Practical tracking control of piezoelectric actuators with time-delay estimation and nonsingular terminal sliding mode

A novel type of nonlinear robust control strategy is proposed in view of uncertain nonlinear factors, such as hysteresis, creep, and high-frequency vibration, of piezoelectric actuators (PEAs). This strategy can be used for the precise trajectory tracking of PEAs. The Bouc–Wen dynamic model is reasonably simplified to facilitate engineering application. The hysteresis term is summarized as an unknown term to avoid its nonlinear parameter identification. The controller robustness is achieved due to the nonsingular terminal sliding mode control, and the online estimation of unknown disturbances is realized because of the delay estimation technology; thus, no prior knowledge of the unknown boundary of the system is required. The precision robust differentiator is used to estimate the speed and acceleration signals in real time on the basis of the obtained displacement signals. The closed-loop stability of the system is proved by the Lyapunov criterion. Experimental results show that the proposed control strategy performs better than the traditional time-delay estimation control in terms of control accuracy and energy conservation. Therefore, the proposed control strategy can play an important role in the micro/nanofield driven by PEAs.

A New Model Ice for Wave-Ice Interaction

The interaction of waves and ice is of significant relevance for engineers, oceanographers and climate scientists. In-situ measurements are costly and bear uncertainties due to unknown boundary conditions. Therefore, physical laboratory experiments in ice tanks are an important alternative to validate theories or investigate particular effects of interest. Ice tanks use model ice which has down-scaled sea ice properties. This model ice in ice tanks holds disadvantages due to its low stiffness and non-linear behavior which is not in scale to sea ice, but is of particular relevance in wave-ice interactions. With decreasing stiffness steeper waves are required to reach critical stresses for ice breaking, while the non-linear, respectively non-elastic, deformation behavior is associated with high wave damping. Both are scale effects and do not allow the direct transfer of model scale test results to scenarios with sea ice. Therefore, the alternative modeling approach of Model Ice of Virtual Equivalent Thickness (MIVET) is introduced. Its performance is tested in physical experiments and compared to conventional model ice. The results show that the excessive damping of conventional model ice can be reduced successfully, while the scaling of the wave induced ice break-up still requires research and testing. In conclusion, the results obtained are considered a proof of concept of MIVET for wave-ice interaction problems.

Too Popular, Too Fast: Optimal Advertising and Entry Timing in Markets with Peer Influence

We study optimal advertising and entry timing decisions for a new product being sold in two-segment markets in which followers are positively influenced by elites, whereas elites are either unaffected or repulsed by product popularity among followers. Key decisions in such markets are not only how much to advertise in each segment over time but also when to enter the follower segment. We develop a continuous-time optimal control model to examine these issues. Analysis yields two sets of two-point boundary value problems where one set has an unknown boundary value condition that satisfies an algebraic equation. A fast solution methodology is proposed. Two main insights emerge. First, the optimal advertising strategy can be U-shaped, that is, decreasing at first to free-ride peer influence but increasing later on to thwart the repulsion influence of overpopularity causing disadoption. Second, in markets where cross-segment repulsion triggers disadoption, advertising is only moderately effective, and entry costs are high, managing both advertising and entry timing can result in significantly higher profits than managing only one of these levers. In markets without disadoption, with high advertising effectiveness or with low entry costs, in contrast, delaying entry may add little value if one already manages advertising optimally. This implies that purveyors of prestige or cool products need not deny followers access to their products in order to protect their profits, and can use advertising to speed up the democratization of consumption profitably. This paper was accepted by Juanjuan Zhang, marketing.

Inverse Problems with Unknown Boundary Conditions and Final Overdetermination for Time Fractional Diffusion-Wave Equations in Cylindrical Domains

Inverse problems to reconstruct a solution of a time fractional diffusion-wave equation in a cylindrical domain are studied. The equation is complemented by initial and final conditions and partly given boundary conditions. Two cases are considered: (1) full boundary data on a lateral hypersurface of the cylinder are given, but the boundary data on bases of the cylinder are specified in a neighborhood of a final time; (2) boundary data on the whole boundary of the cylinder are specified in a neighborhood of the final time, but the cylinder is either a cube or a circular cylinder. Uniqueness of solutions of the inverse problems is proved. Uniqueness for similar problems in an interval and a disk is established, too.

