

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20

Bulanchuk, P. O., and A. G. Petrov. "Control of the equilibrium point of simple and double mathematical pendulums with oblique vibration." Doklady Physics 57, no. 2 (2012): 73–77. http://dx.doi.org/10.1134/s1028335812020024.

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21

CHEN, SHENG-JUI, HSIEN-HAO MEI, and WEI-TOU NI. "Q & A EXPERIMENT TO SEARCH FOR VACUUM DICHROISM, PSEUDOSCALAR–PHOTON INTERACTION AND MILLICHARGED FERMIONS." Modern Physics Letters A 22, no. 37 (2007): 2815–31. http://dx.doi.org/10.1142/s0217732307025844.

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A number of experiments are underway to detect vacuum birefringence and dichroism — PVLAS, Q & A, and BMV. Recently, PVLAS experiment has observed optical rotation in vacuum by a magnetic field (vacuum dichroism). Theoretical interpretations of this result include a possible pseudoscalar–photon interaction and the existence of millicharged fermions. Here, we report the progress and first results of Q & A (QED [quantum electrodynamics] and Axion) experiment proposed and started in 1994. We use a 3.5-m high-finesse (around 30,000) Fabry–Perot prototype detector extendable to 7-m with the cavity mirrors suspended using X-pendulum-double pendulums. To polarize the vacuum, we use a 2.3-T dipole permanent magnet rotated at 5–10 rev/s, with 27-mm-diameter clear borehole and 0.6-m field length. Our ellipsometer/polarization-rotation-detection-system is formed by a pair of Glan–Taylor type polarizing prisms with extinction ratio lower than 10-8 together with a polarization modulating Faraday Cell with/without a quarter wave plate. Our first results give (-0.2 ± 2.8) × 10-13 rad/pass with 18,700 passes through a 2.3 T 0.6 m long magnet for vacuum dichroism measurement. We present our experimental limit on pseudo-scalar-photon interaction and millicharged fermions.

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22

Sultan, Ghassan A., and Ziyad K. Farej. "Design and Performance Analysis of LQR Controller for Stabilizing Double Inverted Pendulum System." Circulation in Computer Science 2, no. 9 (2017): 1–5. http://dx.doi.org/10.22632/ccs-2017-252-45.

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Double inverted pendulum (DIP) is a nonlinear, multivariable and unstable system. The inverted pendulum which continually moves toward an uncontrolled state represents a challenging control problem. The problem is to balance the pendulum vertically upward on a mobile platform that can move in only two directions (left or right) when it is offset from zero stat. The aim is to determine the control strategy that deliver better performance with respect to pendulum's angles and cart's position. A Linear-Quadratic-Regulator (LQR) technique for controlling the linearized system of double inverted pendulum model is presented. Simulation studies conducted in MATLAB environment show that the LQR controller are capable of controlling the multi output double inverted pendulum system. Also better performance results are obtained for controlling heavy driven part DIP system.

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23

Czerwiński, Ernest, Paweł Olejnik, and Jan Awrejcewicz. "Modeling And Parameter Identification Of Vibrations Of A Double Torsion Pendulum With Friction." Acta Mechanica et Automatica 9, no. 4 (2015): 204–12. http://dx.doi.org/10.1515/ama-2015-0033.

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Abstract The purpose of this paper is to investigate a double torsion pendulum with planar frictional contact. The single torsion pendulum with one-degree-of-freedom is an angular equivalent of the linear harmonic oscillator. The second degree of freedom has been obtained by adding a free body to the inverted single torsion pendulum. The free body’s angular displacement is caused by frictional forces appearing in the interface (contact zone) between the free body and the pendulum column’s head kinematically excited at its base by a mechanism with torsion spiral spring. An experimental station has been set up and run to find most unknown parameters of the pendulum from the time series of state variables taken as inputs to the Nelder-Mead method of identification. The obtained results proved significant usability of the identification method in the case of numerical simulation of the pendulum’s dynamical model. It has not been satisfactorily proved in the case of time characteristics coming from a real system that exhibits also some unrecognized physical effects.

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24

Kudra, Grzegorz, Michał Szewc, Michał Ludwicki, and Jan Awrejcewicz. "Modeling and Simulation of Bifurcation Dynamics of a Double Spatial Pendulum Excited by a Rotating Obstacle." International Journal of Structural Stability and Dynamics 19, no. 12 (2019): 1950145. http://dx.doi.org/10.1142/s0219455419501451.

