Residual Modes Research Articles

Electrode Pattern Design of Piezoelectric Sensors and Actuators Using Genetic Algorithms

A distributed piezoelectric sensor and actuator have been designed for the efficient vibration control of a plate. Optimization of the electrode pattern of polyvinylidene fluoride (PVDF) film has been performed to realize the concept of modal transducer for a two-dimensional structure. The finite element method is used to model the structure that includes the PVDF sensor and actuator. Various lamination angles of transducers are taken into consideration to utilize the anisotropy of the PVDF film, The electrode pattern over the entire surface of the plate is determined by deciding on or off of each electrode segment. The actuator design is based on the criterion of minimizing the system energy in the control modes under a given initial condition. The sensor is designed to minimize the observation spillover, Modal control forces for the residual (uncontrolled) modes have been minimized during the sensor design. A genetic algorithm, which is suitable for this kind of discrete problem, has been utilized for optimization. A discrete linear quadratic Gaussian control law has been applied to the integrated structure for real-time vibration control. The performance of the sensor, the actuator, and the integrated smart structure has been demonstrated by experiments.

剛結合された2本のビームのモデリングとロバスト制御

Summary form only given. In this paper, modeling and robust control of a flexible structure with a closed-loop mechanism are discussed. It is important to derive a mathematical model and construct a controller for such complicated space structures. We consider two connected flexible beams as a simple model of the space structures with the closed-loop mechanism. This structure can be regarded as an element of the truss structure. We derive dynamic equations of the connected flexible beams by means of Hamilton's principle. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. The solution of an eigenvalue problem related to the distributed parameter system yields eigenvalues and corresponding eigenfunctions. On the basis of the truncated eigenfunction expansion, an approximated finite-dimensional modal model are derived. As the original system is infinite dimensional and controllers should be designed on the basis of an approximated finite dimensional model, it is necessary to compensate the spillover instability caused by the residual modes which are neglected at the controller design phase. It is difficult to estimate the physical parameters of the system, for example a flexural rigidity, a damping coefficient, etc., correctly. In order to compensate the unmodeled dynamics and the parameter uncertainty, a robust controller should be constructed. In the paper, an optimal controller with low-pass property and a robust H/sub /spl infin// controller are designed. Simulations have been carried out and responses for the controllers are compared.

New Modal Synthesis Technique Using Mixed Modes

A new modal synthesis technique using mixed modes is introduced. The method not only has a simple form, high precision, and efficiency, but it also provides two reliable criteria for determining the truncation frequency of system synthesis modes. These have been demonstrated in detail by the numerical examples. The key point of the method is as follows. The exact residual modes containing the effects of higher-order, free-interface modes are expressed analytically in terms of some lower-order, fixed-interface modes, and then the substructural displacements are expressed accurately in terms of some lower-order, mixed modes, i.e., the linear combinations of the lower-order, fixed-interface modes and lower-order, free-interface modes, instead of the assumed substructural displacements employed in general modal synthesis, so that only linear synthesis equations are involved in this new method, although the contributions of all higher-order modes are included.

Finite-Dimensional [formula omitted]∞Control of a Class of Infinite-Dimensional Linear Time-Varying Systems

In this paper, we consider H∞control of infinite-dimensional linear time-varying (IDLTV) systems whose homogeneous parts are of modal type, by using a finite-dimensional controller. The aim is to construct a finite-dimensional stabilizing controller for the IDLTV system that makes the norm of the closed-loop operator less than a given positive number δ. To this end, a finite-dimensional model is firstly derived for the IDLTV system, and a stabilizing controller that makes the norm of the closed-loop operator less than another positive number γ(<δ) is constructed for the finite-dimensional model. Then it is shown that a controller, which consists of a residual mode filter and the controller mentioned above, becomes a finite-dimensional stabilizing controller for the given IDLTV system such that the closed-loop operator has norm less than δ, if the order of the residual mode filter is chosen sufficiently large.

Exponentially Stable Feedback Control of Discrete-Time Nonlinear Distributed Parameter Systems on Banach Spaces

Practical engineering systems require feedback control implementation in discrete-time; however, stable control of an infinite-dimensional distributed parameter system (DPS) is not always guaranteed. We introduce two nonlinear controllers, a DPS one and a finite-dimensional one with residual mode filter (RMF) compensation, which produce local exponential closed-loop stability for nonlinear discrete-time DPS on Banach spaces under appropriate local Lipschitz continuity conditions. Both controllers operate in discrete-time and our results place no restrictions on the smoothness of the initial data in the Banach space.

