Time-varying Sliding Mode Controls in Rigid Spacecraft Attitude Tracking

AbstractTo solve the problem of attitude tracking of a rigid spacecraft with an either known or measurable desired attitude trajectory, three types of time-varying sliding mode controls are introduced under consideration of control input constraints. The sliding surfaces of the three types initially pass arbitrary initial values of the system, and then shift or rotate to reach predetermined ones. This way, the system trajectories are always on the sliding surfaces, and the system work is guaranteed to have robustness against parameter uncertainty and external disturbances all the time. The controller parameters are optimized by means of genetic algorithm to minimize the index consisting of the weighted index of squared error (ISE) of the system and the weighted penalty term of violation of control input constraint. The stability is verified with Lyapunov method. Compared with the conventional sliding mode control, simulation results show the proposed algorithm having better robustness against inertia matrix uncertainty and external disturbance torques

Global existence of solutions for fuzzy second-order differential equations under generalized H-differentiability

AbstractIn this paper, we study the global existence of solutions for second-order fuzzy differential equations with initial conditions under generalized H-differentiability. Second derivative of the H-difference of two functions under generalized H-differentiability is obtained. Two theorems which assure global existence of solutions for second-order fuzzy differential equations are given and proved. Some examples are given to illustrate these results

Investigating the motility of Dictyostelium discodeum using high frequency ultrasound as a method of manipulation

Cell motility is an essential process in the development of all organisms. The earliest stages of embryonic development involve massive reconfigurations of groups of cells to form the early body structures. Embryos are very complex systems, and therefore to investigate the molecular and cellular basis of development a simpler genetically tractable model system is used. The social amoeba Dictyostelium Discoideum is known to chemotax up a chemical gradient. From previous work, it is clear that cells generate forces in the nN range. This is above the limit of optical tweezers and therefore we are investigating the use of acoustic tweezers instead. In this paper, we present recent progress of the investigation in to the use of acoustic tweezers for the characterisation of cell motility and forces. We will describe the design, modelling and fabrication of several devices. All devices use high frequency (>15MHz) ultrasound to exert a force on the cells to position and/or stall them. Also, each device is designed to be suitable for the life-sciences laboratory where form-factor and sterility is concerned. A transducer (LiNo) operating at 24 MHz excites resonant acoustic modes in a rectangular glass capillary (100um by 2mm). This device is used to alter the directionality of the motile cells inside the fluid filled capillary. A quarter-ring PZT26 transducer operating at 20.5MHz is shown to be useful for manipulating cells using axial acoustic radiation forces. This device is used to exert a force on cells and shown to pull them away from a coverslip. The presented devices show promise for the manipulation of cells in suspension. Currently the forces produced are below that required for adherent cells; the reasons for this are discussed. We also report on other issues that arise when using acoustic waves for manipulating biological samples such as streaming and heating

Thick film PZT transducer arrays for particle manipulation

This paper reports the fabrication and evaluation of a two-dimensional thick film PZT ultrasonic transducer array operating at about 7.5 MHz for particle manipulation. All layers on the array are screen-printed and sintered on an Al2O3 substrate without further processes or patterning. The measured dielectric constant of the PZT is 2250 ± 100, and the dielectric loss is 0.09 ± 0.005 at 10 kHz. Finite element analysis has been used to predict the behaviour of the array and impedance spectroscopy and laser vibrometry have been used to characterise its performance. The measured deflection of a single activate element is on the order of tens of nanometres with 20 Vpp input. Particle manipulation experiments have been performed by coupling the thick film array to a capillary containing polystyrene microspheres in water

Implementation of a PMN-PT piezocrystal-based focused array with geodesic faceted structure

The higher performance of relaxor-based piezocrystals compared with piezoceramics is now well established, notably including improved gain-bandwidth product, and these materials have been adopted widely for biomedical ultrasound imaging. However, their use in other applications, for example as a source of focused ultrasound for targeted drug delivery, is hindered in several ways. One of the issues, which we consider here, is in shaping the material into the spherical geometries used widely in focused ultrasound. Unlike isotropic unpoled piezoceramics that can be shaped into a monolithic bowl then poled through the thickness, the anisotropic structure of piezocrystals make it impossible to machine the bulk crystalline material into a bowl without sacrificing performance. Instead, we report a novel faceted array, inspired by the geodesic dome structure in architecture, which utilizes flat piezocrystal material and maximizes fill factor. Aided by 3D printing, a prototype with f# ≈ 1.2, containing 96 individually addressable elements was manufactured using 1–3 connectivity PMN-PT piezocrystal–epoxy composite. The fabrication process is presented and the array was connected to a 32-channel controller to shape and steer the beam for preliminary performance demonstration. At an operating frequency of 1 MHz, a focusing gain around 30 was achieved and the side lobe intensities were all at levels below −12 dB compared to main beam. We conclude that, by taking advantage of contemporary fabrication techniques and driving instrumentation, the geodesic array configuration is suitable for focused ultrasound devices made with piezocrystal