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Scientific phenomena are often studied through collections of related scalar fields such as data generated by simulation experiments that are parameter or time dependent . Exploration of such data requires robust measures to compare them in a feature aware and intuitive manner. Topological data analysis is a growing area that has had success in analyzing and visualizing scalar fields in a feature aware manner based on the topological features. Various data structures such as contour and merge trees, Morse-Smale complexes and extremum graphs have been developed to study scalar fields. The extremum graph is a topological data structure based on either the maxima or the minima of a scalar field. It preserves local geometrical structure by maintaining relative locations of extrema and their neighborhoods. It provides a suitable abstraction to study a collection of datasets where features are expressed by descending or ascending manifolds and their proximity is of importance. In this thesis, we design a measure to understand the similarity between scalar fields based on the extremum graph abstraction. We propose a topological structure called the complete extremum graph and define a distance measure on it that compares scalar fields in a feature aware manner. We design an algorithm for computing the distance and show its applications in analyzing time varying data such as understanding periodicity, feature correspondence and tracking, and identifying key frames.

Master of Science / Department of Mechanical and Nuclear Engineering / Guoqiang Hu / Warren N. White / In recent years, the concern has risen to establish clean sources for electric power generation. In 2009, Kansas established an RPS (Renewable Portfolio Standard) mandating utilities acquire 20% of their electricity from renewable energy by 2020 [32]. One of the most prominent renewable energy sources is wind energy. Utility companies now are investing more in wind capture systems to comply with this mandate. This increase in the manufacture of wind turbines has caused researchers to investigate methods to improve the efficiency of captured wind energy and where improvements can be made. This thesis takes a control theory approach to maximizing the power capture of a wind turbine using the concepts of robust estimation, nonlinear control, and Lyapunov-based maximization. A two step control approach to optimize the power capture of a wind turbine is proposed. First, a robust controller is used to estimate unknown aerodynamic properties and regulate the wind turbine tip-speed ratio as it tracks a desired trajectory. Once the tip-speed ratio is regulated within a given tolerance, a Lyapunov-based control approach is developed to provide the robust controller with a desired trajectory to track. This is done by estimating the unknown coefficient of performance of the wind turbine. A discrete update law is then developed to alter the tip-speed ratio and the blade pitch of the wind turbine so that the coefficient of performance is maximized. A simulation is provided of this control strategy and tested under time varying wind conditions and measurement noise in order to demonstrate the controller’s performance. The system simulated is intended to emulate a commercial wind turbine operating in a realistic environment. A detailed discussion of the simulation model, control scheme, and results will be provided to supplement the theoretical controller development, as well as future work for this control application.

Master of Science / Department of Mechanical and Nuclear Engineering / Guoqiang Hu / In some types of renewable energy systems such as wind turbines or solar power plants, the optimal operating conditions are influenced by the intermittent nature of these energies. This fact, along with the modeling difficulties of such systems, provides incentive to look for non-model based adaptive techniques to address the maximum power point tracking (MPPT) problem. In this thesis, a novel extremum seeking algorithm is proposed for systems where the optimal point and the optimal value of the cost function are allowed to be time varying. A sinusoidal perturbation based technique is used to estimate the gradient of the cost function. Afterwards, a robust optimization method is developed to drive the system to its optimal point. Since this method does not require any knowledge about the dynamic system or the structure of the input-to-output mapping, it is considered to be a non-model based adaptive technique. The proposed method is then employed for maximizing the energy capture from the wind in a variable speed wind turbine. It is shown that without any measurements of wind velocity or power, the proposed method can drive the wind turbine to the optimal operating point. The generated power is observed to be very close to the maximum possible values.

