黒田 雅治

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method correspond-ing to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

© 2020, The Author(s). A new approach to the active fault diagnosis (AFD) for input redundant plants is presented in this paper. A test signal which helps the diagnosis is injected to the plant in addition to nominal control input in the AFD typically. One feature of the proposed AFD is adaptive allocation of the test signal. The adaptive allocator which distributes the test signal and injects it to the redundant actuators is introduced in this paper. A fault-diagnosis (FD) system that estimates fault location and its magnitude from adaptive parameter of the adaptive allocator is constructed with a simple neural network (NN) model. Furthermore, a A fault-tolerant adaptive control system which includes the adaptive test signal allocator is designed based on the model reference adaptive control (MRAC) technique. The adaptive laws of the adaptive allocator and controller are derived by using a suitable Lyapunov function. By performing experiments using a two-input redundant plant, we show the effectiveness and applicability of the proposed AFD and MRAC system.

This paper describes a novel vibration-mode filtering method for one-dimensional structures such as a cantilevered beam using a two-mode optical fiber as a distributed-effect sensor. One of the most important problems regarding the optical measurement is how to alter the sensor sensitivity spatially along the longitudinal direction of the beam when the sensor is mounted on the beam surface. In this study spatial variation of the sensor orientation with respect to the longitudinal direction is included in the sensor model. The sensor sensitivity can be experimentally measured and used for design, incorporating the orthogonality of the mode shapes of the structure. Moreover, in the light of practical considerations, a design procedure of optimal fiber placement utilizing bipolar weighting functions is presented. Finally, theoretical predictions are confirmed by experimental results and efficient vibration-mode filtering is demonstrated.

This paper deals with the active power flow control of a simply supported thin plate. Particular emphasis is placed on the vortex power flow pattern that has the potential of confining external energy, a cause of exciting vibration modes, into a restricted area and of diverting the power flow out of a specific region where vibration is to be prohibited. With a view to observing the power flow occurring in a plate, a wave visualization system has been developed. Based upon the visualization system, it is verified experimentally that the vortex power flow can be produced at an arbitrary position of a plate. An energy stream function as well as a vorticity function is derived in a general form. Furthermore, both the energy stream and vorticity functions are calculated as a function of vibration modes which are selected in the order of magnitude of their contribution to the total kinetic energy of the plate. As a result, as many as 100 vibration modes are found to be necessary to form a vortex power flow pattern.

This paper considers the modal filtering of a planar structure using point sensors designed for extracting a particular modal amplitude of the structure. It is purpose of this paper to establish the design procedure of a modal filtering based upon point sensors. Much as a distributed modal sensor outstrips a point sensor in the sensing potential, the handling and maintenance are odious. To cope with this problem, this paper presents a design methodology of modal filtering using point sensors easy to handle and maintain it. It is found that modal filtering design of point sensors can be achieved by simply following the design procedure of distributed modal sensors already presented by the authors. It is also found that point sensors perfectly replace the distributed sensors for modal filtering in the frequency range of interest. Experiment is conducted, demonstrating the validity of the point sensor-based modal filtering.

This paper deals with distributed parameter sensors designed with a view to extracting a vibration mode. Compared to conventional point type sensors such as acceleration pickups, displacement sensors etc., the distributed parameter sensors have many benefits provided that they are properly designed. First, this paper overviews a conventional modal filter designed by use of point sensors, and enumerates the problems it involves. To overcome the drawbacks of the point sensor based modal filtering, a novel modal filtering technique based upon a PVDF film sensor, a distributed parameter sensor, is proposed. Two dimensional modal filters are discussed, and then, by taking into consideration a practicability of the sensors, a design procedure of one dimensional modal filters is presented; the number, location and shaping of the one dimensional sensors are clarified. Finally, an experiment is conducted, showing the capability of the distributed parameter modal filtering.

This paper deals with the acoustic power minimization problem from the viewpoint of an active noise and vibration control. This paper places a particular emphasis on the phenomenon in which the acoustic power output of the control source under optimal condition always becomes zero. It is found that the acoustic radiation impedance at and around the control points source becomes reactive under the optimal condition, and hence power output of the control source results in null. It is also shown that the reactive acoustic intensity dominates even in the vicinity of the primary source in order to impede the sound radiation from its source. In active vibration control, the power flow in terms of a control force, applied directly to a vibrating structure in an effort to attenuate the radiated sound is found to be zero. Under the optimal condition for minimizing the tool acoustic radiation power, the effect of the reactive sound field outweighs that of the active sound field significantly over the vibrating plate.

