The thesis aims at building an experimental setup for conducting the boundary ejection and resonance ejection experiments on wide variety of ion trap mass analyzers. The experimental setup has two parts namely power electronics circuits and mechanical assembly. The focus of the thesis is on the electronics hardware which provides various power sources required for the operation of ion trap mass spectrometer. The electronics circuits discussed in the thesis have better performance, flexibility and ruggedness compared to the existing setup. The traditional power supplies used in ion trap mass spectrometers are all linear supplies. But one major drawback of these supplies is the high power dissipation and consequently, the power efficiency degrades. We are trying to introduce switch mode power supplies to reduce the power dissipation loss and eventually increase the power efficiency. In the course of the work the following power supplies have been developed. The supplies are - 1.Constant current source, 2.Filament base, 3.gating power supply and pulsing circuit, 4.High voltage DC power supply and 5. High voltage RF generator.

The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers. The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics. Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions. The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions. The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good. Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments. / QC 20100628

Modelling and simulation are essential ingredients of the analysis and design process in power electronics. It helps a design engineer gain an increased understanding of circuit operation. Accordingly, for a set of specifications given, the designer will choose a particular topology, select component types and values, estimate circuit performance etc. Typically hierarchical modelling, analysis and simulation rather than full detailed simulation of the system provides a crucial insight and understanding. The combination of these insights with hardware prototyping and experiments constitutes a powerful and effective approach to design. Obtaining the mathematical model of the power electronic systems is a major task before any analysis or synthesis or simulation can be performed. There are circuit oriented simulators which uses inbuilt mathematical models for components. Simulation with equation solver needs mathematical models for simulation which are trimmed according to user requirement. There are various methods in the literature to obtain these mathematical models. However, the issues of multi-domain system modelling and causality of the energy variables are not sufficiently addressed. Further, specifically to power converter systems, the issue of switching power models with fixed causality is not addressed. Therefore, our research focuses on obtaining solutions to the above using relatively untouched bond graph method to obtain models for power electronic systems. The power electronic system chosen for the present work is Switched Mode Power Converters (SMPC’s) and in particular PWM DC-DC converters. Bond graph is a labelled and directed graphical representation of physical systems. The basis of bond graph modelling is energy/power flow in a system. As energy or power flow is the underlying principle for bond graph modelling, there is seamless integration across multiple domains. As a consequence, different domains (such as electrical, mechanical, thermal, fluid, magnetic etc.) can be represented in a unified way. The power or the energy flow is represented by a half arrow, which is called the power bond or the energy bond. The causality for each bond is a significant issue that is inherently addressed in bond graph modelling. As every bond involves two power variables, the decision of setting the cause variable and the effect variable is by natural laws. This has a significant bearing in the resulting state equations of the system. Proper assignment of power direction resolves the sign-placing problem when connecting sub-model structures. The causality will dictate whether a specific power variable is a cause or the effect. Using causal bars on either ends of the power bond, graphically indicate the causality for every bond. Once the causality gets assigned, bond graph displays the structure of state space equations explicitly. The first problem we have encountered in modelling power electronic systems with bond graph is power switching. The essential part of any switched power electronic system is a switch. Switching in the power electronic circuits causes change in the structure of the system. This results in change in dynamic equations of the circuit according to position of the switch. We have proposed the switched power junctions (SPJ) to represent switching phenomena in power electronic systems. The switched power junctions are a generalization of the already existing 0-junction and 1-junction concepts of the bond graph element set. The SPJ’s models ideal switching. These elements maintain causality invariance for the whole system for any operational mode of the system. This means that the state vector of the resulting state equation of the system does not change for any operating mode. As SPJs models ideal power switching, the problem of stiff systems and associated numerical stability problems while simulating the system is eliminated. Further, it maintains one to one correspondence with the physical system displaying all the feasible modes of operation at the same time on the same graph. Using these elements, the switched mode power converters (SMPC's) are modelled in bond graph. Bond graph of the converter is the large signal model of the converter. A graphical procedure is proposed that gives the averaged large signal, steady state and small signal ac models. The procedure is suitable for the converters operating in both Continuous Conduction Mode (CCM) and in Discontinuous Conduction Mode (DCM). For modelling in DCM, the concept of virtual switch is used to model the converter using bond graph. Using the proposed method, converters of any complexity can be modelled incorporating all the advantages of bond graph modelling. Magnetic components are essential part of the power electronic systems. Most common parts are the inductor, transformer and coupled inductors which contain both the electric and magnetic domains. Gyrator-Permeance approach is used to model the magnetic components. Gyrator acts as an interface between electric and magnetic domain and capacitor model the permeance of the magnetic circuits. Components like inductor, tapped inductor, transformer, and tapped transformer are modelled. Interleaved converters with coupled inductor, zero ripple phenomena in coupled inductor converters as well as integrated magnetic Cuk converter are also modelled. Modelling of integrated magnetic converters like integrated magnetic forward converter, integrated magnetic boost converter are also explored. To carry out all the simulations of proposed bond graph models, bond graph toolbox is developed using MATLAB/SIMULINK. The MATLAB/SIMULINK is chosen since it is general simulation platform widely available. Therefore all the analysis and simulation can be carried out using facilities available in MATLAB/SIMULINK. Symbolic equation extraction toolbox is also developed which extracts state equations from bond graph model in SIMULINK in symbolic form.