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This work focuses on analyzing the dynamical behavior of a mechanical system consisting of a double spatial pendulum in contact with a movable obstacle. The pendulum’s ability to move in space is achieved by the use of special Cardan–Hook joints as the links of the pendulum. The mechanical system is equipped with a special movable obstacle, i.e. a rotating circular plate situated below the pendulum, which limits the space of admissible positions. A significant part of this work is devoted to the modeling of the contact between the pendulum and the obstacle. In this regard, a special class of reduced models is derived with the resultant friction force and moment acting on the finite size of the contact area along with a compliant model of impact based on the Hertz stiffness. Finally, the effective model suitable for fast and realistic numerical simulations is obtained. The contact model is tested numerically and the effect of its parameters on the system bifurcation dynamics is investigated.

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25

Lisowski, Bartłomiej, Clement Retiere, José Pablo Garcia Moreno, and Paweł Olejnik. "Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform planar stick–slip friction and elastic barriers." Nonlinear Dynamics 100, no. 4 (2020): 3215–34. http://dx.doi.org/10.1007/s11071-020-05684-6.

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Abstract The purpose of this study is to identify the nonlinear dynamics of the double torsion pendulum with planar friction and elastic barriers. The original experimental stand consists of a disk-shaped body that rotates freely on top of a forced column with a system of barriers limiting the torsional vibrations of the pendulum bodies that create an nonuniform planar rotational friction contact. Two beam springs form soft barriers modeled by Voigt elements that limit the angular displacement of one of the pendulum bodies—the disk, while the second limiting system, made of a much more rigid barrier, limits the movement of the pendulum’s second body. The dynamic behavior of the asymmetrical system of two degrees of freedom with discontinuities is identified with the use of the described strategy, numerical solutions of the derived mathematical model and the Nelder–Mead simplex algorithm. The actual measurement series and numerical solutions show a good similarity of the dynamical reaction of the mechanical system and its virtual analog.

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26

Perez, Joel P., Jose P. Perez, Francisco Rdz, and Angel H. Flores. "PD Control Law for Trajectory Tracking of Chaotic Pendulum." Advanced Materials Research 646 (January 2013): 208–15. http://dx.doi.org/10.4028/www.scientific.net/amr.646.208.

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This paper presents the application of trajectory tracking using the adaptive neural network to the double chaotic pendulum. The proposed controller structute is composed of a neural identifier and a PD Control. Experimental results with the chaotic pendulun shown the usefulness of the proposed approach. To verify the analytical results, an example of dynamical network is simulated and a theorem is proposed to ensure the tracking of the nonlinear system.

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27

Faraji, Salman, and Auke J. Ijspeert. "3LP: A linear 3D-walking model including torso and swing dynamics." International Journal of Robotics Research 36, no. 4 (2017): 436–55. http://dx.doi.org/10.1177/0278364917708248.

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In this paper, we present a new mechanical model for biped locomotion, composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to a double support phase, this model has different actuation possibilities in the swing hip and stance ankle which produce a broad range of walking gaits. Without the need for numerical time-integration, closed form solutions help to find periodic gaits which could simply scale in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can potentially provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such a property comes from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract template space. The proposed model produces human-like torque and ground reaction force profiles, and thus, compared to point-mass models, it is more promising for the generation of dynamic walking trajectories. Despite being linear and lacking many features of human walking like center of mass excursion, knee flexion and ground clearance, we show that the proposed model can explain one of the main optimality trends in human walking, i.e. the nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis remains for future works.

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28

Tot, Jonathan. "Spinning double pendulum." ACM Communications in Computer Algebra 49, no. 2 (2015): 57. http://dx.doi.org/10.1145/2815111.2815137.

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29

Li, Ai Lian, Hong Yu Qi, and Li Liang. "Based on T-S Fuzzy Classification of the Double Inverted Pendulum Multi Mode Adaptive Control." Advanced Materials Research 902 (February 2014): 300–305. http://dx.doi.org/10.4028/www.scientific.net/amr.902.300.

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Double Inverted pendulum as an important object of study on robotics and aviation field, is also a major platform for teaching and scientific research.Usually double Inverted pendulum modeling is usually will be linearized processing system, ignoring the effect of the angle of system. But the realization of double inverted pendulum is a nonlinear system, the angle affect the stability control. From the actual situation of double Inverted pendulum motion, double Inverted pendulum system of the input space is divided into 9 sub-space, by T-S fuzzy and feedback gain matrix to select the corresponding state equation, making the system more close to its dynamic performance. The multi mode adaptive control and T-S fuzzy method of combining the successful implementation of double inverted pendulum system simulation and real-time control.The number of rules they use far less than Mamdani fuzzy, but also successfully resolved the fuzzy control algorithm due to the presence of multiple variables and the resulting "rule explosion problem".