This paper deals with the modal control of a planar structure using distributed-parameter sensors designed with a view to extracting a particular vibration mode. First, this paper overviews the modal control based upon distributed-parameter sensors and actuators. It is found that the utilization of either distributed-parameter sensors or distributed-parameter actuators leads to the elimination of spillover destabilization of a feedback control system. In addition, the distributed-parameter sensors have the advantage of achieving the modal control of a targeted mode of the structure; however, a mere usage of the distributed-parameter actuators results in uncontrollability of the targeted mode. Finally, with one-dimensional PVDF film sensors attached to the planar structure, an experiment is conducted, demonstrating the capability of the distributed-parameter sensors for suppressing the mode of interest without causing any effect on the remaining modes of the structure.

<p>In this paper, we propose a null-space compensation control for linear first-order systems with redundant two input channels. In the input redundant systems, control input vector generally has null-space component of the plant parameter vector. The null-space component does not contribute to the generation of the control force which drives the plant state. If a control input that does not include the null-space component can be generated, efficient control is achieved from the viewpoint of minimizing the norm of the control input. In the proposed method, an adaptive control method is used to design a control system that compensates for the null-space component, even if the plant parameter vector is unknown. The effectiveness is shown by numerical examples.</p>

<p>In this paper, we propose a design method of an adaptive control system for input redundant 2 input 1 output system. The feature of the proposed method is that the control input can be adjusted by an arbitrary external signal by utilizing the degree of freedom of the control input in the input redundant system, and the reference model output tracking can be achieved. A numerical example is shown at the end of this paper, and the proposed method is verified.</p>

© 2019 L & H Scientific Publishing, LLC. The existence of active wave control has been known in the field of the vibration control of large-size space structures (LSS) since the 1960s. Recently, with the goal of energy and resource conservation, active wave control has come into the spotlight again in the field of the vibration suppression of light and thin members widely used in mechanical structures, including automobiles. Therefore, achieving active wave control is both an old and a new problem. A vibration suppression problem for a thin cantilevered beam is presented as an example for discussion. Results clarified √s that the active wave controller includes s and s √ s terms. Those terms are realized as a 1/2-order derivative and a 3/2-order derivative using fractional calculus. The active wave controller is realized through fractional calculus, which is shown to be an important step in the analysis of this problem. Specifically, the active wave controller can be implemented using fractional derivative feedback. The controller involving the fractional derivatives is realized with a digital signal processor based on definitions of fractional calculus. The vibration suppression effect of active wave control is demonstrated both numerically and experimentally.

本研究ではマイクロカンチレバーに振動を付与して加工を行う方法に注目し，実験により加工時のマイクロカンチレバーの振動現象を明らかにすることを目的とした．加工の実現に向けて試料とマイクロカンチレバーの距離に応じたダイナミクスを把握するために，強制加振状態でのフォースカーブ（動的フォースカーブ）を計測した．この結果から，マイクロカンチレバーの振動形態を（a）引力タッピング，（b）斥力タッピング，（c）押しつけこすり，（d）引きこみこすりと分類した．また，マイクロカンチレバーを強制加振した状態で加工実験を行い，加工を行うには押しつけこすり状態が有用であることを切削くずの多さから指摘した．

© 2014 AIP Publishing LLC. A method for vibrational viscometers capable of high-viscosity measurements using self-excited oscillations is proposed and assessed both theoretically and experimentally. Such viscometers are well-known for their rapid response and miniaturization. Unlike conventional methods based on Q-value estimations obtained experimentally from the frequency response or resonance curve, we describe the use of self-excited oscillations in viscosity measurements using positive velocity feedback control without relying on the frequency response curve. Such measurements become possible even for high viscosities where the peak of the frequency response curve is ambiguous or does not exist, i.e., the Q-value cannot be estimated from such curves. Furthermore, the validity of the proposed method is experimentally tested using a prototype self-excited viscometer. Downsized oscillators such as micro- or nanoscale cantilevers can be self-excited following a straightforward application of the method. They are expected to enable not only localized monitoring of changes in high viscosity with time but also spatial high-viscosity measurements by the distributed arrangement of the devices.

