Length Of Pendulum Research Articles

Vibration Control of Large Wind Turbine Blades with Unidirectional Cable Pendulum Damper

A unidirectional cable pendulum damper is proposed to mitigate vibration responses of large-scale wind turbine blades in the edgewise direction, and the effectiveness of the proposed device for vibration response control is investigated. First, the configuration and working principles of the vibration damper are introduced. Second, the Euler–Lagrange equation of the single blade vibration damping system with the vibration damper is derived based on the Hamilton’s principle. At last, considering the effect of blade rotation, the wind load that applied on the blade was calculated using the rotating sample spectrum. The dynamic responses of blades are also calculated using the MATLAB/Simulink platform. The peak value and standard deviation of blade responses were taken as evaluation indexes to evaluate the vibration control efficiency of the device with varying the parameters such as the mass ball pendulum length, the fixed pulley block installation position, the stiffness and the pre-stress of the flexible cable. The optimal parameters of the vibration damper are investigated and obtained based on the assumption that no pounding happens between the mass ball of the vibration damper and the inner wall of the blade. Results show that the length of the mass ball pendulum and the installation position of the fixed pulley block, the values of which are within a reasonable range, can ensure the optimal performance of the vibration damper. The displacement of the mass sphere can be effectively reduced by increasing the stiffness of the flexible cable, and the pre-stress shows marginal beneficial effect on the damping performance and the displacement control of the mass sphere. Using the optimum parameters, the vibration damper can keep the mass ball within a safe running distance. The reduction of the peak value and the standard deviation of the blade displacement can reach 89.36% and 89.83%, respectively. The proposed device space can effectively reduce the blade tip response of the wind turbine by occupying less space. Moreover, the size of the device installation space can be changed by adjusting the weight ball swing length, which is suitable for the vibration control of the wind turbine blade edgewise direction.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Dynamic simulation analysis of inertial pendulum energy converter for underwater power generation

The inertial pendulum energy converter for underwater power generation can convert the marine kinetic energy into electrical energy which can promote the utilization of marine kinetic energy and the development of marine equipment. In recent years, this energy converter method gets more and more attention since it is no need to consider the underwater sealing which is hard to realize in the deep sea. To further clarify the energy conversation mechanism of energy converter and improve its power generation capacity, this paper establishes the electromechanical coupling dynamic model of the inertial pendulum energy converter based on Matlab. In this model, a torque balance equation was employed to describe relationship between the motion characteristics of the pendulum and the output characteristics of the DC generator. The influences of pendulum angle, pendulum length and generator load on the power generation performance are simulated and analyzed with the established model. The results show that power generation capacity of the inertial pendulum energy converter increases with the increase of the pendulum angle and pendulum length, while increases firstly and then decreases with the increase of generator load. These results provide theoretical basis for the further optimization design of the inertial pendulum energy converter.

2 The Ancient Sumerian Roots of the British - Pre- Imperial System of Measurement

When the French proposed their first metric system in 1723, they had no idea it had been invented by the ancient Mesopotamians 5000 years earlier. Just as the French proposed to use the length of a one-second pendulum to create standards of length, volume, and weight, the Sumerians created nearly identical meters, liters and kilograms. Our research shows that the Sumerians in ancient Mesopotamia used both the Moon and the Sun as their clock. It appears that the Egyptians improved on this timing accuracy by using the stars. Later the Minoans introduced the use of the planet Venus as a clock. These concepts spread throughout the ancient world from Britain in the West to Japan in the East. The Minoan standards are immortalized in the Magna Carta of 1215. The old English saying “a pint a pound the world around” had been true for over 3000 years. In the 19th Century, both Stuart and Penrose accurately measured the dimensions of the Parthenon, finding its width to be 0.9997 arc seconds on the polar circumference of the Earth. This accuracy puzzled scholars for 150 years. Our research shows the width of the Parthenon in Athens was designed to be 1/30 of the perimeter of the Great Pyramid of Giza. The same Pendulum Formula, when timed with Venus rather than the Sun, increased the pendulum length just the right amount. This precision was not dumbfounding – it was just dumb luck.

