EQUATION OF MOTION FOR NOVEL FRICTION PENDULUM SYSTEM WITH DUAL ROLLERS

A novel friction pendulum system （FPS） with dual rollers is studied based on the multibody dynamics theory. By analyzing kinematic characteristics of the system, it is reduced to a one degree-of-freedom system. Then the equation of motion for the system is analytically derived by applying the theorem of the relative kinetic energy for a system of particles in differential form in the non-inertial reference system described as a nonlinear differential equation. In the case of the small angular displacement, the natural frequency of the corresponding undamped linear system is obtained, which is consistent with the experimental observation. The derived equation is useful for the study of dynamic characteristics of novel FPS, and its solution directly expedites the simulation of the system in a control loop, and further facilitates the semi-active control process including novel FPS.

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.

Tri-directional shaking table tests of vibration sensitive equipment with static dynamics interchangeable-ball pendulum system

Recently, the high-tech industry has become a key industry for economic development in many countries. However, vibration sensitive equipment located in these industrial buildings is vulnerable during earthquakes, which may cause huge economic loss. In this study, an innovative isolator for safeguarding the vibration sensitive equipment, namely, the static dynamics interchangeable^all pendulum system （SDI-BPS） is proposed and investigated to examine its protective capability for the vibration sensitive equipment during earthquakes through a series of tri-directional shaking table tests. The experimental results illustrate that the SDI-BPS isolator can provide significant damping to rolling types of base isolation systems for reducing the bearing displacement and size, and avoid the stress concentration, which can cause damage or scratches on the rolling surface of the isolator, to prolong its life span of service. The SDI-BPS isolator also provides excellent capability in protecting the vibration sensitive equipment and exhibits a stable behavior under long terms of service loadings and earthquakes.

Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays:Application to A Visual Servo Inverted Pendulum System

A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.

Collective dynamics in a non-dissipative two-coupled pendulum system

We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Fu~.hermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincar6 sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.

Novel active fault-tolerant control scheme and its application to a double inverted pendulum system

On the basis of the gain-scheduled H∞ design strategy, a novel active fault-tolerant control scheme is proposed. Under the assumption that the effects of faults on the state-space matrices of systems can be of affine parameter dependence, a reconfigurable robust H∞ linear parameter varying controller is developed. The designed controller is a function of the fault effect factors that can be derived online by using a well-trained neural network. To demonstrate the effectiveness of the proposed method, a double inverted pendulum system, with a fault in the motor tachometer loop, is considered.

Pendulum systems for harvesting vibration energy from railroad tracks and sleepers during the passage of a high-speed train: A feasibility evaluation

We evaluate the feasibility of recovering energy from the vibrations of track and sleepers,during passage of a high-speed train,by means of a pendulum harvester.A simple mathematical model of the parametric pendulum is employed to obtain numerical predictions,while measured data of vibration tests during the passage of a Thalys high-speed train are considered as input forcing.Since a sustained rotation is the most energetic motion of a pendulum,the possibility of achieving such state is evaluated,taking into account the influence of initial conditions,damping and other factors.Numerical simulations show that rotating pendulum harvesters with sufficiently low viscous damping could be able to generate a usable average power on the order of 5–6 W per unit.Considering a modular arrangement of devices,such energy is enough to feed variety of rail-side equipment,as wireless sensors or warning light systems.However,a suitable choice of initial conditions could be a difficult task,leading to the need of a control action.

Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback

This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4.Such a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in NDDEs.In addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.

Nonlinear dynamics of a classical rotating pendulum system with multiple excitations

We report an attempt to reveal the nonlinear dynamic behavior of a classical rotating pendulum system subjected to combined excitations of constant force and periodic excitation.The unperturbed system characterized by strong irrational nonlinearity bears significant similarities to the coupling of a simple pendulum and a smooth and discontinuous(SD)oscillator,especially the phase trajectory with coexistence of Duffing-type and pendulum-type homoclinic orbits.In order to learn the effect of constant force on this pendulum system,all types of phase portraits are displayed by means of the Hamiltonian function with large constant excitation especially the transitions of complex singular closed orbits.Under sufficiently small perturbations of the viscous damping and constant excitation,the Melnikov method is used to analyze the global structure of the phase space and the feature of trajectories.It is shown,both theoretically and numerically,that this system undergoes a homoclinic bifurcation and then bifurcates a unique attracting rotating limit cycle.Finally,the estimation of the chaotic threshold of the rotating pendulum system with multiple excitations is calculated and the predicted periodic and chaotic motions can be shown by applying numerical simulations.

The Design of Inverted Pendulum System Based on Virtual Prototype Technology and PID Control

A design scheme of a single Inverted Pendulum Virtual Prototype based on the combination of software and hardware is introduced.It uses hardware platform of C8051F020 single chip and the software of Matlab,Visual Basic and Kingview.It can simulate the force and movement of Inverted Pendulum expediently and intuitively.The combination of software and hardware makes the system closer to the reality.The concrete scheme is introduced in the paper and the result of PID control which verifies the correctness of the scheme.

Using Adaptive Gain Scheduling LQR Method Control of Arm Driven Inverted Pendulum System Based on PIC18F4431

The arm driven inverted pendulum system is a highly nonlinear model, muhivariable and absolutely unstable dynamic system so it is very difficult to obtain exact mathematical model and balance the inverted pendulum with variable position of the ann. To solve this problem, this paper presents a mathematical model for arm driven inverted pendulum in mid-position configuration and an adaptive gain scheduling linear quadratic regulator control method for the stabilizing the inverted pendulum. The proposed controllers for arm driven inverted pendulum are simulated using MATLAB-SIMULINK and implemented on an experiment system using PIC 18F4431 mieroeontroller. The result of experiment system shows the control performance to be very good in a wide range stabilization of the arm position.