The eigenstate shift in two nearly identical and weakly coupled cantilevers provides a means to realize much higher-sensitivity mass detection compared with the eigenfrequency shift approach. We propose using self-excited oscillations for eigenstate detection without using frequency response or resonance curve normally used in conventional methods. Mass sensing thus becomes possible even in high-viscosity environments, where the peak of the frequency response curve is ambiguous or does not exist. The feedback control method is theoretically clarified to produce self-excited oscillation and the validity of the proposed method is investigated experimentally using macroscale coupled cantilevers. © 2013 AIP Publishing LLC.

We report a development of MEMS based viscosity sensor 'η-MEMS' suitable for in-process measurement for industrial uses. The sensor is based on the principle of the vibrating viscometer. The vibrating body of the viscosity sensor is unique dual spiral structure. The geometry provides a seamless surface and a simple structure of the pseudo-parallel wall in order to create the Couette flow for sensing the viscous stress. In the present study, we propose an improved chip holder having an electromagnet coil and verified the capability of viscosity measurement by using the new holder in preliminary measurement of the viscosity standard liquids. © 2013 IEEE.

This study examined a probe cantilever in an atomic force microscope made to vibrate as a van der Pol-type self-excited oscillator using linear and nonlinear feedback to maintain a sufficiently small amplitude of the probe cantilever. Sample surface shape measurements were conducted based on the method proposed herein. In a liquid environment, changes in the amplitude and the equivalent natural frequency of the probe cantilever depending on the atomic force acting between the sample and the probe were investigated experimentally. Results show that even with the noncontact mode using the proposed method in liquid, observation of the sample surface shape can be performed to nanometer order, which is equivalent to the capabilities of existing techniques.

This paper proposes a measurement method of cubic nonlinear elasticity. The measurement system consists of a vibrator and a control circuit. We apply a nonlinear feedback to actuate the vibrator for inducing van der Pol type self-excited oscillation, so that the response amplitude of the oscillation can be arbitrarily set by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity causes a natural frequency shift related to the vibration amplitude of the object. We can set the response amplitude various values by changing the nonlinear feedback gain and measure the shift of the response frequency depending on the magnitude of the response amplitude. As a result, the bend of the backbone curve reflecting the nonlinear elasticity of the object is obtained. Copyright © 2013 by ASME.

We report a development of MEMS based viscosity sensor suitable for in-process measurement for industrial uses. The sensor is based on the principle of the vibrating viscometer. The vibrating body of the viscosity sensor is unique dual spiral structure. The geometry provides a seamless surface and a simple structure of the pseudo-parallel wall in order to create the Couette flow for sensing the viscous stress. On Si wafer, the spiral structure is formed by penetrating trenches(40 μm width, 400 μm depth) which were formed by deep reactive ion etching. In the present study, we verified the principle of viscosity measurement by using the viscosity standard liquids.

This paper proposes the measurement system of cubic nonlinear elasticity of tissues. The system consists of a vibrator, a measuring object and a control circuit. We apply a nonlinear feedback proportional to velocity and displacement squared of the vibrator to actuate the vibrator for inducing van der Pol type self-excited oscillation and control the amplitude of the oscillation by changing the nonlinear feedback gain. When the vibrator touches the measuring object, the frequency shift of the vibrator occurs depending on elasticity of the object. When the object has nonlinear elasticity, it causes a natural frequency shift related to the amplitude of the vibrator. Therefore, by the change of the response amplitude based on the variation of the nonlinear feedback gain, we estimate the nonlinear elasticity of the object. We theoretically examine the validity of the above proposed measurement method for the cubic nonlinear elasticity of the object and experimentally confirm the performance for the cubic nonlinear elasticity of the system with magnetic restoring force.

A control method is proposed in order to reduce the steady-state amplitude of a self-excited cantilever probe in atomic force microscopy. The control method induces van der Pol oscillation by applying both linear and nonlinear feedback. Oscillation of the controlled cantilever cannot easily be stopped, even with the modulation of the viscous damping effect in the measurement environment, because the self-excited oscillation is produced far from the Hopf bifurcation point by high-gain linear feedback. Also, high-gain nonlinear feedback realizes a low steady-state amplitude to enable noncontact measurement. Finally, the feasibility of the practical application of a van der Pol-type self-excited microcantilever probe to nanoscale imaging is examined. © 2011 The Japan Society of Applied Physics.

