This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck) regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current (DC-AC) inverter. These are widely used for power transfer in a variety of industrial and personal applications. This motivates the precise quantification of conditions under which existing modeling and design methods yield satisfactory designs, and the study of alternatives when they don’t. This dissertation describes a method utilizing Fourier components of the input square wave and the inductor-capacitor (LC) filter transfer function, which doesn’t require the small ripple approximation. Then, trade-offs associated with the choice of the filter order are analyzed for integrated buck converters with a constraint on their chip area. Design specifications which would justify using a fourth or sixth order filter instead of the widely used second order one are examined. Next, sampled-data (SD) control of a buck converter is analyzed. Three methods for the digital controller design are studied: analog design followed by discretization, direct digital design of a discretized plant, and a “lifting” based method wherein the sampling time is incorporated in the design process by lifting the continuous-time design plant before doing the controller design. Specifically, controller performance is quantified by studying the induced-L2 norm of the closed loop system for a range of switching/sampling frequencies. In the final segment of this dissertation, the inner-outer control loop, employed in inverters with an inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the loop broken at the error and the control are examined, demonstrating that traditional methods only address these properties for one loop-breaking point. New controllers are then provided for improving both sets of properties.

This thesis addresses the design and control of three phase inverters. Such inverters are

used to produce three-phase sinusoidal voltages and currents from a DC source. They

are critical for injecting power from renewable energy sources into the grid. This is

especially true since many of these sources of energy are DC sources (e.g. solar

photovoltaic) or need to be stored in DC batteries because they are intermittent (e.g. wind

and solar). Two classes of inverters are examined in this thesis. A control-centric design

procedure is presented for each class. The first class of inverters is simple in that they

consist of three decoupled subsystems. Such inverters are characterized by no mutual

inductance between the three phases. As such, no multivariable coupling is present and

decentralized single-input single-output (SISO) control theory suffices to generate

acceptable control designs. For this class of inverters several families of controllers are

addressed in order to examine command following as well as input disturbance and noise

attenuation specifications. The goal here is to illuminate fundamental tradeoffs. Such

tradeoffs include an improvement in the in-band command following and output

disturbance attenuation versus a deterioration in out-of-band noise attenuation.

A fundamental deficiency associated with such inverters is their large size. This can be

remedied by designing a smaller core. This naturally leads to the second class of inverters

considered in this work. These inverters are characterized by significant mutual

inductances and multivariable coupling. As such, SISO control theory is generally not

adequate and multiple-input multiple-output (MIMO) theory becomes essential for

controlling these inverters.