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To obtain the rupture history of the Parkfield, California, earthquake, we perform 12 kinematic inversions using elliptical sub-faults. The preferred model has a seismic moment of 1.21 x 10^18 Nm, distributed on two distinct ellipses. The average rupture speed is ~2.7 km/s. The good spatial agreement with previous large earthquakes and aftershocks in the region, suggests the presence of permanent asperities that break during large earthquakes. We investigate our inversion method with several tests. We demonstrate its capability to retrieve the rupture process. We show that the convergence of the inversion is controlled by the space-time location of the rupture front. Additional inversions show that our procedure is not highly influenced by high-frequency signal, while we observe high sensitivity to the waveforms duration. After considering kinematic inversion, we present a full dynamic inversion for the Parkfield earthquake using elliptical sub-faults. The best fitting model has a seismic moment of 1.18 x 10^18 Nm, distributed on one ellipse. The rupture speed is ~2.8 km/s. Inside the parameter-space, the models are distributed according the rupture speed and final seismic moment, defining a optimal region where models fit correctly the data. Furthermore, to make the preferred kinematic model both dynamically correct while fitting the data, we show it is necessary to connect the two ellipses. This is done by adopting a new approach that uses b-spline curves. Finally, we relocate earthquakes in the vicinity of the Darfield, New-Zealand earthquake. 40 years prior to the earthquake, where there is the possibility of earthquake migration towards its epicentral region. Once it triggers the 2010-2011 earthquake sequence, we observe earthquakes migrating inside regions of stress increase. We also observe a stress increase on a large seismic gap of the Alpine Fault, as well as on some portions of the Canterbury Plains that remain today seismically quiet.

The aim of this thesis is to design a controller for an unmanned helicopter to perform target engagement. This mission is briefly defined as / the helicopter flies to a firing point under the commands of a trajectory controller, and then it is aligned to the target with attitude control. After weapon firing, the helicopter initiates a return maneuver under again the commands of the trajectory controller. This mission where the continuous systems and discrete guidance decisions are to be executed in coherence can be studied as a hybrid control problem. One hybrid control approach which is used in this study is the representation based on two motion primitives: trim trajectories and maneuvers. To obtain the desired trim trajectories and the maneuvers, a dynamic inversion based controller is developed. The controller has two loops: the inner loop which controls the helicopter attitudes and the outer loop which controls the helicopter trajectory. A guidance algorithm is developed which enables the controller to switch from the inner loop to the outer loop or vice versa. Simulations are generated to test the controller performance.

This thesis describes the implementation of Yao’s adaptive robust control to an aircraft control system. This control law is implemented as a means to maintain stability and tracking performance of the aircraft in the face of failures and changing aerodynamic response. The control methodology is implemented as an outer loop controller to an aircraft under nonlinear dynamic inversion control. The adaptive robust control methodology combines the robustness of sliding mode control to all types of uncertainty with the ability of adaptive control to remove steady state errors. A performance measure is developed in to reflect more subjective qualities a pilot would look for while flying an aircraft. Using this measure, comparisons of the adaptive robust control technique with the sliding mode and adaptive control methodologies are made for various failure conditions. Each control methodology is implemented on a full envelope, high fidelity simulation of the F-15 IFCS aircraft as well as on a lower fidelity full envelope F-5A simulation. Adaptive robust control is found to exhibit the best performance in terms of the introduced measure for several different failure types and amplitudes.

Thesis (M.S.)--Auburn University, 2007. / Abstract. Includes bibliographic references (ℓ. 94-95)