© Springer Science+Business Media B.V. 2011. AFM (atomic force microscope) has widely used in the fields of surface science, biological science, and so on. The measurement of biological samples requires the detection without contact between the samples and the micro-cantilever probe, because the contact damages the observation objects. The self-excitation technique for the micro-cantilever probe is a powerful tool for the detection in a liquid environment where the micro-cantilever has a very low quality factor Q. In the previous study, we propose an amplitude control method for a van der Pol type self-excited micro-cantilever probe by nonlinear feedback based on bifurcation control. In this presentation, we experimentally investigate the characteristics of detection depending on the magnitude of the response amplitude of the micro-cantilever probe by using our own making AFM. We change the response steady state amplitude of the micro-cantilever probe by setting the nonlinear feedback gain to some values. Based on frequency modulation method, we detect the sample surface and discuss the effect of the magnitude of the amplitude on the performance in air. It is concluded from experimental results that the micro-cantilever probe with small amplitude under high gain nonlinear feedback control enhances the detection performance of AFM.

AFM (atomic force microscope) has widely used in the fields of surface science, biological science, and so on. The measurement of biological samples requires the detection without contact between the samples and the micro-cantilever probe, because the contact damages the observation objects. The self-excitation technique for the micro-cantilever probe is a powerful tool for the detection in a liquid environment where the micro-cantilever has a very low quality factor Q. In the previous study, we propose an amplitude control method for a van der Pol type self-excited micro-cantilever probe by nonlinear feedback based on bifurcation control. In this presentation, we experimentally investigate the characteristics of detection depending on the magnitude of the response amplitude of the micro-cantilever probe by using our own making AFM. We change the response steady state amplitude of the micro-cantilever probe by setting the nonlinear feedback gain to some values. Based on frequency modulation method, we detect the sample surface and discuss the effect of the magnitude of the amplitude on the performance in air. It is concluded from experimental results that the micro-cantilever probe with small amplitude under high gain nonlinear feedback control enhances the detection performance of AFM. © Springer Science + Business Media B.V. 2011.

© Springer Science+Business Media B.V. 2011. For the dynamics described by an equation of motion including fractional-order-derivative terms, the fractional-order-derivative responses cannot be measured directly through experiments. In the present study, three solutions are proposed that enable the fractional-order-derivative responses to be measured by a combination of signals obtained by existing sensors. Specialized sensors or complicated signal processing are not necessary. Fractional-order-derivative responses at a certain point on a structure can be expressed through linear combinations of the displacement signal and the velocity signal at each point on the structure. Although their calculation processes are different, all three methods eventually reach the same result.

We propose a van der Pot-type self-excited cantilever beam by positive velocity feedback and nonlinear feedback. Self-excited oscillation keeps the resonant condition independent of the modulation of system parameters and the resonance characteristic of self-excited oscillation is suitable to realize auto-resonance machines such as AFM micro-cantilever proble. Because the amplitude of self-excited oscillation grows with time, a special control method is required for the amplitude control. To this end, we propose the application of the nonlinear dynamics of van der Pol oscillator. Making use of the characteristic of a stacked-type piezoelectric actuator, we demonstrate that the amplitude control of a cantilever beam by using only integral controller without differential controller. We show the equation of motion in which the nonlinear effect is taken into account and the averaged equation which is derived by applying the method of multiple scales. The bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever beam can be controlled by setting the nonlinear feedback gain. Furthermore, a van der Pol-type self-excited cantilever beam is realized by using a simple apparatus and the validity of amplitude control method by integral control is experimentally confirmed.

We propose a van der Pol-type self-excited cantilever beam by positive velocity feedback and nonlinear feedback. Self-excited oscillation keeps the resonant condition independent of the modulation of system parameters and the resonance characteristic of self-excited oscillation is suitable to realize auto-resonance machines such as AFM micro-cantilever proble. Because the amplitude of self-excited oscillation grows with time, a special control method is required for the amplitude control. To this end, we propose the application of the nonlinear dynamics of van der Pol oscillator. Making use of the characteristic of a stacked-type piezoelectric actuator, we demonstrate that the amplitude control of a cantilever beam by using only integral controller without differential controller. We show the equation of motion in which the nonlinear effect is taken into account and the averaged equation which is derived by applying the method of multiple scales. The bifurcation diagram is theoretically described. Then, it is clarified that the amplitude of the cantilever beam can be controlled by setting the nonlinear feedback gain. Furthermore, a van der Pol-type self-excited cantilever beam is realized by using a simple apparatus and the validity of amplitude control method by integral control is experimentally confirmed.

