This dissertation deals with smooth feedback stabilization of control-affine systems via Interconnection and Damping Assignment - Passivity-Based Control (IDA-PBC). The IDA-PBC methodology is a feedback control design technique that aims to establish or manipulate a port-Hamiltonian structure of the closed-loop system. For a mechanical control system, a port-Hamiltonian system is a natural description of the dynamics, and several effective controller designs have been presented for this class of systems. In other fields of engineering, the development of such controller design is an active area of research. In particular, applications of IDA-PBC techniques prove to be difficult in practice for process control applications where the concept of energy is usually ill-defined. This thesis seeks to extend the application of the IDA-PBC methodology beyond mechanical control systems. This is achieved by following three directions of research. First, we establish conditions under which a port-Hamiltonian system can be written as a feedback interconnection of two port-Hamiltonian system. We identify such an interconnection structure for linear control systems based on their intrinsic properties. Second, as observed in application of IDA-PBC to non-mechanical systems, several additional assumptions on the structure of the desired port-Hamiltonian system can effectively reduce the complexity of the matching problem. We establish a unified approach that considers these additional assumptions. Third, we connect the matching problem to the classical feedback equivalence approach. We show that feedback equivalence between control-affine systems can be employed to construct some feasible interconnection and damping structures. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2011-01-31 12:59:56.828

Στις μέρες μας, οι ολοένα αυξανόμενες ενεργειακές ανάγκες καθώς και οι η μόλυνση του περιβάλλοντος είναι οι κύριοι λόγοι που η χρήση των ανανεώσιμων πηγών ενέργειας στα σύγχρονα συστήματα ενέργειας έχει αυξηθεί τις τελευταίες δεκαετίες. Τα φωτοβολταϊκά συστήματα είναι μια από τις πιο συνήθεις και αποτελεσματικές ανανεώσιμων πηγών για συνδεδεμένα στο δίκτυο ή αυτόνομα συστήματα. Ο σκοπός της παρούσας εργασίας είναι η μελέτη και προσομοίωση έλεγχου σε μετατροπέα δυο βαθμίδων για σύνδεση φωτοβολταικού συστήματος. Αρχικά, θα μελετήσουμε θεωρητικά διάφορους τύπους τοπολογιών που περιλαμβάνουν αντιστροφέα, στην περίπτωση μας, θα μοντελοποιήσουμε και προσομοιώσουμε ένα DC-DC μετατροπέα σε σύνδεση αλυσίδας με έναν τριφασικό DC-AC αντιστροφέα σε ένα απομονωμένο σύστημα. Ειδικότερα θα παρουσιάσουμε θεωρητικά και πειραματικά αποτελέσματα έλεγχου της τάσης εξόδου του μετατροπέα. Το βασικό κομμάτι αυτής της εργασίας είναι τα αποτέλεσμα του ελεγκτή που είναι βασισμένος στην παθητικότητα διασύνδεσης και εκχώρηση απόσβεσης (IDA PBC). Τέλος, θα μοντελοποιήσουμε και προσομοιώσουμε τον DC-AC μετατροπέα, του οποίου ελέγχουμε την τάση εξόδου από τους γνωστούς μας σε όλους αναλογικούς-ολοκληρωτικούς (PI) ελεγκτές. / Nowadays, increased energy needs and the increasing pollution levels of the environment are the main reasons that usage of renewable energy sources to modern power systems has significantly increased in the last decades. Photovoltaic (PV) generator systems are one of the most common and efficient renewable energy applications for grid-connected or stand-alone systems. The aim of the present thesis is the study and the simulation of control of a two level power converter used in photovoltaic systems. Firstly, we will study theoretically different types of topologies that include inverters, in our case, we model and simulate a DC-DC boost power converter string connected with a three phase DC-AC inverter to a stand-alone system. Especially we will present theoretical and experimental results controlling the DC-DC converter output voltage. The basic part of this thesis are the results of the controller, which is designed following the passivity-based interconnection and damping assignment methodology (IDA PBC). Finally, we will model and simulate the DC-AC inverter, where its output voltage is controlled by the well-known, proportional-integral (PI) controllers.

Electrical Power System is one of the most complex real time operating systems. It is probably one of the best examples of a large interconnected nonlinear system of varying nature. The system needs to be operated and controlled with component or system problems, often with combinatorial complexity. In addition, time scales of operation and control can vary from milliseconds to minutes to hours. It is difficult to maintain such a system at constant operating condition due to both small and large disturbances such as sudden change in loads, change in network configuration, fluctuations in turbine output, and various types of faults etc. The system is therefore affected by a variety of instability problems. Among all these instability problems one of the important modes of instability is related to dynamic instability or more precisely the small perturbation oscillatory instability. Oscillations of small magnitude and low frequency (in the range of 0.1Hz to 2.5Hz) could persist for long periods, limiting the power transfer capability of the transmission lines. Power System Stabilizers (PSS) were developed as auxiliary controllers on the excitation system to improve the system damping performance by modulating the generator excitation voltage. However, the synthesis of an effective PSS for all operating conditions still remains a difficult and challenging task. The design and tuning of PSS for robust operation is a laborious process. The existing PSS design techniques require considerable expertise, the complete system information and extensive eigenvalue calculations which increases the computational burden as the system size increases. Conventional automatic voltage regulator (AVR) and PSS designs are based on linearized models of power systems which fail to stabilize the system over a wide range of operating conditions. In the last decade or so, a variety of nonlinear control techniques have become available. In this thesis, an attempt is made to explore the suitability of some of these design techniques for designing excitation controllers to enhance small perturbation stability of power systems over a wide range of operating and system conditions. This thesis first proposes a method of designing power system stabilizers based on local measurements alone, in multi-machine systems. Next, a method has been developed to analyze and quantify the small signal performance benefits of replacing the existing AVR+PSS structure with nonlinear voltage regulators. A number of new nonlinear controller designs have been proposed subsequently. These include, (a) a new decentralized nonlinear voltage regulator for multi machine power systems with a single tunable parameter that can achieve effective trade of between both the voltage regulation and small signal objectives, (b) a decentralized Interconnection and Damping Assignment Passivity Based Controller in addition to a proportional controller that can achieve all the requirements of an excitation system and (c) a Nonlinear Quadratic Regulator PSS using Single Network Adaptive Critic architecture in the frame work of approximate dynamic programming. Performance of all the proposed controllers has been analyzed using a number of multi machine test systems over a range of operating conditions.