Les systèmes critiques de vol tels que les actionneurs électromécaniques ainsi que les calculateurs de commande moteur (ECU) et de vol (FCU),sont conçus en tenant compte des contraintes aéronautiques sévères de sureté defonctionnement. Dans le cadre de cette étude, une architecture calculateur pourla commande et la surveillance d’actionneurs moteur et de surfaces de vol est proposée et à fait l’objet d’un brevet [13]. Pour garantir ces mesure de sureté, les ECU et FCU présentent des redondances matérielles multiples, mais engendrent une augmentation de l’encombrement, du poids et de l’énergie consommée. Pour ces raisons, les redondances à base de modèles dynamiques, présentent un atout majeur pour les calculateurs car elles permettent dans certains cas de maintenir les exigences d’intégrité et de disponibilité tout en réduisant le nombre de capteurs ou d’actionneurs. Un rappel sur les méthodes de diagnostic par générateurs de résidus et estimateurs d’états [58, 26, 47] est effectué dans cette étude. Les propriétés de platitude différentielle et la linéarisation par difféomorphisme et bouclage endogène [80, 41, 73] permettent d’utiliser des modèles linéaires équivalents avec les générateurs de résidus. Un banc d’essai a été conçu afin de valider les performances des algorithmes de diagnostic. / Flight-Critical Systems such as Electromechanical Actuators driven by Engine Control Units (ECU) or Flight Control Units (FCU) are designed and developed regarding drastic safety requirements. In this study, an actuator control and monitoring ECU architecture based on analytic redundancy is proposed. In case of fault occurrences, material redundancies in avionic equipment allow certaincritical systems to reconfigure or to switch into a safe mode. However, material redundancies increase aircraft equipment size, weight and power (SWaP). Monitoring based on dynamical models is an interesting way to further enhance safetyand availability without increasing the number of redundant items. Model-base dfault detection and isolation (FDI) methods [58, 26, 47] such as observers and parity space are recalled in this study. The properties of differential flatness for nonlinear systems [80, 41, 73] and endogenous feedback linearisation are used with nonlinear diagnosis models. Linear and nonlinear observers are then compared with an application on hybrid stepper motor (HSM). A testing bench was specially designed to observe in real-time the behaviour of the diagnosis models when faults occur on the stator windings of a HSM.

A run-of-mine ore milling circuit is primarily used to grind incoming ore containing precious metals to a particle size smaller than a specification size. A traditional run-of-mine (ROM) ore single-stage closed milling circuit comprises of the operational units: mill, sump and cyclone. These circuits are difficult to control because of significant nonlinearities, large time delays, large unmeasured disturbances, process variables that are difficult to measure and modelling uncertainties. A nonlinear model predictive controller with state estimation could yield good control of the ROM ore milling circuit despite these difficulties. Additionally, the ROM ore milling circuit is an energy intensive unit and a controller or power optimizer could bring significant cost savings. A nonlinear model predictive controller requires good state estimates and therefore a neural network for state estimation as an alternative to the particle filter has been addressed. The neural network approach requires fewer process variables that need to be measured compared to the particle filter. A neural network is trained with three disturbance parameters and used to estimate the internal states of the mill, and the results are compared with those of the particle filter implementation. The neural network approach performed better than the particle filter approach when estimating the volume of steel balls and rocks within the mill. A novel combined neural network and particle filter state estimator is presented to improve the estimation of the neural network approach for the estimation of volume of fines, solids and water within the mill. The estimation performance of the combined approach is promising when the disturbance magnitude used is smaller than that used to train the neural network. After state estimation was addressed, this work targets the implementation of a nonlinear controller combined with full state estimation for a grinding mill circuit. The nonlinear controller consists of a suboptimal nonlinear model predictive controller coupled with a dynamic inversion controller. This allows for fast control that is asymptotically stable. The nonlinear controller aims to reconcile the opposing objectives of high throughput and high product quality. The state estimator comprises of a particle filter for five mill states as well as an additional estimator for three sump states. Simulation results show that control objectives can be achieved despite the presence of noise and significant disturbances. The cost of energy has increased significantly in recent years. This increase in price greatly affects the mineral processing industry because of the large energy demands. A run-of-mine ore milling circuit provides a suitable case study where the power consumed by a mill is in the order of 2 MW. An attempt has been made to reduce the energy consumed by the mill in the two ways: firstly, within the nonlinear model predictive control in a single-stage circuit configuration and secondly, running multiple mills in parallel and attempting to save energy while still maintaining an overall high quality and good quantity. A formulation for power optimization of multiple ROM ore milling circuits has been developed. A first base case consisted not taking power into account in a single ROM ore milling circuit and a second base case split the load and throughput equally between two parallel milling circuits. In both cases, energy can be saved using the NMPC compared to the base cases presented without significant sacrifice in product quality or quantity. The work presented covers three topics that has yet to be addressed within the literature: a neural network for mill state estimation, a nonlinear controller with state estimation integrated for a ROM ore milling circuit and power optimization of a single and multiple ROM ore milling circuit configuration. / Dissertation (MEng)--University of Pretoria, 2015. / Electrical, Electronic and Computer Engineering / Unrestricted

