Wave Algorithm Analysis of Periodic Perfect Energy Transfer between Two Globally Coupled Vibro-Impact Oscillators(in Case of Perfect Elastic Collision at Balanced Position)

Mechanical Engineering Journal

Ichizaki

2017

Self Cite

Although more than 55 years have been passed since its first development, it remains unknown whether a posicast-shaped function (PSF) is a unique intermittent input command for a one-time rapid rest-to-rest motion in one natural period. In addition, it has not been determined whether more generalized expressions exist. We recently deduced an intermittent input command of a feedforward formula, called a vibration manipulation function for one natural period (oVMF), to manipulate an undamped 1-DOF linear floating oscillator in an arbitral operational period based on the dynamics of three vibro-impact oscillators under a Grover algorithm in the field of quantum information. As a special case of oVMF, we can define the formula of an input command for a restto-rest motion in one natural period, called roVMF. In this study, we proved that any PSF for an undamped 1-DOF oscillator (uPSF) can be expressed as an infinite series of roVMF. Moreover, because uPSF has a stricter symmetrical property than roVMF, we have concluded that the set of uPSF, Uup, is contained in the set of roVMF, UroV. Hence roVMF is a more general expression than uPSF.

Section: Vibration Manipulation Function Obtained From Grover Algoritmentioning

confidence: 99%

Relation between posicast-shaped function and vibration manipulation function of undamped 1-DOF linear oscillator for one-time rest-to-rest motion in a natural period

Mechanical Engineering Journal

Ichizaki

2017

Self Cite

“…The multibody model of three vibro-impact oscillators along Grover algorithm was firstly proposed by A.D. Patel (9) . The conditions of the oscillators were precisely formulated by S. Takata et al (4) . In this model, wave function consists of coherent phonons, which are treated as various modes of vibration in classical mechanics.…”

Section: Vibration Manipulation Function Obtained From Grover Algorithmmentioning

confidence: 99%

“…Recently, we have deduced analytical intermittent function of the base trajectory, called vibration manipulation function (VMF), from the system of three vibro-impact oscillators which is designed under Grover algorithm (4) . The trajectories of the oscillators are determined from free motions of the system under Hamilton's principle of least action during operational period between neighboring instants of impact.…”

Section: Introductionmentioning

confidence: 99%

Active Sampled-data Controlled Suspension in Automobile with Vibration Manipulation Functions

Kawakita

2016

IJAE

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The intermittent feedforward function, termed vibration manipulation function (VMF), was proposed for sampled-data control of an actuator to achieve active suspension of an automobile with road profile undulation. The function can manipulate the position and velocity of a sprung mass of a 1DOF quarter car model in every arbitral operational period. Elongation or force of the actuator can be determined from VMF, which works to suppress vibration of the sprung mass without knowing road profile. Since required power of the actuator can be made smaller and intermittently-feedbacked feedforward control is much easier to be realized, proposed method could provide an alternative guiding principle for active suspension of automobile.

“…Since the algorithm can be applied to the classical wave phenomena of the oscillators, it is called wave algorithm, instead of quantum. The phenomenon of energy transfer in the oscillators has been studied by S. Takata et al as almost periodical oscillation [12] and Graze phenomena in the impact oscillator [13]. K. Yagi et al have derived the function of enforced displacement for steady vibration of a 1DOF oscillator [14] from the algorithm.…”

Section: B Grover Algorithm In Three-vibro-impact Oscillatorsmentioning

confidence: 99%

Vibration manipulation function as general lifting function for discrete sampled-data tracking control of 1DOF oscillator

2015 IEEE/SICE International Symposium on System Integration (SII)

2015

Self Cite

Intermittent lifting function, termed vibration manipulation function (VMF), is proposed as a general formula of inverse problem to manipulate a linear one-degree-of-freedom (1DOF) oscillator. Discrete sampled-data tracking control is realized by using the continuous intermittent feedforward control and discrete sampled-data feedback decided from previously determined discrete aimed states in every operating instant. Since VMF can be modified repeatedly from the discrete error deviation, we can minimize error deviation between discrete sampled output and discrete aimed value in order to make the system robust.