Adaptive-passive tuned mass damper for structural aseismic protection including soil–structure interaction

As one of the most traditional vibration mitigation devices, tuned mass dampers (TMDs) are applied widely in aseismic protection of building structures. The control effect of a passive TMD is depended on its parameters, especially the frequency ratio. Nevertheless, passive TMDs are high sensitive to the frequency detuning issue, and a mistuned TMD will lose its aseismic protection. Soil-structure interaction (SSI) will deviate the structural frequency and lead to a mistuned TMD. Besides, different soil conditions will lead to different frequency deviations of the primary structure. However, it may be difficult to obtain parameters of the soil exactly. To solve this problem, a recently developed adaptive-passive eddy current pendulum TMD (APEC-PTMD) is applied to a benchmark 40-story tall building including SSI in this study, and four different soil conditions are considered. The APEC-PTMD can identify the optimal TMD frequency in the building with different soil types, and then retune itself through adjusting the pendulum length, and also the air gap between the conduct plate and permanent magnets to reset its damping ratio. Therefore, no prior knowledge of the soil condition is needed for the APEC-PTMD. To verify the aseismic protection effect, 44 far-field earthquake excitations are chosen, and two passive TMDs are used for comparison, while one is optimized for the base-fixed structure and the other is optimized based on the dense-soil model. The passive TMD will become mistuned when SSI is considered or soil parameters are changed, while APEC-PTMD can adapt to the structural dominant frequency with different SSI. Therefore, it always works as a passive TMD with well-tuned parameters. Results show that the APEC-PTMD has a better aseismic protection than the passive TMD, especially in the soft-soil model, and it has an excellent control effect compared to the without TMD case at the same time.

Self-Adaptive Pendulum-Ball Switches for Piezoelectric Synchronous-Extraction Circuits.

Electronic synchronous switches are usually used to enhance the performance of piezoelectric energy-extraction circuits, but the electronic components leading to additional power consumption are not desired for energy extraction. In view of the advantage of mechanical switches without power consumption, this article proposed a synchronous-switch circuit which can adapt to the amplitude of a cantilever-beam-vibration generator with less energy loss. This mechanical switch consists of two pendulum balls and two buffer springs. This switch mechanism can automatically adapt to the cantilever-displacement amplitude, control the closing and opening of switches with the decrease in phase advance angle, and increase in energy-extraction efficiency. Different from previous adaptive mechanical switches, this unique pendulum-ball mechanism can not only reduce the weight and volume of the generator to improve the energy density, but can also simply adjust the pendulum length to achieve better harvesting performance. It is verified experimentally that the adaptive mechanical switch can close and open automatically under different cantilever amplitudes and excitation frequencies; the results show that the optimal power of the proposed circuit can reach 4.2 times that of the standard circuit. In order to further optimize the adaptive mechanical switch, the parameters of the swing-ball mechanism affecting harvesting performance is analyzed.

Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit

<p style='text-indent:20px;'>We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We consider the case where the rods of the pendulum have variable length, varying according to the radius vector of the elliptic orbit. We make an Hamiltonian view of the problem, find four linearly stable equilibrium positions and construct the boundary curves of the stability/instability regions in the space of the parameters associated with the pendulum length and the eccentricity of the orbit.</p>

Design of Ocean Wave Power Plant with a Two-Axis Vertical Pendulum Mechanism System

Renewable energy is a promising potential for the future, where this energy is low emission and environment friendly. One of the renewable energies that are abundant and rarely used is ocean waves. Energy from ocean waves can be extracted using an ocean wave power plant with a pendulum system (PLTGL-SB). The main components of PLTGL-SB are pontoon and pendulum, where the pendulum will oscillate when ocean waves hit the pontoon. This research will analyze PLTGL-SB with a two-axis mechanism. The analyzes were performed with simulations using CFD applications (computational fluid dynamics) and only used three degrees of freedom (pitching, rolling, and heaving). The design of PLTGL-SB has a length of 2.2 m, a width of 1.3 m, a height of 1.61 m, and an overall mass of 199.5 kg with two axes and two pendulums on each axis. The highest simulation results obtained a maximum deviation angle of 32.31° and an angular velocity of 1.44 rad/s with 10 kg pendulum mass and 1.0 m pendulum length at 0.5 m wave amplitude. If this design is used in the rumah apung Bangsring, it will require seven modules of PLTGL-SB and two additional 12V 50Ah batteries.

Controlador Nebuloso Aplicado ao Equilíbrio de um Pêndulo Invertido Simples

The concept of Fuzzy Logic was created by Loftali Askar-Zadeh in 1965 and is considered one of the main artificial intelligence techniques of the last 50 years. In this contribution, an analytical approach was initially developed of an inverted pendulum in a cart that was numerically simulated in Python language. Then, a fuzzy controller was also developed in Python to keep the inverted pendulum in the vertical position according to the mechanical properties of the system and initial conditions. The controller considers the angle and angular velocity of the pendulum in the adjustment process for the response of the horizontal force applied to the cart. In conclusion, observing the results presented, the fuzzy controller was able to react to the system in a satisfactory way, obtaining an equilibrium position in different configurations of pendulum length.