Swinging up a Real-Time Inverted Pendulum System

In this study, a real-time control of the cart inverted pendulum system was developed using Mamdani type Fuzzy Logic Controller. Swing-up and stabilization of the inverted pendulum were implemented directly in a Fuzzy Logic Controller. The fuzzy logic controller was designed in the Matlab-Simulink environment and applied into in a Quasar controller board. Swing-up algorithm brings the pendulum near to its inverted position in 5 seconds from downward position. External forces were applied on the inverted pendulum to test the robustness of the fuzzy logic controller under internal as well as external disturbances. The inverted pendulum system showed an acceptable robustness to the external and internal disturbances.

Modelling and Analysis of Base Isolated Structures with Friction Pendulum System Considering near Fault Events

The seismic behavior of base isolated structures with friction pendulum slide bearings devices subjected to near fault events characterized by significant vertical ground motion components is investigated. In particular, in order to evaluate the effects of vertical components on seismic response, non-linear dynamic analysis, carried out by using several numerical models, have been performed by considering two near-fault seismic events, L’Aquila 2009 and Emilia Romagna 2012. The obtained results show that increasing vertical seismic motion base shear significantly increases while relative displacements increase very little.

Fast Detection of Chaotic or Regular Behavior of Double Pendulum System： Application of the Fast Norm Vector Indicator Method

It is well known that for non-linear Hamiltonian systems there exist ordered regions with quasi-periodic orbits and regions with chaotic orbits. Usually, these regions are distributed in the phase space in very complicated ways, which often makes it very difficult to distinguish between them, especially when we are dealing with many degrees of freedom. Recently, a new, very fast and easy to compute indicator of the chaotic or ordered nature of orbits has been introduced by Zotos （2012）, the so-called ＂Fast Norm Vector Indicator （FNV1）＂. Using the double pendulum system, in the paper we present a detailed numerical study comporting the advantages and the drawbacks of the FNVI to those of the Smaller Alignment Index （SALI）, a reliable indicator of chaos and order in Hamiltonian systems. Our effort was focused both on the traditional behavior of the FNVI for regular and fully developed chaos but on the ＂sticky＂ orbits and on the quantitative criterion proposed by Zotos, too.

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions.The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.

Design of A Hydraulic Power Take-off System for the Wave Energy Device with An Inverse Pendulum

This paper describes a dual-stroke acting hydraulic power take-off （PTO） system employed in the wave energy converter （WEC） with an inverse pendulum. The hydraulic PTO converts slow irregular reciprocating wave motions to relatively smooth, fast rotation of an electrical generator. The design of the hydraulic PTO system and its control are critical to maximize the generated power. A time domain simulation study and the laboratory experiment of the full-scale beach test are presented. The results of the simulation and laboratory experiments including their comparison at full-scale are also presented, which have validated the rationality of the design and the reliability of some key components of the prototype of the WEC with an inverse pendulum with the dual-stroke acting hydraulic PTO system.

Mathematical modeling of elastic inverted pendulum control system

Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.

PERFORMANCE OF ULTRA-LOW FREQUENCY PASSIVE VERTICAL VIBRATION ISOLATION SYSTEM WITH REVERSE PENDULUM

A novel long period passive vertical vibration isolatorconstructed by mounting reverse pendu- lums on two pairs of torsionsprings is presented. By theoretical analysis and numericalcalculation, it is shown that the isolator can achieve much longerresonant period due to gravitational positive feedback and is smallerin size than the current torsion spring isolators with the samegeometric parameters.

Seismic response of selective pallet racks isolated with friction pendulum bearing system

The concept of base isolation for storage racks is still a developing subject and has not been addressed in the recently updated seismic codes for storage racks.The friction pendulum bearing system(FPS)generates a natural period independent of the structure's seismic mass.This property makes FPS an ideal choice for isolating rack structures since merchandise may be placed on the racks in several possible arrangements.The results of a comprehensive parametric study aimed at evaluating the seismic performance of a four-shelf,two-bay selective pallet rack isolated with FPS is presented in this paper.The influence of radius of curvature of the FPS,seismic mass,and mass irregularity on the rack's seismic response is examined.The effect of variation of the coefficient of friction due to axial loading is studied by choosing friction values from two distinct friction characterization studies.The coefficient of friction calculated from these studies shows mild and significant variations,respectively,for the whole range of static axial loads expected on the isolator,and from different pallet mass arrangements considered.The optimum radius of curvature and the appropriate range of friction coefficient,for the defined range of static axial loads,to attain a desirable seismic performance are determined.

The Property of Dichotomy for a Class of Interconnected Pendulum-like Systems

The property of dichotomy of interconnected second-order pendulum-like systems with multiple equilibria is investigated. This interconnection can be viewed as harmonic control of independent sub-systems. Linear interconnections and a class of input and output interconnections are considered in this paper. The effects of input and output interconnections are shown through a permutation matrix. Frequency domain and linear matrix inequality (LMI) conditions of dichotomy of interconnected pendulum-like systems are derived. It is shown that global properties of two coupled systems can be changed significantly through interconnections. Examples are given to illustrate the results.