Volterra Series Approximation for Multi-Degree of Freedom, Multi-Input, Multi-Output, Aircraft Dynamics

An analytical model of a second order system is extended from a single-axis framework, to a multi-axis, multi-degree of freedom framework for a multiple input, multiple output system. This mathematical model is built from the variational approach of the Volterra series representation of nonlinear systems. The new representation describes the second order, oscillatory natural modes of a system, and shows how to organize the Volterra terms in intuitive ways. The constructed mathematical model aims to establish an organization of the Volterra kernels to allow for analytical cause and effect type analysis on system behavior. To demonstrate the accuracy of the developed Volterra model, the model is applied to atmospheric flight dynamics. A numerical simulation of an F-16 aircraft was developed based on the experimental data collected at NASA Langley and is compared to the Volterra model. Both longitudinal and latitudinal aircraft dynamics are analyzed, and the results show that the Volterra model effectively tracks the numerical simulations and has less error than a more conventional linearized system. The results show that weak nonlinearities of a system are predicted based on this new model. The construction of the model allows for a more effective analysis to the cause and effect of the response. Individual responses of each nonlinear component are separated for analysis, and each component’s effects on the total system response are observed

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Automation and Control Architecture for Hybrid Pipeline Robots

The aim of this research project, towards the automation of the Hybrid Pipeline Robot (HPR), is the development of a control architecture and strategy, based on reconfiguration of the control strategy for speed-controlled pipeline operations and self-recovering action, while performing energy and time management. The HPR is a turbine powered pipeline device where the flow energy is converted to mechanical energy for traction of the crawler vehicle. Thus, the device is flow dependent, compromising the autonomy, and the range of tasks it can perform. The control strategy proposes pipeline operations supervised by a speed control, while optimizing the energy, solved as a multi-objective optimization problem. The states of robot cruising and self recovering, are controlled by solving a neuro-dynamic programming algorithm for energy and time optimization, The robust operation of the robot includes a self-recovering state either after completion of the mission, or as a result of failures leading to the loss of the robot inside the pipeline, and to guaranteeing the HPR autonomy and operations even under adverse pipeline conditions Two of the proposed models, system identification and tracking system, based on Artificial Neural Networks, have been simulated with trial data. Despite the satisfactory results, it is necessary to measure a full set of robot’s parameters for simulating the complete control strategy. To solve the problem, an instrumentation system, consisting on a set of probes and a signal conditioning board, was designed and developed, customized for the HPR’s mechanical and environmental constraints. As a result, the contribution of this research project to the Hybrid Pipeline Robot is to add the capabilities of energy management, for improving the vehicle autonomy, increasing the distances the device can travel inside the pipelines; the speed control for broadening the range of operations; and the self-recovery capability for improving the reliability of the device in pipeline operations, lowering the risk of potential loss of the robot inside the pipeline, causing the degradation of pipeline performance. All that means the pipeline robot can target new market sectors that before were prohibitive

Digital signal processing for coherent optical fibre communications

In this thesis investigations were performed into digital signal processing (DSP) algorithms for coherent optical fibre transmission systems, which provide improved performance with respect to conventional systems and algorithms. Firstly, an overview of coherent detection and coherent transmission systems is given. Experimental investigations were then performed into the performance of digital backpropagation for mitigating fibre nonlinearities in a dual-polarization quadrature phase shift keying (DP-QPSK) system over 7780 km and a dual-polarization 16- level quadrature amplitude modulation (DP-QAM16) system over 1600 km. It is noted that significant improvements in performance may be achieved for a nonlinear step-size greater than one span. An approximately exponential relationship was found between performance improvement in Q-factor and the number for required complex multipliers. DSP algorithms for polarization-switched quadrature phase shift keying (PS-QPSK) are then investigated. A novel two-part equalisation algorithm is proposed which provides singularity-free convergence and blind equalisation of PS-QPSK. This algorithm is characterised and its application to wavelength division multiplexed (WDM) transmission systems is discussed. The thesis concludes with an experimental comparison between a PS-QPSK transmission system and a conventional DP-QPSK system. For a 42.9 Gb/s WDM system, the use of PS-QPSK enabled an increase of reach of more than 30%. The resultant reach of 13,640 km was, at the time of publication, the longest transmission distance reported for 40 Gb/s transmission over an uncompensated link with standard fibre and optical amplification