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PEDS 2007 Digital Control Generations -- Digital Controls for Power Electronics through the Third Generation Philip T. Krein Grainger Center for Electric Machinery and Electromechanics Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, Illinois Abstract - Digital control in power electronics can be divided into three "generations." First-generation digital controls use digital "outside the loop" in communications, setup, and supervisory roles. Second generation digital controls use digital processes "inside the loop," including discrete-time feedback loops and sometimes even digital signal processing. Today, first-generation digital methods are expanding quickly, as new communication protocols and adjustable analog loops become common. Even companies that continue to design analog controls for power electronics often include these types of digital processes. Second-generation digital controls are a hot topic right now, as real-time digital controllers become feasible. In third-generation digital controls, the digital process functions directly with individual switches to push performance up to the physical limits of power electronics. A digital switch decides when it must turn on or off. The control is on direct switch timing rather than a converter duty ratio or a setting. Extreme performance is possible with this approach, such as converters that do not exhibit output disturbances when confronted with load or line step changes. The talk compares these different arenas, all of which are current active topics in power electronics, and shows what can become possible as the third generation develops I. INTRODUCTION Digital control in power electronics, treated now as a hot topic area and debated in many forums, has a long history. The general approaches and contexts are perhaps better understood by dividing the developments into three "generations." In this paper, the concept of digital control generations is introduced. The emphasis is on third-generation techniques that are beginning to capture interest in research laboratories. Although the general value of digital control continues to be a matter of debate, the broad question of how control adds value in a power electronic system, and whether digital techniques offer special value, is the underlying issue that motivates this work. The concepts in this paper may be of value in discussions of digital control. As digital control is discussed, it is important to keep in mind the fundamental analog processing to be accomplished. We are not free to create arbitrary digital representations of energy, in contrast to most communications and information 1 This paper is provided under the Distinguished Lecturer Program of the IEEE Power Electronics Society. This material is based in part upon work supported by the U.S. National Science Foundation under Grant No. ECS-062 1643. 61801 USA processing applications. Power electronics in the end is characterized by large-signal nonlinear systems with analog functions. No matter how much digital processing is involved, its merit is always determined by the ability to better perform these analog functions. The generations are defined as follows: * First-generation digital control: digital processing outside a control loop, in a management or supervisory role. * Second-generation digital control: digital processing inside a control loop. The ultimate formulation includes digital loop designs and real-time control processes. * Third-generation digital control: digital processing is responsible for the moment-by-moment direct action of active switching devices in a converter. The ultimate formulation is a digital switch with built-in computational capability that functions in real time as the device operates. Although the digital control generations defined in this paper have a certain time evolution sequence, they are not meant to imply obsolescence. First-generation digital controls, which have the longest history, are quickly becoming dominant and are not likely to leave the stage in the foreseeable future. Second-generation digital controls seem to be at the heart of present debates. Third-generation controls open the way to unique performance improvements, but are rare. II. FIRST-GENERATION DIGITAL CONTROL IN POWER ELECTRONICS The earliest power electronics controllers, dating to the TL494 and similar chips, were some of the first mixed-mode integrated circuits. These ICs include simple logic along with oscillators and amplifiers, and thus combine digital and analog functions. In this sense, digital control has been a fundamental aspect ofpower electronics for 40 years or more. In this paper, first-generation digital controls are assumed to be more than just mixed-mode circuits. In first-generation digital controls, a digital process manages a power electronic process. The objectives typically include communication, programming, or protection. Motor drives were an early example of first-generation controls. When electronic 1-4244-0645-5/07/$20.00©2007 IEEE P-1 adjustable-speed drives emerged in the 1970s, many already had displays and internal interactions governed by digital logic. Modern drives are designed with dedicated digital signal processors [1, 2], which often manage nearly all the power electronics through computer control. A more recent example is the PMBusTm architecture for power supply communications and interaction [3]. Today, first-generation digital controls for power electronics are widespread. In addition to the PMBus architecture, various smart battery charging interfaces and other communication configurations are becoming common. Dc-dc converters for processors often have external digital settings to support adaptive output voltage. Even those manufacturers "dedicated" to analog power management have embraced digital communication and control interfaces. As a result, first-generation techniques are not really part of the present debate about digital control, and should be taken as a routine extension of other control methods in power electronics. First-generation controls provide a wide array of advantages. Two crucial advantages are the ability to managing event-driven actions and the ability to provide numerical settings. Event-driven actions, such as responses to overloads, transitions among various modes, or even the ability to control different converter topologies bring fundamental performance advantages to this class of control. Since real-time performance demands are avoided in digital part of the system, these capabilities are possible without compromise