The motivation of this research is to propose innovative nonlinear and optimal control design algorithms, which can be used in real life. The algorithms need to be computationally efficient, should deal with control constraints and should operate under state feedback. To show the efficacy of algorithms, automatic therapy for different cancer problems is chosen to be the field of application. In this thesis, first an advanced control design technique called ’optimal dynamic in-version’ has been successfully experimented with control constraints. The proposed approach has subsequently been shown to be quite effective in proposing automatic drug delivery schemes with simultaneous application of chemo and immunotherapy drugs for complete elimination of cancer cells in melanoma (a skin cancer) as well as glioma (a brain cancer). As per the current practice, the amount of drug dosages are generally given based on some apriori statistical study with a very small sample size, which in reality may either also lead to drug toxicity (due to excessive drug) or may become ineffective (due to insufficient drug) for a particular patient. Subject to the fidelity of the mathematical model (which has been taken from published literature), it has been shown in this thesis that nonlinear control theory can be used for computation of drug dosages, which can then be used in a feedback strategy, thereby customizing the drug for the patient’s condition, to cure the disease successfully. Next, attention has been shifted to impulsive control of systems. Such impulsive con-trol systems appear in many other applications such as control of swings, control of spacecrafts and rockets using reaction control system, radiotherapy in cancer treatment and so on. Two impulsive control design philosophies are proposed in this thesis. In one approach, recently proposed model predictive static programming (MPSP) has been extended for impulsive control systems and has been named as impulsive-MPSP (I-MPSP). In other approach, another recent development, namely the Pseudospectral method has been utilized to consider both the magnitude of the control impulses as well as the time instants at which they are applied as the decision variables. It can be noted, that to the best of the knowledge of the author, the time instants of control application, being considered as decision variables is being proposed for the first time in the nonlinear and optimal control framework. Both I-MPSP and Pseudospectral methods are computationally quite efficient and hence can be used for feedback control (I-MPSP happens to be computationally more efficient than the Pseudospectral method). Applicability of the proposed extensions have been shown by solving various benchmark problems such as (i) a scalar linear problem, (ii) Van der Pol’s oscillator problem and (iii) an inverted pendulum problem. Finally the applicability of the proposed I-MPSP strategy has been shown by solving challenging problems such as radiotherapy treatment of head and neck and adenocarcimona cancers. Radio-therapy model is considered with oxygen effect, in which radiosensitivity parameters are considered in different forms. Head and neck cancer is considered with constant radiosensitivity parameters and adenocarcinoma is considered with constant, linear, quadratic and saturation model of radiosensitivity parameters. Note that toxicity constraints on normal tissue, which are nonlinear control constraints, are also successfully incorporated in this control design.

This master's thesis deals with the control design method called Non-linear Dynamic Inversion (NDI) and how it can be applied to Unmanned Aerial Vehicles (UAVs). In this thesis, simulations are conducted using a model for the unmanned aerial vehicle SHARC (Swedish Highly Advanced Research Configuration), which Saab AB is developing. The idea with NDI is to cancel the non-linear dynamics and then the system can be controlled as a linear system. This design method needs much information about the system, or the output will not be as desired. Since it is impossible to know the exact mathematical model of a system, some kind of robust control theory is needed. In this thesis integral action is used. A problem with NDI is that the mathematical model of a system is often very complex, which means that the controller also will be complex. Therefore, a controller that uses pure NDI is only discussed, and the simulations are instead based on approximations that use a cascaded NDI. Two such methods are investigated. One that uses much information from aerodata tables, and one that uses the derivatives of some measured outputs. Both methods generate satisfying results. The outputs from the second method are more oscillatory but the method is found to be more robust. If the signals are noisy, indications are that method one will be better.

<p>This master's thesis deals with the control design method called Non-linear Dynamic Inversion (NDI) and how it can be applied to Unmanned Aerial Vehicles (UAVs). In this thesis, simulations are conducted using a model for the unmanned aerial vehicle SHARC (Swedish Highly Advanced Research Configuration), which Saab AB is developing. </p><p>The idea with NDI is to cancel the non-linear dynamics and then the system can be controlled as a linear system. This design method needs much information about the system, or the output will not be as desired. Since it is impossible to know the exact mathematical model of a system, some kind of robust control theory is needed. In this thesis integral action is used. </p><p>A problem with NDI is that the mathematical model of a system is often very complex, which means that the controller also will be complex. Therefore, a controller that uses pure NDI is only discussed, and the simulations are instead based on approximations that use a cascaded NDI. Two such methods are investigated. One that uses much information from aerodata tables, and one that uses the derivatives of some measured outputs. Both methods generate satisfying results. The outputs from the second method are more oscillatory but the method is found to be more robust. If the signals are noisy, indications are that method one will be better.</p>