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30

LIN, Jian, Makoto KAJITANI, and Tadashi MASUDA. "Control of double pendulum." Transactions of the Japan Society of Mechanical Engineers Series C 56, no. 522 (1990): 431–34. http://dx.doi.org/10.1299/kikaic.56.431.

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31

Nikolai, Bezdenejnykh, Andres Mateo Gabin, and Raul Zazo Jimenez. "Double Pendulum Induced Stability." International Journal of Applied Mechanics 07, no. 06 (2015): 1550088. http://dx.doi.org/10.1142/s175882511550088x.

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In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa’s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy — positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.

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32

Selyutskiy, Yury D., Andrei P. Holub, and Marat Z. Dosaev. "Elastically Mounted Double Aerodynamic Pendulum." International Journal of Structural Stability and Dynamics 19, no. 05 (2019): 1941007. http://dx.doi.org/10.1142/s0219455419410074.

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Elastically mounted double aerodynamic pendulum is an aeroelastic system with two rotational degrees of freedom. A wing is attached to the second link of the pendulum. It is shown that it is possible to select values of parameters in such a way as to make the trivial equilibrium (where both links of the pendulum are stretched along the flow) unstable. Numerical simulation of behavior of the system in such situations is performed, and arising limit cycles are studied. Experimental investigation of such aerodynamic pendulum is performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University. Characteristics of periodic motions are registered for different values of parameters of the system. It is shown that experimental data are in qualitative agreement with results of numerical simulation.

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33

Sanjeewa, Sondarangallage DA, and Manukid Parnichkun. "Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller." International Journal of Advanced Robotic Systems 16, no. 2 (2019): 172988141983327. http://dx.doi.org/10.1177/1729881419833273.

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Balancing control of a rotary double inverted pendulum system is a challenging research topic for researchers in dynamics control field because of its nonlinear, high degree-of-freedom, under actuated and unstable characteristics. The system always works under uncertainties and disturbances. Many control algorithms fail or ineffectively control the rotary double inverted pendulum system. In this article, mixed sensitivity H∞ control is proposed to balance the rotary double inverted pendulum system. The controller is proposed to ensure the robust stability and enhance the time domain performance of the system under uncertainties and disturbances. Structure of the system, dynamics model and controller synthesis are presented. For performance evaluation, the proposed mixed sensitivity H∞ controller is compared with linear quadratic regulator from both simulation and experiment on the rotary double inverted pendulum system. The results show high performance of the proposed controller on the rotary double inverted pendulum system with model uncertainties and external disturbances.

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34

Zhou, Fangyuan, Weilin Xiang, Kun Ye, and Hongping Zhu. "Theoretical study of the double concave friction pendulum system under variable vertical loading." Advances in Structural Engineering 22, no. 8 (2019): 1998–2005. http://dx.doi.org/10.1177/1369433219831474.

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The double concave friction pendulum system has been recognized as an efficient device for decreasing the seismic response of a structure during an earthquake excitation. Previous studies have focused mainly on the properties of the double concave friction pendulum system under constant vertical loading, and the width of the hysteretic loop changed by the vertical ground motion is less considered. In view of this, a theoretical study of the double concave friction pendulum system under variable vertical loading is conducted in this article. Meanwhile, the properties of the hysteretic loops of the double concave friction pendulum system with different friction coefficients between the articulated slider with the upper and lower sliding surfaces are investigated. The results show that the hysteretic loops of the double concave friction pendulum system will be affected by the variation of the vertical loading and the difference of the friction coefficients between the articulated slider with the upper and lower sliding surfaces.

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35

Estevez, Julian, Jose Manuel Lopez-Guede, Gorka Garate, and Manuel Graña. "A Hybrid Control Approach for the Swing Free Transportation of a Double Pendulum with a Quadrotor." Applied Sciences 11, no. 12 (2021): 5487. http://dx.doi.org/10.3390/app11125487.

