Digital control has drawn increased attention to the area of pulse-width modulation (PWM) converters. Digital controllers (Figure 1) are attractive for their low power dissipation, immunity to analog component variations, compatibility with digital systems, and ability to implement sophisticated control schemes [1].
In this project, we have addressed system issues that are unique to digital control, such as the impact of the signal quantization in the feedback control loop. The quantization of the output voltage (Vout) in digital controllers can result in periodic oscillations of Vout (limit cycling) at frequencies lower than the PWM switching frequency, producing possibly undesirable output noise and electro-magnetic interference (EMI). We have developed a set of conditions necessary for the elimination of limit cycles in digital controllers [2]. This project further deals with the quantization resolution of digital controllers. In particular, we have analyzed and successfully used controlled digital dither to increase the effective resolution of digital PWM (DPWM) modules, while minimizing the dither ripple incurred on the regulated output voltage [2]. Also, we explore the use of a very low resolution analog-to-digital converter (ADC) module in the controller, its implementation, and the resulting control issues [3]. Finally, we have demonstrated an implementation of the above-mentioned techniques in a prototype digitally controlled PWM converter.
We are currently aiming to develop online power optimization techniques for a digital PWM controller. The idea is to minimize the power dissipation of the converter by dynamically adjusting parameters such as the synchronous rectification dead time [4] and the current sharing in multi-phase converters. The ability of the digital controller to implement complex computation algorithms offers a major advantage for this application.

Figure 1: Block diagram of a digitally controlled PWM converter
The current trend in microprocessor design is characterized on the one hand by decreasing supply voltages (~1 V), regulation windows (~100 mV), and conversion ratios (1/12), and on the other hand by increasing supply currents (~100 A) and supply current slew rates (~50 A/us). These trends present a challenge to the design of microprocessor voltage regulation modules (VRMs). We are developing a VRM topology and a control strategy that can meet these requirements, while maintaining efficiency [1]. Our design is based on a multi-phase buck converter supplemented by a low-inductance output clamp to handle fast output unloading transients (Figure 1).
We have analyzed the response of the buck converter under fast output current transients, and we have developed sensing and control methods for its implementation with a digital PWM controller [2,3]. This analysis has been done in the framework of low effective series resistance (ESR) ceramic capacitors, which are the expected choice for the next generation VRMs. We have further explored the effect of power train parameter variations on the current matching among the phases of the converter, and are currently working on an online multi-phase current sharing optimization scheme.
We are currently building a second generation digitally controlled VRM prototype with an FPGA-implemented controller to test the topology in Figure 1, as well as various control and optimization concepts.

Figure 1: Four-phase VRM with low-inductance clamp to ground
In this project, we plan to investigate the feasibility of a distributed generation technology based on low-concentration-ratio non-imaging optical concentrators [1], used in conjunction with moderate efficiency integrated thermal-to-electric energy converters. The latter device is intended to be based on a Stirling engine design [2, 3] incorporating integrated electric generation capability. A specific innovative contribution to the Stirling engine technical area is in the conception and deployment of a multi-phase multiple-free-piston machine. Refer to Figures 1-3 for a sketch of the proposed device. We note that flat panel photovoltaic generation technology is available at roughly a cost of $5/Watt, and that it is believed in the energy community that a similar technology offered at roughly $1/Watt would lead to widespread deployment at residential and commercial sites. Thus, a project goal is to consider cost and focus on complete system designs that meet or exceed the cost goal of $1/Watt. We intend to target the concentrator-collector operation at moderate temperatures. Furthermore, these low ratio concentrators admit wide angles of radiation acceptance and are thus compatible with no diurnal tracking, and no or only a few seasonal adjustments (Figure 1). Thus, we do not anticipate any costs or reliability hazards associated with tracking hardware systems. We are outlining a strategy for exploiting solar resources in a cost effective manner. We believe the cost of the technology based on output power per dollar is the most important parameter, as opposed to efficiency. In contrast, photovoltaic devices based on silicon technology have needed to achieve high efficiency because of the inherent cost of the silicon wafer area.

Figure 1: Solar collector schematic. Rectangular region incorporates Stirling engines and linear alternators as shown in Figure 2.

Figure 2: Three-piston Stirling engine linear alternator schematic configuration. Details are shown in Figure 3.

Figure 3: Technical drawing of one piston connected to the linear alternator.
One of the enabling technologies for practical flywheel energy storage is the magnetic bearing. As part of an effort to develop flywheel energy storage for use in hybrid electric vehicles, we have designed and constructed a self-sensing, homopolar magnetic bearing. This bearing would make it possible to spin flywheels at very high speeds, thus increasing power density and efficiency.
Homopolar magnetic bearings feature extremely low rotating losses. The term homopolar refers to the arrangement of the DC permanent magnet flux and the AC control flux in our design. The term self-sensing refers to the fact that our design senses the position of the rotor through the same coils that are used to actuate the rotor, so no external sensors are needed to operate the bearing. Eliminating the need for extraneous sensors is a major advantage because it reduces complexity, eliminates sensor reliability problems, and eliminates difficulties with locating sensors in tight areas.
We have successfully demonstrated a prototype self-sensing homopolar magnetic bearing, and are currently working on integrating the bearing into a flywheel system.

Figure 1: Cutaway view of magnetic bearing

Figure 2: Plot of sensor output versus rotor displacement
Flywheel energy storage is an important technology for power quality systems and uninterruptible power supplies. The high power density, environmental friendliness, and high reliability of flywheel systems make them a very attractive alternative to existing battery technologies for these applications. However, reductions in cost and complexity need to be achieved before they become more widely used.
Other flywheel systems have been built using carbon fiber or other expensive composite materials for their flywheel rotor. This drives up the material and manufacturing costs significantly. By using a slotless synchronous homopolar motor design and integrating the containment and vacuum housing with the motor housing, a much simpler flywheel system can be constructed [1]. The single-piece steel rotor design can achieve comparable performance at lower cost and higher reliability. A prototype 30 kW, 140 W-hr flywheel energy storage system has been built, and we are currently conducting performance tests.
Other flywheel-related research conducted by the UC Berkeley Power Electronics Group includes the design of high-speed, low-loss synchronous reluctance motors and self-sensing magnetic bearings [2, 3].

Figure 1: Cross-section of prototype flywheel energy storage system

Figure 2: Stator and rotor