As described herein, we develop a method to obtain a fractional derivative response of a vibratory system with multiple degrees of freedom (DOF). To obtain fractional-order derivatives/integrals of dynamic response at a certain point on a structure presents technical difficulties because measurements of fractional-order derivative/integral responses in structural dynamics yield some implementation techniques. However, our method obviates special sensors with additional signal- conversion functions. Therefore, existing displacement and velocity sensors can work. Obtaining fractional derivative responses can be accomplished using three methods. Using any of the three methods, fractional states can be expressed with complex vibration modes, in which each point of the system oscillates with a phase that is different from "in-phase" or "out-of-phase." Copyright © 2009 by ASME.

We propose a van der Pol type self-excited micro-cantilever probe for AFM (atomic force microscope) . Because the response frequency of self-excited oscillators is its natural frequency, the equivalent natural frequency depending on the atomic force is easily measured from detecting the response frequency of the self excited micro-cantilever probe. While the amplitude of the linear self-excited oscillator grows with time, it can be kept very small by the nonlinear effect as van ver Pol oscillator. Therefore, if the micro-cantilever probe has the same dynamics as that of van Pol oscillator, the contact of the micro-cantilever to the material surface is prohibited and non-contact mode AFM is realized. In the present study, we design a van der Pol type micro-cantilever for the application to the practical AFM system. Copyright © 2009 by ASME.

Grazing behavior in soft impact dynamics of a harmonically based excited flexible cantilever beam is investigated. Numerical and experimental methods are employed to study the dynamic behavior of macro- and micro-scale cantilever beam-impactor systems. For off-resonance excitation at two and a half times the fundamental frequency, the response of the oscillating cantilever experiences period doubling as the separation distance or clearance between the beam axis and the contact surface is decreased. The nonlinear phenomenon is studied by using phase portraits, Poincaré sections, and spectral analysis. Motivated by atomic force microscopy, this general dynamic behavior is studied as a means to locating the separation distance corresponding to grazing where the contact force is minimized. © 2008 Springer Science+Business Media B.V.

As described herein, we develop a method to obtain a fractional derivative response of a vibratory system with multiple degrees of freedom (DOF). To obtain fractional-order derivatives/integrals of dynamic response at a certain point on a structure presents technical difficulties because measurements of fractional-order derivative/integral responses in structural dynamics yield some implementation techniques. However, our method obviates special sensors with additional signal-conversion functions. Therefore, existing displacement and velocity sensors can work. Obtaining fractional derivative responses can be accomplished using three methods. Using any of the three methods, fractional states can be expressed with complex vibration modes, in which each point of the system oscillates with a phase that is different from "in-phase" or "out-of-phase." © 2009 by ASME.

We propose a van der Pol type self-excited micro-cantilever probe for AFM (atomic force microscope). Because the response frequency of self-excited oscillators is its natural frequency, the equivalent natural frequency depending on the atomic force is easily measured from detecting the response frequency of the self-excited micro-cantilever probe. While the amplitude of the linear self-excited oscillator grows with time, it can be kept very small by the nonlinear effect as van ver Pol oscillator. Therefore, if the micro-cantilever probe has the same dynamics as that of van Pol oscillator, the contact of the micro-cantilever to the material surface is prohibited and non-contact mode AFM is realized. In the present study, we design a van der Pol type micro-cantilever for the application to the practical AFM system. © 2009 by ASME.

For usage of noncontact atomic force microscopy (NC-AFM) in a liquid environment, we propose a "van der Pol"-type self-excited cantilever probe whose steady state amplitude can be controlled to be sufficiently small so as not to damage the surface of the observation object. The self-exciting technique for the micro cantilever probe has become a powerful tool for obtaining atomically resolved images in environments where the cantilever has a very low quality factor Q. It is important to maintain the steady state amplitude of the cantilever to prevent damage to the surface, to reduce the contact force with the sample surface, and to avoid destruction of a soft material having an irregular surface such as biomolecules. In contrast to external excitation, the response amplitude of a self-excited oscillator is generally determined by the amount of nonlinearity of the system. The greater the nonlinearity, the smaller the steady state amplitude. We apply nonlinear feedback control in addition to linear feedback control to increase inherent nonlinearity in the system. Thereby, the cantilever probe has nonlinear characteristics that are equivalent to a van der Pol oscillator. It is shown analytically via an asymptotic perturbation approach that the self-excited oscillation has small steady state amplitude. Experiments are performed using a micro cantilever that is fabricated from a Pt/Ti/PZT/Pt/Ti/SiO2/SOI multi-layered structure. The validity and advantage of the proposed control method are confirmed to realize the stable self-excited oscillation with as small an amplitude as possible for the NC-AFM for a liquid environment. © 2008 Springer Science+Business Media LLC.