The Bouncing Ball Apparatus as an Experimental Tool

2005 ◽  
Vol 128 (2) ◽  
pp. 330-340 ◽  
Author(s):  
Ananth Kini ◽  
Thomas L. Vincent ◽  
Brad Paden
Keyword(s):  
Control Algorithm ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Domain Of Attraction ◽  
Coefficient Of Restitution ◽  
Initial State ◽  
Domains Of Attraction ◽  
Chaotic Control ◽  
Bouncing Ball ◽  
And Control

The bouncing ball on a sinusoidally vibrating plate exhibits a rich variety of nonlinear dynamical behavior and is one of the simplest mechanical systems to produce chaotic behavior. A computer control system is designed for output calibration, state determination, system identification, and control of a new bouncing ball apparatus designed in collaboration with Magnetic Moments. The experiments described here constitute the first research performed with the apparatus. Experimental methods are used to determine the coefficient of restitution of the ball, an extremely sensitive parameter needed for modeling and control. The coefficient of restitution is estimated using data from a stable one-cycle orbit both with and without using corresponding data from a ball map. For control purposes, two methods are used to construct linear maps. The first map is determined by collecting data directly from the apparatus. The second map is derived analytically using a high bounce approximation. The maps are used to estimate the domains of attraction to a stable one-cycle orbit. These domains of attraction are used to construct a chaotic control algorithm for driving the ball to a stable one-cycle from any initial state. Experimental results based on the chaotic control algorithm are compared and it is found that the linear map obtained directly from the data not only gives a more accurate representation of the domain of attraction, but also results in more robust control of the ball to the stable one-cycle.

On Nonlinear Dynamics and Control of an Inverted Flexible Pendulum System With Chaos

2019 ◽  
Author(s):  
Hartiny Kahar ◽  
Dirk Söffker
Keyword(s):  
Control Method ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Energy Content ◽  
Dynamical Behavior ◽  
Pendulum System ◽  
Time Frequency ◽  
Dynamics And Control ◽  
Specific Frequency ◽  
And Control

Abstract In this paper, the dynamical behavior of a nonlinear mechanical system is considered, namely an inverted flexible pendulum excited in its base by a cart driven by a motor. In this experimental procedure, the chaotic motion of the pendulum tip was identified, in combination with a specific range of parameters. Time-frequency energy analysis is performed to be used for modeling the transition between the equilibria of the chaotic systems. Controlling the chaotic behavior of the system is realized using impulsive control method, where additive impulses are injected into the system, designed with specific impulses energy content at a specific frequency band. The experimental results are presented and discussed in detail, concentrating on how the designed impulses have to be injected to affect the system, specifically the transition between states of equilibria. The results from this experimental modeling procedure show that both additive impulse design and frequency filtering of the injected additive impulses are able to stimulate the equilibrium shift and therefore to control the chaotic behavior of the system.

scholarly journals Chaos Analysis and Control of Relative Rotation System with Mathieu-Duffing Oscillator

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Yu Zhang ◽  
Longsuo Li
Keyword(s):  
Chaotic Behavior ◽  
Duffing Oscillator ◽  
Dynamical Behavior ◽  
Gaussian White Noise ◽  
Stable State ◽  
Phase Portraits ◽  
Relative Rotation ◽  
Chaos Analysis ◽  
Rotation System ◽  
And Control

Chaos analysis and control of relative rotation nonlinear dynamic system with Mathieu-Duffing oscillator are investigated. By using Lagrange equation, the dynamics equation of relative rotation system has been established. Melnikov’s method is applied to predict the chaotic behavior of this system. Moreover, the chaotic dynamical behavior can be controlled by adding the Gaussian white noise to the proposed system for the sake of changing chaos state into stable state. Through numerical calculation, the Poincaré map analysis and phase portraits are carried out to confirm main results.

Iterative learning control algorithm for sensor fault nonlinear systems

2020 ◽  
pp. 1-8
Author(s):  
Zimian Lan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Sensor Fault ◽  
Initial State ◽  
Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

The Research of Air Precooling System Based on Generalize Predictive Control Strategy

2013 ◽  
Vol 433-435 ◽  
pp. 1091-1098
Author(s):  
Wei Bo Yu ◽  
Cui Yuan Feng ◽  
Ting Ting Yang ◽  
Hong Jun Li
Keyword(s):  
Predictive Control ◽  
Control Strategy ◽  
Control Algorithm ◽  
Exchange Process ◽  
Generalized Predictive Control ◽  
Matlab Simulation ◽  
Control Effect ◽  
Heat Exchange Process ◽  
Complex Control System ◽  
And Control

The air precooling system heat exchange process is a complex control system with features such as: nonlinear, lag and random interference. So choose Generalized Predictive Control Algorithm that has low model dependence, good robustness and control effect, as well as easy to implement. But due to the large amount of calculation of traditional generalized predictive control and can't juggle quickness and overshoot problem, an improved generalized predictive control algorithm is proposed, then carry out the MATLAB simulation, the experimental results show that the algorithm can not only greatly reduce the amount of computation, but also can restrain the overshoot and its rapidity.

Modelling and control of a photovoltaic energy system with battery storage

2018 ◽  
Author(s):  
Carlos Y. García-Ramos ◽  
Jose M. González-Cava ◽  
José F. Gómez González ◽  
Sara González Pérez
Keyword(s):  
Energy Management ◽  
Control Algorithm ◽  
Hotel Industry ◽  
Energy System ◽  
Energy Management System ◽  
Battery Storage ◽  
Photovoltaic Generation ◽  
Renewable Power ◽  
First Results ◽  
And Control

"This work presents a simulated study of the energy management of an energy system connected to the grid with photovoltaic generation and battery storage. The work proposes a energy management system based on fuzzy logic. It is intended to be used in the hotel industry. The objective of the proposed controller is to maximise the renewable power source but including also economic criteria in the management. The proposal was implemented in simulation considering a 5,1kW peak photovoltaic installation and a set of batteries with a capacity of 384Ah. First results obtained show that the system achieves the specifications proposed. Thus, the study evidences the potential of the proposed control algorithm and demonstrate the suitability of the use of intelligent techniques for the energy management in hotels."

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