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.

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.

Research on Planar Double Compound Pendulum Based on RK-8 Algorithm

Establishing the Lagrangian equation of double complex pendulum system and obtaining the dynamic differential equation,we can analyze the motion law of double compound pendulum with application of the numerical simulation of RK-8 algorithm.When the double compound pendulum swings at a small angle,the Lagrangian equation can be simplified and the normal solution of the system can be solved.And we can walk further on the relationship between normal frequency and swing frequency of double pendulum.When the external force of normal frequency is applied to the double compound pendulum,the forced vibration of the double compound pendulum will show the characteristics of beats.

A special hierarchical fuzzy neural-networks based reinforcement learning for multi-variables system

Proposes a reinforcement learning scheme based on a special Hierarchical Fuzzy Neural-Networks (HFNN)for solving complicated learning tasks in a continuous multi-variables environment. The output of the previous layer in the HFNN is no longer used as if-part of the next layer, but used only in then-part. Thus it can deal with the difficulty when the output of the previous layer is meaningless or its meaning is uncertain. The proposed HFNN has a minimal number of fuzzy rules and can successfully solve the problem of rules combination explosion and decrease the quantity of computation and memory requirement. In the learning process, two HFNN with the same structure perform fuzzy action composition and evaluation function approximation simultaneously where the parameters of neural-networks are tuned and updated on line by using gradient descent algorithm. The reinforcement learning method is proved to be correct and feasible by simulation of a double inverted pendulum system.

Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller

This paper presents LQR sliding surface-based Sliding Mode Controller(LQR-SMC)for balancing control of a Rotary Double Inverted Pendulum(RDIP)system.It is a challenging research topic in control engineering due to its nonlinearity and instability.The RDIP system uses only a motor to control two serially connected pendulums to stand at the upright position.The sliding surface is designed based on the LQR optimal gain.Nonsingular gain matrix is obtained by using the left inverse of the input matrix in the state space form of the system dynamics.The Lyapunov stability theory is used to determine the stability of the controller.To evaluate the performance of LQR-SMC,some performance indices,including the Integral Absolute Error(IAE),Integral Time Absolute Error(ITAE),and the Integrated Square Error(ISE),are used.System stability can be maintained by LQR-SMC under external disturbances as well as model and parameter uncertainties.

THE KAM THEORY OF DOUBLE PENDULUM

The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “total generalized momentum” conservation of the gravity free system can be kept when the gravity is small in comparison with the total enery.

Optimizing the Double Inverted Pendulum′s Performance via the Uniform Neuro Multiobjective Genetic Algorithm

An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before those programmes are applied in real situations. This study aims to find the optimum input setting for a double inverted pendulum（DIP）, which requires an appropriate input to be able to stand and to achieve robust stability even when the system model is unknown. Such a DIP input could be widely applied in engineering fields for optimizing unknown systems with a limited budget. Previous studies have used various mathematical approaches to optimize settings for DIP, then have designed control algorithms or physical mathematical models.This study did not adopt a mathematical approach for the DIP controller because our DIP has five input parameters within its nondeterministic system model. This paper proposes a novel algorithm, named Uni Neuro, that integrates neural networks（NNs） and a uniform design（UD） in a model formed by input and response to the experimental data（metamodel）. We employed a hybrid UD multiobjective genetic algorithm（HUDMOGA） for obtaining the optimized setting input parameters. The UD was also embedded in the HUDMOGA for enriching the solution set, whereas each chromosome used for crossover, mutation, and generation of the UD was determined through a selection procedure and derived individually. Subsequently, we combined the Euclidean distance and Pareto front to improve the performance of the algorithm. Finally, DIP equipment was used to confirm the settings. The proposed algorithm can produce 9 alternative configured input parameter values to swing-up then standing in robust stability of the DIP from only 25 training data items and 20 optimized simulation results. In comparison to the full factorial design, this design can save considerable experiment time because the metamodel can be formed by only 25 experiments using the UD. Furthermore, the proposed algorithm can be applied to nonlinear systems with multiple constraints.

Study on Galloping Stability Mechanism of Conductor and Its Application to Anti-Galloping of Transmission Lines

Galloping of conductor is a major hazard to safe operation of transmission lines. This paper introduces the basic galloping stability mechanism of conductor, design method of anti-galloping and the application of anti-galloping double pendulum and integral eccentric pendulum in China. Galloping stability mechanism of conductor was established based on vertical galloping mechanism developed by Den Hartog and torsional galloping mechanism developed by O. Nigel. A design method of anti-galloping was derived and anti-galloping double pendulum and integral eccentric pendulum were developed. Applications to several transmission lines including a 500 kV transmission line of large span indicated that they have played important roles in anti-galloping.