CLINICAL AND SUBCLINICAL CHARACTERISTICS ON BREAST CANCER PATIENTS TREATED WITH ANTHRACYCLINES

Objective: Describing the clinical and subclinical characteristics on breast cancer patients treated with Anthracyclines at Thong Nhat hospital.Subjects and methods: a prospective descriptive study on 43 patients with breast cancer was treated with Anthracyclines with 4 to 6 cycles as determined by clinical doctor at Thong Nhat hospital. Results: Average age: 49.2 ± 3.2 years old. The age group accounted for the largest proportion in the study object was the 50-60 age group (48.84%). The percentage of patients who self-examined the tumor was the highest with 79.07%. There were 9.30% of patients with pain symptoms, 11.63% of patients with nipple discharge. Tumor position in the upper-external quadrant accounted for the largest percentage with 55.81%. The average size of tumors was 2.56 ± 1.2 (cm). The main form of lesions detected on ultrasound was the local lesion with over 80% with an unknown boundaryfeature (81.40%) and predominantly invasive (76.74%). The histopathological type accounted for the highest percentage was the invasive tubular carcinoma (79.07%), the medullary carcinoma andmucinous carcinoma body accounted for the lowest rate with 2.33% and 0%, respectively. The histological degree accounted for the highest percentage among the research subjects was degree 2with 50.18%. Stage III accounted for the highest rate with 46.51%.Conclusion: The most common age group for breast cancer was 50-60 years old, the main symptom was self-examination with breast tumors, breast cancer were mainly local tumor at the upper-externalposition. On ultrasound, the lesions were the local, unknown boundary, and invasive lesions. Breast cancer was mainly invasive ductal carcinoma, histologic degree 2.

METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

Compactness theorems for problems with unknown boundary

The compactness theorem is proved for sequences of functions that have estimates of the higher derivatives in each subdomain of the domain of definition, divided into parts by a sequence of some curves of class W_2^1. At the same time, in the entire domain of determining summable higher derivatives, these sequences do not have. These results allow us to make limit transitions using approximate solutions in problems with an unknown boundary that describe the processes of phase transitions.

Photogrammetric Process to Monitor Stress Fields Inside Structural Systems

This research employs displacement fields photogrammetrically captured on the surface of a solid or structure to estimate real-time stress distributions it undergoes during a given loading period. The displacement fields are determined based on a series of images taken from the solid surface while it experiences deformation. Image displacements are used to estimate the deformations in the plane of the beam surface, and Poisson’s Method is subsequently applied to reconstruct these surfaces, at a given time, by extracting triangular meshes from the corresponding points clouds. With the aid of the measured displacement fields, the Boundary Element Method (BEM) is considered to evaluate stress values throughout the solid. Herein, the unknown boundary forces must be additionally calculated. As the photogrammetrically reconstructed deformed surfaces may be defined by several million points, the boundary displacement values of boundary-element models having a convenient number of nodes are determined based on an optimized displacement surface that best fits the real measured data. The results showed the effectiveness and potential application of the proposed methodology in several tasks to determine real-time stress distributions in structures.

Nonlinear dynamic response of seismically excited rectangular concrete liquid filled tanks

The effect of nonlinearity on behaviour of rectangular concrete tanks partially filled with water is studied. The nonlinearity in the numerical modeling of the surface liquid sloshing performance and hydrodynamic pressure initiates from unknown boundary conditions of contained liquid volume. The nonlinear simulations are performed for Time-History seismic analysis using the finite element software ABAQUS/CAE. The nonlinear results are compared with linear analytical solutions and ACI 350.3-06 code. A Paramedic study is conducted to investigate the effect of tank plan dimension, frequency content of different seismic ground motions, nature of earthquake movements, and interaction of bi-directional component of earthquake on the maximum sloshing height of liquid. The results reveal that the nonlinearity is more significant in shallow tanks. Moreover, nonlinear hydrodynamic pressure distribution has no important difference with linear calculated pressure except for the surface sloshing pressure acting on the top of tanks. The linear ratio of depth of liquid to tank plan dimension used in ACI 350.3-06 formulation is found to be less accurate for calculating the maximum sloshing height of liquid.