On-Orbit Robust Control Experiment of Flexible Spacecraft ETS-VI

An on-orbit attitude and vibration control experiment has been performed as a part of experiments of the ETS-VI, which was launched by the H-II rocket in August 1994. The purpose is to develop precise attitude control technology for future large spacecraft or large space structures. To this end, we have designed three types of controllers in linear quadratic Gaussian and H 1 frameworks to achieve the robust stability against residual modes and modal parameter errors. The experiments were done at the beginning of 1995, and their feasibility has been proved. The  ight experiment results and the modeling and the controller synthesis methods are reported. Based on the on-orbit results, the capabilities of controllers are compared and discussed.

Electron Density Study of Garnets: Z3Ga 5O 12; Z=Nd, Sm, Gd, Tb

The electron density distribution in garnets, Z 3Ga 5O 12, Z=Nd, Sm, Gd, Tb, has been studied with single-crystal X-ray diffraction methods through scattering factor refinement procedures. The Zsite shows a variety of electron density residual distribution modes, implying contribution of the felectrons. Residual electron density regions of 0.9–4.0 e/Å 3height seen for all four garnets at an interstitial site (Wyckoff position 48 g) suggest coexistence of domains with alternatively oriented structural motifs within the single crystals. [Cubic Ia 3 d; a=12.5051(4) Å ( Z=Nd), a=12.4361(3) Å ( Z=Sm), a=12.3829 (5) Å ( Z=Gd), a=12.3474(5) Å ( Z=Tb), final Rafter anharmonic refinement: Z=Nd, 0.0114 (for 660 equivalent-averaged data); Z=Sm, 0.0111 (647); Z=Gd, 0.0152 (428); Z=Tb, 0.0118 (454).]

EXACT MODAL SYNTHESIS TECHNIQUES USING RESIDUAL CONSTRAINT MODES

A new exact modal synthesis method for finding natural frequencies and modes of structures is proposed, in which the exact residual constraint modes based upon an incomplete set of normal modes of substructures with fixed interfaces are expressed in two parts. These are the static constraint modes and a residual term with which it represents exactly the effect of normal modes not retained. The modal synthesis uses a Ritz procedure and an iterative technique is presented for solving the non-linear equations of modal synthesis. This has the advantage that the results given by its first iteration are exactly those given by the Craig–Bampton–Hurty modal synthesis method, which leads to rapid convergence of subsequent iterations. The proposed method is an improvement of Hu's exact modal synthesis method and is also shown to have as its limit the method of exact dynamic condensation. Numerical examples show that using the proposed method yields superior accuracy when only a few lower modes are used. © 1997 by John Wiley & Sons, Ltd.

Active robust vibration control of flexible composite beams with parameter perturbations

In this paper, a time domain approach is presented to treat the problem of active controlling simultaneously the bending and torsional vibration of flexible composite beams under both mode truncations and parameter perturbations. In the proposed approach, the residual model, which is known as unstructured uncertainty, is viewed as an additive perturbation to the controlled model. Based on a state space model, which incorporates both bending and torsional deformation effects, of the flexible composite beam with piezoelectric sensors and actuators, a robust stability condition is derived to guarantee that both bending and torsional vibration of the flexible composite beam, which is subject to both mode truncation and linear time-varying parameter perturbations, can be actively controlled by an observer-based controller. The proposed robust stability condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effects and additive time-varying parameter perturbations. Finally, an active robust vibration control problem of a cantilevered flexible composite beam with piezoelectric sensors and actuators is provided for illustration.

Statistically Generated Weighted Curve Fit of Residual Functions for Modal Analysis of Structures

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure to modal test large structures in a free-free environment to measure the effects of higher order modes and stiffness at distinct degree of freedom interfaces. Due to the present damping estimate limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of irregular data, which should be a smooth curve in a second-order polynomial form. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure, which is used to predict constrained mode shapes.

Deducing droplet concentration and supersaturation in marine boundary layer clouds from surface aerosol measurements