Calculus of variations and optimal control for generalized functions

We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove the higher order Euler–Lagrange equations, the D’Alembert principle in differential form, the du Bois–Reymond optimality condition and the Noether’s theorem. We start the theory of optimal control proving a weak form of the Pontryagin maximum principle and the Noether’s theorem for optimal control. We close with a study of a singularly variable length pendulum, oscillations damped by two media and the Pais–Uhlenbeck oscillator with singular frequencies.

Controlling the variable length pendulum: Analysis and Lyapunov based design methods

The analysis and design of methods to damp the swing of the variable length pendulum by adjusting its length are presented here. To analyze the theoretical limits of such Coriolis force based damping, a comprehensive open-loop numerical analysis is performed for a two-dimensional model having the string length as the controlled input. Further, for a four dimensional model, having the force applied to the string as the controlled input, a smooth static state feedback controller is designed using backstepping. Results are verified both in simulations and through extensive laboratory experiments, and compared with previously published results achievable using an identical experimental setting.

Modeling, Simulation, and Analysis of a Variable-Length Pendulum Water Pump

Due to the long-term problem of electricity and potable water in most developing and undeveloped countries, predominantly rural areas, a novelty of the pendulum water pump, which uses a vertically excited parametric pendulum with variable-length using a sinusoidal excitation as a vibrating machine, is presented. With this, more oscillations can be achieved, reducing human effort further and having high output than the existing pendulum water pump with the conventional pendulum. The pendulum, lever, and piston assembly are modeled by a separate dynamical system and then joined into the many degrees-of-freedom dynamical systems. The present work includes friction while studying the system dynamics and then simulated to verify the system’s harmonic response. The study showed the effect of the pendulum length variability on the whole system’s performance. The vertically excited parametric pendulum with variable length in the system is established, giving faster and longer oscillations than the pendulum with constant length. Hence, more and richer dynamics are achieved. A quasi-periodicity behavior is noticed in the system even after 50 s of simulation time; this can be compensated when a regular external forcing is applied. Furthermore, the lever and piston oscillations show a transient behavior before it finally reaches a stable behavior.

Moving objects by imagination? Amount of finger movement and pendulum length determine success in the Chevreul pendulum illusion.

Hand-held pendulums can seemingly oscillate on their own, without perceived conscious control. This illusion, named after Chevreul, is likely a result of ideomotor movements. While this phenomenon was originally assumed to have a supernatural basis, it has been accepted for over 150years that the movements are self-generated. However, until now, recordings of the small movements that create these oscillations have not been performed. In this study, we examined how participants produce these unconscious oscillations using a motion capture system. As expected, the Chevreul pendulum illusion was produced when the fingers holding the pendulum generated an oscillating frequency close to the resonant frequency of the pendulum, where very small driving movements of the arm are sufficient to produce relatively large pendulum motion. We found that pendulum length significantly affected the ability to produce the illusion - participants were much more successful with a 40cm compared to an 80cm pendulum. Further, we found that participants that tended to move their fingers more were more successful in producing the illusion but did not find a connection between inter-joint coordination and ability to generate the illusion.

Differential design based on double pendulum anti-galloping device for important line

Based on the differential anti-galloping concept and Double Pendulum Anti-galloping Device, optimization analysis was carried out for the ordinary span and long span of 1000 kV Ultra-High-Voltage AC transmission project. Based on the full investigation of the design conditions of ordinary span and long span of the UHV AC line, and the stability mechanism, the influence of the theoretical pendulum length values of Double Pendulum Anti-galloping Device on the instability characteristics of iced conductor with different icing thickness and ambient wind speed were calculated and analyzed. The results showed that 900 mm should be taken as the theoretical pendulum length of the ordinary span, and 800 mm for the long span, which can obtain the best anti-galloping effect, which provides a reliable reference for the anti-galloping design of subsequent UHV transmission lines.

Demonstrating Conical Pendulum Stable and Unstable States

This article analyzes and experimentally verifies the stability behavior of the equilibrium states of a conical pendulum. An analysis of the motion presents that the equilibrium states of the pendulum are determined by the pendulum angular speed. For a given pendulum length there exists a critical angular speed that determines stability conditions. Experimental results obtained using a variable speed rotator confirm the relationship between angular speed and equilibrium state conditions. An initially at rest pendulum has a stable equilibrium position that is vertically hanging straight down; however, it is shown that when gradually increasing the speed of a mechanical rotator to approach and surpass the pendulum critical speed, the initial stable equilibrium state becomes unstable. Furthermore, the pendulum, now in an unstable equilibrium, moves to a new stable equilibrium position that did not exist at speeds below the critical speed.

