Control of the Cart-Pendulum System Based on Discrete Mechanics — Part I: Theoretical Analysis and Stabilization Control —

2012 ◽  
Vol E95-A (2) ◽  
pp. 525-533 ◽  
Author(s):  
Tatsuya KAI
Keyword(s):  
Theoretical Analysis ◽  
Discrete Mechanics ◽  
Pendulum System ◽  
Stabilization Control

Study on Dynamical Behaviors Mechanism of Sine Voltage Compensation in Buck Converters

2014 ◽  
Vol 536-537 ◽  
pp. 1497-1500
Author(s):  
Fang Ying Zhang ◽  
Wei Hu ◽  
Xiao Li Long ◽  
Xin Bing Chen
Keyword(s):  
Theoretical Analysis ◽  
Duty Cycle ◽  
Monodromy Matrix ◽  
Buck Converter ◽  
Buck Converters ◽  
Stabilization Control ◽  
Dynamical Behaviors ◽  
Voltage Compensation ◽  
Signal Changes ◽  
Compensation Signal

This paper analyzes the effect of stable behaviors when amplitude, phase of sine voltage compensation signal are added in the system, reveals that the dynamical behaviors mechanism that sine voltage compensation signal changes feedback voltage-mode controlled buck converter lies in changing the duty cycle without impacting the system stable error via analyzing the change of period multiplier in Monodromy matrix and conditions of period bifurcation, and finally achieves stabilization control for bifurcation and chaotic behaviors. The simulation and experimental results prove the correctness of the theoretical analysis.

Soft-Target-Based Predictive Fuzzy Control for a Cart-Pendulum System with Dynamic Constraints

2007 ◽  
Vol 11 (8) ◽  
pp. 931-936 ◽  
Author(s):  
Yougen Chen ◽  
◽  
Seiji Yasunobu
Keyword(s):  
Self Regulation ◽  
Target Setting ◽  
Pendulum System ◽  
Dynamic Constraints ◽  
Intelligent Controller ◽  
Stabilization Control ◽  
Single Target ◽  
Self Adaptation ◽  
Soft Target ◽  
Target Sets

Human decisions to act are based on broad targets and respond flexibly in different situations. Such, self-adaptation to dynamic constraints is difficult but important for autonomous control. Conventional control usually uses a single target that results in inflexibility in responding to dynamic environments such as changes in constraints. We propose a predictive fuzzy intelligent controller based on soft targets defined as a series of target sets that include many target elements with different satisfaction grades and are converted to target setting knowledge by fuzzy logic. This controller was applied to upswing and stabilization control of a cart-pendulum system with dynamic changing limit positions as constraints to realize situational self-adaptation and target self-regulation. Simulation and experiments demonstrated the feasibility of our soft-target-based intelligent controller.

Nonlinear Responses of Dual-Pendulum Dynamic Absorbers

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Theoretical Analysis ◽  
Frequency Response ◽  
Pitchfork Bifurcation ◽  
Hopf Bifurcations ◽  
Response Curves ◽  
Pendulum System ◽  
Mode Localization ◽  
Bifurcation Points ◽  
Chaotic Vibrations ◽  
Nonlinear Responses

The nonlinear responses of a single-degree-of-freedom system with two pendulum tuned mass dampers under horizontal sinusoidal excitation are investigated. In the theoretical analysis, van der Pol’s method is applied to determine the expressions for the frequency response curves. In the numerical results, the differences between the responses in single- and dual-pendulum systems are shown. A pitchfork bifurcation occurs followed by mode localization where both identical pendula vibrate at constant but different amplitudes. Hopf bifurcations occur, and then amplitude- and phase-modulated motions including chaotic vibrations appear in the identical dual-pendulum system. The Lyapunov exponents are calculated to prove the occurrence of chaotic vibrations. In a nonidentical dual-pendulum system, a perturbed pitchfork bifurcation occurs and saddle-node bifurcation points appear instead of pitchfork bifurcation points. Hopf bifurcations and amplitude- and phase-modulated motions also appear. The deviation of the tuning condition is also investigated by showing the frequency response curves and bifurcation sets. The numerical simulations are shown to be in good agreement with the theoretical results. In experiments, the imperfections of the two pendula were taken into consideration, and the validity of the theoretical analysis was confirmed.

Nonlinear Responses of Dual Pendulum Dynamic Absorbers

2009 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Theoretical Analysis ◽  
Frequency Response ◽  
Pitchfork Bifurcation ◽  
Hopf Bifurcations ◽  
Response Curves ◽  
Pendulum System ◽  
Bifurcation Points ◽  
Chaotic Vibrations ◽  
Nonlinear Responses ◽  
Pitchfork Bifurcations

The nonlinear responses of a single-degree-of-freedom (SDOF) system with two pendulum tuned mass dampers (TMDs) under horizontal sinusoidal excitation are investigated. In the theoretical analysis, van der Pol’s method is applied to determine the expressions for the frequency response curves. In the numerical results, the differences between single- and dual-pendulum systems are shown. Pitchfork bifurcations occur followed by mode localization where both identical pendulums vibrate but at different amplitudes. Hopf bifurcations occur and then amplitude modulated motions including chaotic vibrations appear in the identical dual-pendulum system. The Lyapunov exponents are calculated to prove the occurrence of chaotic vibrations. In a non identical dual-pendulum system, perturbed pitchfork bifurcations occur and saddle-node bifurcation points appear instead of pitchfork bifurcation points. Hopf bifurcations and amplitude modulated motions also appear. The deviation of the tuning condition is also investigated by showing the frequency response curves and bifurcation sets. The numerical simulations are shown to be in good agreement with the theoretical results. In experiments, the imperfections of the two pendulums were taken into consideration and the validity of the theoretical analysis was confirmed.

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