in dynamic performance. Numerical settings, including gains, output reference values, or operating frequency add software-like flexibility to hardware devices. Other potential advantages include communications interfaces and control buses, memory for various programming functions, and the ability for IC designers to add new features as blocks. The latter allows a vendor to create comprehensive product families from a single base design. Many present first-generation implementations emphasize communication and basic settings, but a range of opportunities remain. Potential innovations include variable-gain tuning, in which gain settings depend on actual line or load conditions, frequency tuning to or from resonances, and various types of control tuning. On-line calibration and active digital trimming, common in many drive applications, can be extended to most power converters. The use of various frequency-domain techniques, such as Fourier Transforms for compensation [4], nonlinear filters [5], and more sophisticated signal processing for fault detection, has been a topic of previous study that is well worth a closer look. III. SECOND-GENERATION DIGITAL CONTROLS IN POWER ELECTRONICS In second-generation control, the digital process moves inside the control loop and operates a power converter in real time. Like first-generation approaches, the basic technique is not new. Once motor drives moved to digital PWM processes more than a decade ago, many of them used complete digital loops for operation and control. At the research level, complete digital controls were presented almost twenty years ago [6]. In motor drive applications, computation time is usually ample and computation cost is a modest fraction of total system cost. The net result has been early adoption of all-digital implementations in that industry. In power supplies and dc-dc converters, real-time operation tends to work against second-generation designs, which are often characterized by intensive analog-digital (A-D) conversion requirements and short computation time windows. The development of second-generation digital controls for these applications is perhaps the most active topic in digital control for power electronics and is the subject of controversy. Many designers still question the value of digital implementations compared to conventional analog hardware. To see the rate challenge, consider a counter-based digital PWM generator intended to support 250 kHz switching for a dc-dc converter. If this device provides 0.1% pulse-width resolution, its clock must run at 250 MHz or more. A PWM generator to support 500 kHz switching with 16-bit pulse-width resolution demands 31 ps time resolution. This requires a 33 GHz clock. Resolution and operating requirements such as these, which have little meaning in the context of analog controls, quickly become unwieldy in a digital application. Digital controls of this type can chatter and operate in limit cycles [7], although known methods such as integral controls can help avoid the problems. Many second-generation digital controls involve a direct mapping from analog implementations to discrete-time implementations. This practice supports the numerical setting advantages of digital controls, but does not fundamentally alter performance compared to analog implementations. Much of the controversy about digital control in power electronics today is concerned with whether a discrete-time implementation offers special advantages over an analog version given a conventional average-model controller. In this paper, the controversy is not entirely germane: there are valid analog controls that use external digital management, as in first-generation digital control, and evolution towards digital control need not place real-time digital processing inside a loop. A. Discussion ofsampling issues Given the linkage between second-generation digital control and A-D/D-A conversion, sampling challenges become a significant aspect. One relatively misunderstood aspect is the Nyquist rate, which reflects the results of sampling theory. As is well known [8], a bandlimited signal can be reconstructed perfectly from properly selected samples taken at higher than the Nyquist rate. This rate is normally taken as half the period associated with the signal band limit. It is tempting to infer that any periodic signal can be reconstructed from samples taken at half the period, but this is not correct. P-2 1111111111111111111111111 Sample times Fig. 1. A square wave with arbitrary duty ratio cannot be reconstructed from uniform samples. Here samples taken five times per switching cycle are not adequate. Consider a square wave of unknown (but constant) duty ratio, as might be measured as the voltage drop across a switch in a power converter or as the ESR jump on a capacitor. As Fig. 1 shows, no set of uniform samples, no matter how often they are taken, will permit the waveform to be sampled and reconstructed perfectly. This is because for arbitrary duty ratio the probability of sampling exactly at the switching instant is zero. What does the Nyquist rate not apply here? A square wave is not a bandlimited signal, so conventional sampling theory does not apply. Curiously, the fundamental Nyquist rate problem associated with the square wave in Fig. 1 can be circumvented. The integral of the square wave yields a triangle wave, as in Fig. 2. This waveform, although also not bandlimited, is easy to reconstruct if the sampling rate is sufficient to ensure two samples during each rising portion and two during each falling portion. This means that for any duty ratio between 0 and 1, a sampling frequency suitable to permit perfect reconstruction can always be found. Indeed, the underlying square wave can be reconstructed from the same samples by taking the derivative of the computed triangle. The sampling frequency is not really a Nyquist rate in the conventional sense, but waveform reconstruction is possible. It is also clear that non-uniform samples can be used to advantage: if samples are taken just before and just after each switch operation, the information needed to reconstruct the waveform will be available. The possibility of reconstructing square waves from limited samples gives rise to the notion of integral sampling [9], but in contrast to the hold process in [9], samples are to be taken during the integration process. The addition of a single analog block - the integrator - adds considerable signal processing capability to a power converter since it support signal reconstruction from a small number of well-place samples. Notice that the