Critical parameters for the robust stabilization of the inverted pendulum with reaction delay: State feedback versus predictor feedback

AbstractThe critical length that limits stabilizability for delayed proportional‐derivative‐acceleration (PDA) feedback and for predictor feedback (PF) is analyzed for the inverted pendulum paradigm. The aim of this work is to improve the understanding of human balancing tasks such as stick balancing on the fingertip, which can be modeled as a pendulum cart system. The relation between the critical length of the balanced stick and the reaction time delay in the presence of sensory uncertainties, which are modeled as static parameter perturbations in the control gains, is investigated rigorously. Robust stabilizability analysis is performed using the real structured stability radius. Performance is assessed by the length of the shortest pendulum (critical length) that can still be balanced for a fixed reaction delay. For both PDA feedback and PF control with delay mismatch, it is observed that the relation between the critical length and the reaction delay remains quadratic in the presence of perturbations on the control gains (of fixed size). Numerical comparison shows that predictor feedback is superior over PDA feedback in terms of critical length: shorter pendulum can be balanced by PF than by PDA feedback for the same reaction delay and for the same static parameter perturbation. Furthermore, it is found that both control concepts are more sensitive to the change in the feedback delay than on the same relative change in the parameter uncertainties. Interpretation to human balancing suggests that it is more challenging for the nervous system to cope with reaction delay than with sensory uncertainties.

Damping Oscillation of Suspended Payload by Varying String Length

Abstract Many modern-day applications involve transport of objects suspended through cables such as in overhead cranes or landing of rovers on the Martian surface. Any undesired oscillation of the payload has the potential risk of instability, and the problem of damping such oscillation and stabilizing the payload at the desired length is the control objective of this article. The system is modeled as a variable length pendulum (VLP), which comprises a payload suspended via a string wrapped around a pulley. The length of the pendulum is varied using clockwise/counterclockwise rotation of the pulley through torque applied by a motor. For a known payload mass, a nonlinear control design is first presented that guarantees asymptotic stability of the desired equilibrium with limited state measurements. The design is then modified for it to handle significant uncertainty in payload mass. The effectiveness of both designs is validated in simulations.

A Passive Adaptive Suspended Mass Pendulum to Compensate Detuning Due to Large Swing Angle

The suspended mass pendulum (SMP) conventionally used is a type of frequency sensitive vibration control device. It is vulnerable to detuning due to large amplitude oscillations, which can lead to a significant loss in vibration control performance. Although active or semi-active control systems can solve the problem of frequency detuning, the reliability and stability of the sensors and actuators in the control system are difficult to guarantee for large-scale civil structures. To overcome this issue, this study proposes a passive adaptive suspended mass pendulum (PASMP) that uses a curved support. First, the mathematical equations describing the curved support are derived to show that it can keep the frequency of the pendulum constant at large swing angles. Then the kinematic equations of a single-degree-of-freedom (SDOF) structure installed with the PASMP are established. A parametric analysis is conducted to verify how the parameters of the control system, including the excitation period, pendulum length and mass ratio, affect the dynamic responses of the main structure. Furthermore, to verify the effectiveness of the PASMP and the validity of the theoretical analysis, a two-story frame structure is chosen as the model structure in shaking table tests. Also, the proposed PASMP is applied to a transmission tower to numerically verify its effectiveness of vibration suppression under different seismic excitations. The numerical and experimental results demonstrate that the PASMP can more effectively suppress the vibration of structures than the conventionally used SMP.

The lengthening pendulum: Adiabatic invariance and bursting solutions

The adiabatic invariance of the action variable of a length varying pendulum is investigated in terms of the two different time scales that are associated with the problem. A length having a general polynomial variation in time is studied; an analytical solution for a pendulum with length which varies quadratically in time is obtained in the small angle approximation. We find that for length with quadratic time variation, the action neither converges (as it does for linear time variation), nor diverges (as it does for exponential time variation), but rather shows oscillatory behaviour with constant amplitude. It is then shown that for a pendulum length which has a combination of periodic and linear time variations, the action is no longer an adiabatic invariant and shows jumps with time. In the case in which the length varies sinusoidally in time, we demonstrate that the full nonlinear system exhibits bursting oscillations.

Theoretical study of the movement of a mobile object in different trajectories with a coupled pendulum

Coupled systems are studied within classical mechanics. In this work, using the formulations of classical mechanics, such as the Lagrange and Hamilton formulations, we analysed the system composed of an object of mass M in motion, to which a pendulum of length l and mass m is coupled. We studied the movement of the object when it moves in a single dimension (y direction) with pendulum oscillations: 1) in 2D (zy-plane) and 2) 3D (surface xyz). Subsequently, the movement of the object is studied when it moves in a circle of radius R with the same oscillation conditions referred to for the pendulum.