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(2007)Conference PaperThis work presents the derivation of a comprehensive mathematical model for an off-road vehicle such as an agricultural tractor that drags behind it a heavy implement. The models are being developed with the aim of designing robust controllers that will enable the high precision control of the implement’s trajectory. The developed model is subjected to real conditions, such as ground undulation and uncertainty, sloping terrain, tyre slippage, and constrained steering of the tractor. The implement is assumed to possess independently steered wheels for aiding in implement alignment. A complete model is presented and simulated under varying conditions. Primarily this work demonstrates and validates the trailed vehicle system behavior when the trailing implement is subjected to large drag forces due to ground engagement and the significantly large lateral disturbances that occur in real life broad acre farming conditions.
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(2001)Journal ArticleWe present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with selffocusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic selfdefocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schr¨ odinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.
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(2023)ThesisPiezoelectric materials are the preferred smart materials for sensing and actuation in the form of micro and nano-engineering structures like beams and plates. Cantilever beams play a significant role as key components in atomic force microscopy and bio and chemical sensors. Adding an active layer such as lead zirconate titanate (PZT) thin-film to form smart cantilever beams with sensing and actuation capabilities is highly desirable to facilitate miniaturization, enhance performance and functionali- ties such as enabling on-chip high-speed parallel AFM. During the micro-fabrication process, residual stresses develop in the different layers of the cantilever beam, causes initial deflection. The residual stress in the different layers of the cantilever beam and the application of voltage to the PZT thin-film affects their dynamics. This the- sis investigates the dynamic behaviour and develops a control technique and a novel charge readout circuit to improve the performance of a micro-fabricated multi-layer prestressed piezoelectric cantilever beam as an actuator and a deflection sensor. Firstly, the fabrication process of a unimorph PZT cantilever beam is explained. A low thermal budget Ultra-high vacuum e-beam evaporated polysilicon thin-film (UHVEEpoly) process is used for the fabrication of multi-layered PZT cantilever beam in d31 mode. The sharp peaks at resonant frequencies in the frequency response of the PZT cantilever beam show very little damping and a large settling time of the cantilever beam. Secondly, the dynamic behaviour of the prestressed PZT cantilever beam is in- vestigated subjected to change in driving voltage. Experimental investigations show a shift in resonant frequencies of a PZT cantilever beam. However, there is no reported mathematical model that predicts the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam subjected to a change in driving voltage. This work developed a mathematical model with experimental val- idation to estimate the shift in resonance frequencies of such cantilever beams with the change in the driving voltage. A very good agreement between the model predic- tions and experimental measurements for the frequency response of the cantilever beam at different driving voltages has been obtained. A novel linear formulation has been developed to predict the shift in resonance frequencies of the PZT can- i tilever beam for a wide range of driving voltages. The formulation shows that the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam per unit of applied voltage is dependent on geometric parameters and material properties. Thirdly, a robust resonant controller has been designed and implemented to re- duce the settling time of a highly vibrating PZT cantilever beam. The controller design is based on a mixed negative-imaginary, passivity, and a small-gain approach. The motivation to design a resonant controller using the above-mentioned analyti- cal framework is its bandpass nature and the use of velocity feedback, as the charge collected from a vibrating PZT cantilever beam gives the velocity information of the beam. The proposed controller design results in finite gain stability for a pos- itive feedback interconnection between two stable linear systems with a large gain and phase margin. Experimental results demonstrate that the designed resonant controller is able to effectively damp the first resonant mode of a cantilever, signifi- cantly reducing settling time from 528 ms to 32 ms. The robustness of the designed resonant controller is tested against changes in the cantilever beam dynamics due to residual stress variation and or stress variation due to driving voltage. Finally, to facilitate the miniaturization of on-chip sensors and parallel high- speed AFM, a single layer of a PZT thin-film in a cantilever beam is used as a deflection sensor and an actuator instead of bulky optical deflection sensors. A novel charge readout circuit is designed for deflection sensing by capturing the electrical charge generated due to the vibration of the PZT beam. The signal-to-noise ratio and sensitivity analysis of the readout circuit shows similar results compared to the commercially available optical deflection sensors. Our work highlights very important aspects in the dynamic behaviour and perfor- mance of a multi-layered prestressed piezoelectric cantilever beam. The agreement between the proposed theoretical formulation and experimental investigations in modeling, control design, and a novel readout circuit will provide the platform for further the development and miniaturization of microcantilever-based technologies, including on-chip parallel HS-AFM.
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(2023)ThesisThis thesis presents modeling and control of an on-chip self-sensing novel multi-layered thin-film piezoelectrically-driven micro-lens actuator that has the potential to be used in micro-optic devices. The actuator is made of six unimorph piezoelectric beams connected tangentially with the lens holding platform to hold a PDMS lens and operate in d31 mode. The use of polysilicon instead of single crystal silicon as a passive structural layer allows for manipulation of residual stress to generate out-of-plane displacement for optical zooming. The actuator exhibits intrinsic residual stress due to different thermal expansion coefficients of the films and annealing processing steps during fabrication, and applied driving voltage generates axial stress in the PZT layer. An analytical model of the actuator taking into account residual stress of the film and driving voltage is developed and validated with Finite Element Analysis (FEA) and experiments. The analytical model accurately predicts the dynamic behavior of the actuator and can be applied to other multi-layered piezoelectric microstructures by adjusting boundary conditions. Feedback control improves the dynamic response of the actuator by increasing damping in the resonance mode. A resonant controller designed based on the identified model of the actuator is implemented experimentally, achieving a damping of 21 dB in the first resonance mode and reducing the settling time to 7 ms from the open-loop settling time of 120 ms. An on-chip self-sensing piezoelectric sensor using current feedthrough cancellation instead of voltage is designed, fabricated, and characterized for use in feedback control. The measured dynamic range of the micro-lens actuator and signal-to-noise ratio (SNR) of the on-chip self-sensing piezoelectric sensor are 22 dB and 108 dB, respectively. A passive resonant feedback controller designed based on feedback from an on-chip self-sensing piezoelectric sensor is implemented experimentally on a piezoelectrically driven micro-lens actuator. The closed-loop implementation using the on-chip self-sensing piezoelectric sensor dampened the resonance mode by 20.6 dB, and the settling time for a square wave input was reduced to 10ms from the open-loop 120 ms. The quick settling time achieved by the on-chip self-sensing enables the realization of a fast micro-lens actuator, leading to fast auto-focusing and large optical zooming capabilities in portable micro-optic devices.