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In this article, a control strategy approach is proposed for a system consisting of a quadrotor transporting a double pendulum. In our case, we attempt to achieve a swing free transportation of the pendulum, while the quadrotor closely follows a specific trajectory. This dynamic system is highly nonlinear, therefore, the fulfillment of this complex task represents a demanding challenge. Moreover, achieving dampening of the double pendulum oscillations while following a precise trajectory are conflicting goals. We apply a proportional derivative (PD) and a model predictive control (MPC) controllers for this task. Transportation of a multiple pendulum with an aerial robot is a step forward in the state of art towards the study of the transportation of loads with complex dynamics. We provide the modeling of the quadrotor and the double pendulum. For MPC we define the cost function that has to be minimized to achieve optimal control. We report encouraging positive results on a simulated environmentcomparing the performance of our MPC-PD control circuit against a PD-PD configuration, achieving a three fold reduction of the double pendulum maximum swinging angle.

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36

Whittlesey, Saunders N., and Joseph Hamill. "An Alternative Model of the Lower Extremity during Locomotion." Journal of Applied Biomechanics 12, no. 2 (1996): 269–79. http://dx.doi.org/10.1123/jab.12.2.269.

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An alternative to the Iterative Newton-Euler or linked segment model was developed to compute lower extremity joint moments using the mechanics of the double pendulum. The double pendulum model equations were applied to both the swing and stance phases of locomotion. Both the Iterative Newton-Euler and double pendulum models computed virtually identical joint moment data over the entire stride cycle. The double pendulum equations, however, also included terms for other mechanical factors acting on limb segments, namely hip acceleration and segment angular velocities and accelerations Thus, the exact manners in which the lower extremity segments interacted with each other could be quantified throughout the gait cycle. The linear acceleration of the hip and the angular acceleration of the thigh played comparable roles to muscular actions during both swing and stance.

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Holub, A. P., and Y. D. Selyutskiy. "Elastically Mounted Double Aerodynamics Pendulum." MEHATRONIKA, AVTOMATIZACIA, UPRAVLENIE 19, no. 6 (2018): 380–86. http://dx.doi.org/10.17587/mau.19.380-386.

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Bridges, Thomas J., and Kyriakos V. Georgiou. "A transverse spinning double pendulum." Chaos, Solitons & Fractals 12, no. 1 (2001): 131–44. http://dx.doi.org/10.1016/s0960-0779(99)00180-0.

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39

Bender, Paul A. "A fascinating resonant double pendulum." American Journal of Physics 53, no. 11 (1985): 1114. http://dx.doi.org/10.1119/1.14052.

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40

Shinbrot, Troy, Celso Grebogi, Jack Wisdom, and James A. Yorke. "Chaos in a double pendulum." American Journal of Physics 60, no. 6 (1992): 491–99. http://dx.doi.org/10.1119/1.16860.

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41

Komine, Takayoshi, Masami Iwase, Satoshi Suzuki, and Katsuhisa Furuta. "Rotational Control of Double Pendulum." IFAC Proceedings Volumes 37, no. 14 (2004): 325–30. http://dx.doi.org/10.1016/s1474-6670(17)31124-2.

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42

Ohlhoff, A., and P. H. Richter. "Forces in the Double Pendulum." ZAMM 80, no. 8 (2000): 517–34. http://dx.doi.org/10.1002/1521-4001(200008)80:8<517::aid-zamm517>3.0.co;2-1.

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43

Ali, M. K. "Quantization of the double pendulum." Canadian Journal of Physics 74, no. 5-6 (1996): 255–62. http://dx.doi.org/10.1139/p96-040.

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The double pendulum is one of the best tools for demonstrating classical chaos and yet its quantization has somehow escaped attention. An attempt is made to fill this gap. We show that the constraint-induced Riemann curvature scalar plays an important role in the proper quantization and evaluation of the energy spectra of this system. The quantum energies are compared with the semiclassical results obtained earlier by resumming the Birkhoff–Gustavson normal form series. The general agreement between the two sets of energies demonstrates how a proper resummation makes it possible to use a divergent normal form series for semiclassical analyses.

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Enolskii, Pronine та Richter. "Double Pendulum and θ -Divisor". Journal of Nonlinear Science 13, № 2 (2003): 157–74. http://dx.doi.org/10.1007/s00332-002-0514-0.

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45

Zhou, Ziliang, and Chad Whiteman. "Motions of a double pendulum." Nonlinear Analysis: Theory, Methods & Applications 26, no. 7 (1996): 1177–91. http://dx.doi.org/10.1016/0362-546x(94)00253-e.

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46

Evseenko, Alla, and Dmitrii Romannikov. "Application of Deep Q-learning and double Deep Q-learning algorithms to the task of control an inverted pendulum." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 1-2 (August 26, 2020): 7–25. http://dx.doi.org/10.17212/2307-6879-2020-1-2-7-25.