Αντικείμενο της εργασίας είναι ο έλεγχος του προσανατολισμού ελικοπτέρου Quadrotor με χρήση ελεγκτή PID. Το ελικόπτερο Quadrotor είναι ένα μη γραμμικό, ασταθές, υποενεργοποιούμενο σύστημα. Για αυτούς τους λόγους, ο έλεγχός του παρουσιάζει σοβαρά προβλήματα. Ο ελεγκτής PID αρχικά εφαρμόζεται στο γραμμικοποιημένο μοντέλο του συστήματος, και εν συνεχεία διακριτοποιείται και εξετάζεται στο πλήρες μη γραμμικό μοντέλο του Quadrotor. Ιδιαίτερο βάρος δίνεται στη ρύθμιση του ελεγκτή PID. Αφού παρουσιαστούν οι κυριότερες μέθοδοι ρύθμισης ενός τέτοιου ελεγκτή, επιλέγεται η μέθοδος Extremum Seeking, μία επαναληπτική μέθοδος που βελτιστοποιεί τον PID ώστε να ελαχιστοποιείται τοπικά μια συνάρτηση κόστους. Σημαντικό πλεονέκτημα αυτής της μεθόδου αποτελεί το γεγονός ότι μπορεί να εφαρμοστεί κατ' ευθείαν στο μη γραμμικό μοντέλο του συστήματος βελτιστοποιώντας περαιτέρω τον ελεγκτή. Στη συνέχεια ο ελεγκτής PID εξετάζεται σε ένα πραγματικό ελικόπτερο που κατασκευάστηκε στο εργαστήριο. Στο πειραματικό αυτό σύστημα, η υλοποίηση του PID γίνεται σε έναν ηλεκτρονικό υπολογιστή, με τη βοήθεια του προγράμματος Labview ενώ η επικοινωνία ανάμεσα στον υπολογιστή και στο ελικόπτερο επιτυγχάνεται με τη βοήθεια σειριακής θύρας RS232. Μετά τη διεξαγωγή των πειραμάτων και την αξιολόγηση της απόδοσης του ελεγκτή PID, αναφέρονται τα γενικότερα συμπεράσματα της εργασίας, καθώς και προτάσεις για περαιτέρω έρευνα. / This thesis focuses on attitude control of a quadrotor helicopter with PID technique. Quadrotor is a non linear, unstable, underactuated system, so the controller design is a very challenging task. Initially the PID controller is applied to the linearized model of the helicopter, and then to the discretized one, because the controller is later implemented on a personal computer. Then we describe some PID tuning techniques that are often used in practice. In this thesis we use Extemum Seeking which is an iterative, optimization method for the PID tuning that can be used in either linear or non linear models. So Extremum Seeking can be applied to the full non linear model of the quadrotor to further improve the PID parameters. Finally the PID controller is applied to a real Quadrotor helicopter. The controller is implemented on Labview while the communication between the PC and the helicopter is achieved with two RS232 links.

In this work, we propose three control strategies from different perspectives to solve the alignment problem for different optical wireless communication (OWC) systems. • Experimental modeling based strategy: we model and analyze the vibration effects on the stationary OWC system (e.g. urban free-space optical (FSO) communication system in our case). The proposed Bifurcated-Gaussian (B-G) distribution model of the receiver optical power is derived under different vibra- tion levels and link distances using the nonlinear iteration method. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model helps to easily evaluate the link performance of UFSO systems and paves the way for constructing completed auxiliary control subsys- tems for robust UFSO links. • Extremum seeking control based strategy: we propose an extremum seeking control (ESC) based strategy for the mobile OWC system. Our proposed ap- proach consists of coarse alignment and fine alignment. The coarse alignment using feedback proportional-derivative (PD) control is responsible for tracking and following the receiver. For fine alignment, the perturbation-based extremum seeking control (ESC) is adopted for a continuous search for the optimal posi- tion, where the received optical power is maximum in the presence of distur- bance. The proposed approach is simple, effective, and easy to implement. • Time scale theory based strategy: we design a time scale based Kalman filter for the intermittent OWC system. First, the algorithm of Kalman filter on time scales is presented, followed by several numerical examples for interpretation and analysis. The design of Kalman filter on time scales for our simulated vibrating OWC system is then discussed, whose results are analyzed thoroughly and further validated by a reference system. The proposed strategy has great potential for solving the problem of observer design in the case of intermittent received signals (non-uniform measurements) and paves the way for further controller design. The three proposed control strategies directly or indirectly solve the beam align- ment problem for optical communication systems, supporting the development of robust optical communication link.

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