process uses general knowledge about the shape of the waveform ( a square wave or triangle) instead of knowledge about its frequency limits. In effect, a time-domain sampling theorem has been identified in place of a more conventional frequency-domain theorem. B. Real-time limitsfor second-generation controls In second-generation designs, real-time digital control must push the limits. Concerns include the conversion speed of A-D and D-A converters, the time needed for computation, and time needed to obtain low-noise samples. Precision, both in terms of time resolution and quantization, becomes an 11 1 1I1 1 1 1 11 Sample times Fig. 2. The integral of the square wave (a triangle) can be reconstructed if two samples are available during each rising and falling portion. important issue. A fundamental question is how a control can determine whether the output has reached the desired value and that the converter should enter steady state. A important way to manage extreme resolution requirements is to employ dithering or noise shaping methods [10, 11]. In both approaches, a large number of switching periods is used as a group to deliver the desired pulse width. For example, a PWM process with only 10% resolution can deliver effective 1% output resolution if a group of ten cycles is employed. In dithering, the local duty ratio variation needed to deliver higher resolution is randomized. Thus, a desired 5400 duty ratio in a process that can deliver only 500O and 60% values would be obtained by random combinations of 5000 and 60% in the right proportions. In noise shaping, the process is not random, and instead is characterized by a high-pass filter that shifts the output quantization noise away from the baseband duty ratio modulation. As microprocessors improve, real-time computational limits become less important in second-generation controls. Today's DSPs, for instance, perform multiple complicated arithmetic steps in a single clock cycle. At clock frequencies above 100 MHz, there is time for several hundred computations per switching period, even for dc-dc converters operating at up to 500 kHz. One commercial product [12] processes six inverter channels for high-fidelity audio output based on a complete second-generation implementation. Other vendors provide sophisticated adaptive controls in second-generation devices [13]. These examples suggest that second-generation digital controls will continue to be an area of active growth for years to come. IV. THIRD-GENERATION DIGITAL CONTROLS IN POWER ELECTRONICS In any switching power converter, the true control actuation is the time at which switches operate. At the most basic level, the control question is to determine when to operate each switching device in the network to achieve a set of performance objectives. Beyond the implementation of real-time digital control in a closed-loop power converter is the challenge of direct switch control to address this question. The issue can be considered in a manner analogous to averaging: in second-generation digital controls, the control generally computes a desired duty ratio. A counter P-3 implements the final step of a PWM process. The control is altering pulse width, rather than direct timing. Third-generation digital controls act on information to determine specific time-domain action of each switching device. The ultimate objective is the digital switch, an intelligent switching device that operates at just the right times to achieve objectives. The objectives could represent any performance aspect needed by the user. Many of them do not lend themselves to analog controls. For example, in a given dc-dc converter, the detailed performance objectives might include the following: * Deliver an output voltage that is within 0.5% of a specified reference. * Do not allow the current to exceed a given dynamic limit. * Deliver the voltage while minimizing internal converter losses. * Avoid certain frequency bands to prevent noise problems. * Respond to load changes as rapidly as possible while continuing to meet output tolerance requirements. Objectives like these mix steady-state, dynamic, and protection requirements. They imply computation challenges such as those associated with loss minimization and electromagnetic interference (EMI). At the most basic level, performance objectives translate into difficult control requirements: determine when to operate the next switching device in a sequence, such that loss is minimized, EMI is avoided, and steady-state requirements are met. In general, it might be possible to formulate an optimal control problem for a set of objectives: Optimal controlproblem formulation Given a set of n switches and a time interval T, find times ti n for these switches to minimize a performance objective function J(x,t) that is a function of states x and time. With enough constraints and well-defined objective functions, this problem can be solved. For example, in a dc-dc converter in which there is one active switch and the switching period is constrained to be fixed, there is a unique time that delivers the correct output in steady state. This is just the well-known average duty ratio. The general problem deals with dynamics rather than steady state, and a suitable problem formulation should have the switching frequency as a dependent variable rather than a constraint, but at least the steady-state operation is relatively well defined. The general problem, in which there are many performance objectives representing both static and dynamic requirements, may not be tractable, however. Third-generation controls are the subject of present research in a few groups. An early example that follows the general approach is given in [14], although the geometric controls introduced much earlier by Burns [15] are straightforward to represent in terms of third-generation digital methods. Dead-time optimization [16, 17] is a partial a) ct 0 10 20 30 40 50 Time (us) Fig. 3. Hysteresis controlled buck converter responding when a 150 kHz line disturbance is imposed at 20 pts. Top trace: input voltage. Triangle: inductor current. Dotted trace: output voltage across capacitor. Output capacitor is small to show ripple. third-generation example, in which detailed switch timing is controlled inside a loop to minimize loss. Fig. 3 provides a hint - based on an analog control - of what might be possible with third-generation controls. The waveforms shown are the input voltage, output voltage, and output current for a buck converter. The converter operates with a hysteresis control to maintain the output at 5 V. The steady-state switchin