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Today, such a branch of science as «artificial intelligence» is booming in the world. Systems built on the basis of artificial intelligence methods have the ability to perform functions that are traditionally considered the prerogative of man. Artificial intelligence has a wide range of research areas. One such area is machine learning. This article discusses the algorithms of one of the approaches of machine learning – reinforcement learning (RL), according to which a lot of research and development has been carried out over the past seven years. Development and research on this approach is mainly carried out to solve problems in Atari 2600 games or in other similar ones. In this article, reinforcement training will be applied to one of the dynamic objects – an inverted pendulum. As a model of this object, we consider a model of an inverted pendulum on a cart taken from the Gym library, which contains many models that are used to test and analyze reinforcement learning algorithms. The article describes the implementation and study of two algorithms from this approach, Deep Q-learning and Double Deep Q-learning. As a result, training, testing and training time graphs for each algorithm are presented, on the basis of which it is concluded that it is desirable to use the Double Deep Q-learning algorithm, because the training time is approximately 2 minutes and provides the best control for the model of an inverted pendulum on a cart.

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Hou, Yong Jun. "Dynamics Analysis of Vibrating Screen Based on Double Compound Pendulum with Single Motor Driving." Applied Mechanics and Materials 459 (October 2013): 335–41. http://dx.doi.org/10.4028/www.scientific.net/amm.459.335.

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By Lagrange equation, the dynamic equation of vibrating screen based on double compound pendulum with single motor driving was established. With simulation method, dynamic simulating model was built, and influences of pendulum installing position, stiffness of torsion damping spring of pendulum rod, initial installing angle and length of pendulum rod on motion characteristics of vibrating screen was discussed. Research results showed that, by choosing suitable stiffness of torsion damping spring or length of pendulum rod, this kind of vibrating screen may achieve the approximate linear trajectory, or normal elliptic trajectory of deck; when the angle between the rotating joint of pendulum rod and screen surface equals to initial installing angle of pendulum rod, the vibration of deck is most close to translational motion..

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Komarudin, Achmad, Mas Nurul Achmadiah, and Leonardo Kamajaya. "STABILISASI PADA DOUBLE INVERTED PENDULUM MENGGUNAKAN METODE LQR - BAT ALGORTHM." JURNAL ELTEK 16, no. 2 (2018): 33. http://dx.doi.org/10.33795/eltek.v16i2.98.

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Sistem double inverted pendulum digunakan untuk mengkaji metodekontrol dari sistem nonlinear yang kompleks. Pada sistem tersebutditemukan tiga permasalahan, yaitu swing-up, stabilisasi, dan tracking.Pada penelitian ini digunakan metode LQR-Bat Algorithm untukmengoptimasi kestabilan pada sebuah double inverted pendulum. Hasilpenelitian menunjukkan penggunaan Bat Algorithm pada metode LQRdapat menyelesaikan permasalahan stabilisasi. Pada iterasi ke 300-400terjadi pengurangan nilai fitness yang menghasilkan fungsi SSE bernilaisemakin kecil.

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Elkinany, Boutaina, Mohammed Alfidi, Redouane Chaibi, and Zakaria Chalh. "T-S Fuzzy System Controller for Stabilizing the Double Inverted Pendulum." Advances in Fuzzy Systems 2020 (December 5, 2020): 1–9. http://dx.doi.org/10.1155/2020/8835511.

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This article provides a representation of the double inverted pendulum system that is shaped and regulated in response to torque application at the top rather than the bottom of the pendulum, given that most researchers have controlled the double inverted pendulum based on the lower part or the base. To achieve this objective, we designed a dynamic Lagrangian conceptualization of the double inverted pendulum and a state feedback representation based on the simple convex polytypic transformation. Finally, we used the fuzzy state feedback approach to linearize the mathematical nonlinear model and to develop a fuzzy controller H ∞ , given its great ability to simplify nonlinear systems in order to reduce the error rate and to increase precision. In our virtual conceptualization of the inverted pendulum, we used MATLAB software to simulate the movement of the system before applying a command on the upper part of the system to check its stability. Concerning the nonlinearities of the system, we have found a state feedback fuzzy control approach. Overall, the simulation results have shown that the fuzzy state feedback model is very efficient and flexible as it can be modified in different positions.

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Leontev, Victor, Alexey Smirnov, and Boris Smolnikov. "Collinear control of dissipative double pendulum." Robotics and Technical Cybernetics 7, no. 1 (2019): 65–70. http://dx.doi.org/10.31776/rtcj.7109.

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