Air parcels in the marine boundary layer (MBL) are mixed up through nonprecipitating clouds at the top of the MBL many times (on average) before they can be removed by precipitation scavenging. The equivalent dry size of the particles (cloud condensation nuclei, CCN) upon which droplets are formed increases because of liquid phase oxidation of soluble trace gases during the cloud processing. The observed separation of the submicron size distribution into an interstitial mode and cloud droplet residue mode makes it possible to infer the effective MBL cloud supersaturation and cloud droplet concentrations from surface measurements of the aerosol size distribution during periods when nonprecipitating MBL clouds are present in the back trajectory and the MBL is well mixed. The effect of particle composition on the accuracy of the inferred cloud supersaturations is evaluated. A large database of hundreds of size distributions taken on an Atlantic and a Pacific cruise and an airship flight off the Oregon coast are used to calculate the range of effective MBL cloud supersaturations and droplet concentrations encountered during these expeditions. The inferred droplet concentrations on the Pacific cruise were mostly in the 25 to 150 cm−3 range, whereas they were mostly in the 50 to 500 cm−3 range for the Atlantic cruise. The inferred effective supersaturation in the tropical MBL clouds was typically in the 0.15% to 0.25% range. Recent work of Tang and Munkelwitz [1994] would indicate that particles consisting of mixtures of ammonium sulfate and sulfuric acid would not have recrystalized in the differential mobility analyzer (DMA) within the range of relative humidities (45% to 60%) at which the DMA was operated. At these humidities the hydrated size can be as much as 20% greater than the dry size. Corrections for the hydrated size within the DMA at the time of measurement are included and are also used to correct previous measurements of the relationship between dry size and critical supersaturation made using the Naval Research Laboratory (NRL) DMA and NRL thermal gradient CCN counters.

Finite-Dimensional H∞ Controllers for a Class of Infinite-Dimensional Linear Time-Varying Systems

This paper is concerned with a design of finite-dimensional H∞ time-varying controllers for infinite-dimensional linear time-varying systems whose homogeneous parts are of modal type. A finite-dimensional model is derived for the infinite-dimensional system, and an H∞ controller is constructed for the finite-dimensional model. Then, it is shown that a controller, which consists of a residual mode filter and the H∞ controller mentioned above becomes a finite-dimensional H∞ controller for the given infinite-dimensional system if the order of residual mode filter is chosen sufficiently large.

Subsurface and surface cracks under contact loading in transformation-toughened ceramics

The wearing surface in rolling and sliding wear is approximated by a half-plane subjected to frictional contact loading. Under such loading inherent flaws, such as microcracks, voids and inhomogeneities, eventually develop into macrocracks with a resultant deterioration in wear performance. Two macrocrack configurations are studied: a straight subsurface crack parallel to the surface and a straight edge crack perpendicular to the surface. The cracks are modelled using the dislocation formalism, and the contact load is assumed to be Hertzian. In the vicinity of the crack tips, where a high tensile stress field is anticipated, the material is allowed to undergo irreversible phase transformation in accordance with an appropriate transformation criterion. The transformation zone around the crack tip (or tips) is modelled as a collection of minute circular regions. Such a model is a good representation of the transformable precipitates, for example in partially stabilized zirconia. The elastic field from the transformed circular regions is obtained by applying the Eshelby formalism. The phase transformation exerts a strong influence on the behaviour of the cracked material compared to the purely elastic material through a significant closing effect on the crack faces. This results in the mode I stress intensity factor being almost zero. However, as the transformation zone is highly asymmetric relative to the crack faces, because of the non-uniform stress field due to the applied contact load, the mode II loading of the crack tip(s) can be severely enhanced. This results in high residual near tip deformations after unloading, i.e. a high residual mode II stress intensity factor.

Kinetic ballooning mode with negative shear.

Kinetic analysis on the ballooning mode in tokamaks has indicated the existence of a residual ballooning mode in the negative shear region $(s&lt;0)$. The instability has a small threshold in $\ensuremath{\alpha}$ (the ballooning parameter), requires a finite ion temperature gradient $({\ensuremath{\eta}}_{i})$, and is characterized by a broad eigenfunction $\ensuremath{\varphi}(\ensuremath{\theta})$ extending to $\ensuremath{\theta}\ensuremath{\simeq}50$ in the ballooning space.

Optimal Electromagnetic Levitation Control of a Thin Rectangular Steel Plate with Two Opposite Edges Reinforced by a Beam.

In this paper, a method of electromagnetic levitation control of a thin steel rectangular plate (length : 800mm, width : 600mm, thickness : 0.3mm) with free edges is prerented. To carry out fundamental investigation of the restraint of elastic vibration of the plate, the steel plate is reinforced by plastic beams at two opposite edges. This plate is supported in a contactless manner by attractive forces of five electromagnetic actuators which are controlled by feedback signals from five gap sensors to stabilize the levitation behavior. The optimal control theory and the suboptimal control theory are applied in this study. To verify the usefulness of these methods, experiments in which the optimal digital control theory was applied were performed. As a result, it was confirmed that these control methods were very effective in levitating the plate, and it was further observed that the spillover of residual vibration modes was restrained by applying the suboptimal control method.

Reduced-Order Model Based Control of the Flexible, Articulated-Truss Space Crane

The large size and extreme flexibility of an articulated space crane entail tremendous difficulties in precision positioning. We demonstrate the application of a low-order control strategy for the flexible system using a linear, Timoshenko beam finite element model. The model captures the system's low-frequency characteristics. From selected modes of the finite element model, we design a reduced-order model (ROM) controller based on an arbitrary crane configuration. The ROM controller rotates the fixed-shape crane about the base alpha joint to actuate position control. This constructive control design takes place in two pieces: design for performance and compensate for stability. Ignoring the presence of residual modes, we design the low-order control law to achieve our performance criteria. Eigenvalue analysis of the closed-loop system, however, shows the destabilizing interaction of the ROM controller with residuals. Adding a parallel bank of residual mode filters, we restore system stability and performance, without redesign of the original controller. Finally, numeric simulation of the controlled finite element model reveals the effectiveness of a ROM-based control law with residual mode filter compensation. Application to a large-scale data-base highlights the utility of this low-order, noniterative controller design.

Recording Characteristics ring-type-head / perpendicular-longitudinal composite media system

Recording characteristics of perpendicular-longitudinal composite media with high coercivity underlayer with combination of ring-type heads were systematically reviewed on the basis of own investigation. The reproduced voltage of the composite media was higher than simply superposition of the output of perpendicular layer and longitudinal underlayer. It was found that the residual magnetization mode of composite medium was "phase synchronization mode," which formed horse-shoe shape composed with "strong perpendicular magnetization" region of perpendicular layer and longitudinal magnetization of underlayer. Moreover, the magnetization state can be controlled by medium and head parameters, indicating the importance of the optimization of medium and head parameters.

Feedback stabilization of infinite-dimensional systems with Aγ-bounded output operators

This paper is concerned with the stabilization problem of infinite-dimensional systems with A γ-bounded output operators. An operator is said to be A γ-bounded if it can be written as C( A+ c) γ for some bounded operator C and some scalar c (see [1]). For example, the linear diffusion system with distributed (or boundary) control and boundary observation is formulated as an evolution equation with bounded input operator and A γ-bounded output operator in a Hilbert space. The purpose of this paper is to show that the closed-loop system with a finite-dimensional controller containing residual mode filter, which Balas introduced for infinite-dimensional systems with bounded input and output operators, is exponentially stable if the order of residual mode filter is chosen sufficiently large.

Mobility and diffusion of a particle coupled to a Luttinger liquid.

We study the mobility of a particle coupled to a one dimensional interacting fermionic system, a Luttinger liquid. We bosonize the Luttinger liquid and find the effective interaction between the particle and the bosonic system. We show that the dynamics of this system is completely equivalent to the acoustic polaron problem where the interaction has purely electronic origin. This problem has a zero mode excitation, or soliton, in the strong coupling limit which corresponds to the formation of a polarization cloud due to the fermion-fermion interaction around the particle. We obtain that, due to the scattering of the residual bosonic modes, the soliton has a finite mobility and diffusion coefficient at finite temperatures which depend on the fermion-fermion interaction. We show that at low temperatures the mobility and the diffusion coefficient are proportional to $T^{-4}$ and $T^5$ respectively and at high temperatures the mobility vanishes as $T^{-1}$ while the diffusion increases as $T$.

Marine boundary layer measurements of new particle formation and the effects nonprecipitating clouds have on aerosol size distribution

Measurements of aerosol size distributions (0.005 &lt; r &lt; 20 μm), cloud droplet spectra, SO2, O3, CN, and other supporting quantities were made in the cloud‐topped and clear marine boundary layer (MBL) from an airship operating within about 50 km of the Oregon coast. Comparison of size distribution of interstitial aerosol within the cloud with the size distribution below the cloud clearly indicates that the processing of the aerosol through (nonprecipitating) stratus can lead to increased mass of the subset of particles which had served as cloud condensation nuclei (CCN). This increase in mass in the CCN results in a distinct “cloud residue” mode in the size distribution measured below the cloud. In all cases the aerosol mass in the cloud residue mode greatly exceeded the mass in the interstitial mode, even though the number concentration of interstitial particles sometimes exceeded the CCN concentration. Evidence of new particle formation in clear air was also found on numerous occasions. Analyses of the data indicate that the growth of newly formed particles into the observed size range is consistent with gas phase oxidation of SO2 to sulfate and subsequent condensation on the aerosol. However, the exact nucleation process, whether by homogeneous nucleation, ion‐assisted nucleation, or heterogeneous nucleation on precursor embryos, is still an open question.