Recently, constant-on-time V2 control is more and more popular in industry products due to features of high light load efficiency, simple implementation and fast transient response. In many applications such as cell phone, camera, and other portable devices, low-ESR capacitors such as ceramic caps are preferred due to small size and small output voltage ripple requirement. However, for the converters with ceramic caps, the conventional V2 control suffers from the sub-harmonic oscillation due to the lagging phase of the capacitor voltage ripple relative to the inductor current ripple. Two solutions to eliminate sub-harmonic oscillations are discussed in [39] and the small-signal models are also derived based on time-domain describing function. However, the characteristic of constant-on-time V2 with external ramp is not fully understood and no explicit design guideline for the external ramp is provided. For digital constant on-time V2 control, the high resolution PWM can be eliminated due to constant on-time modulation scheme and direct output voltage feedback [43]. However, the external ramp design is not only related to the amplitude of the limit-cycle oscillation, but also very important to the stability of the system. The previous analysis is not thorough since numerical solution is used. The primary objective of this work is to gain better understanding of the small-signal characteristic for analog and digital constant-on-time V2 with ramp compensations, and provide the design guideline based on the factorized small-signal model. First, constant on-time current-mode control and constant on-time V2 control are reviewed. Generally speaking, constant-on-time current mode control does not have stability issues. However, for constant-on-time V2 control with ceramic caps, sub-harmonic oscillation occurs due to the lagging phase of the capacitor voltage ripple. External ramp compensation and current ramp compensation are two solutions to solve the problem. Previous equivalent circuit model extended by Ray Ridley's sample-and-hold concept is not applicable since it fails to consider the influence of the capacitor voltage ripple. The model proposed in [39] successfully considers the influence from the capacitor voltage ripple by using time-domain describing function method. However, the characteristic of constant-on-time V2 with external ramp is not fully understood. Therefore, more research focusing on the analysis is needed to gain better understanding of the characteristic and provide the design guideline for the ramp compensations. After that, the small-signal model and design of analog constant on-time V2 control is investigated and discussed. The small-signal models are factorized and pole-zero movements are identified. It is found that with increasing the external ramp, two pairs of double poles first move toward each other at half of switching frequency, after meeting at the key point, the two double poles separate, one pair moves to a lower frequency and the other moves to a higher frequency while keeping the quality factor equal to each other. For output impedance, with increasing the external ramp, the low frequency magnitude also increases. The recommended external ramp is around two times the magnitude at the key point K. When Duty cycle is larger, the damping performance is not good with only external ramp compensation, unless very high switching frequency is used. With current ramp compensation, it is recommended to design the current ramp so that the quality factor of the double pole is around 1. With current ramp compensation, the damping can be well controlled regardless of the circuit parameters. Next, the small-signal analysis and design strategy is also extended to digital constant on-time V2 control structure which is proposed in [43]. It is found that the scenario is very similar as analog constant on-time V2 control. The external ramp should be designed around the key point to improve the dynamic performance. The sampling effects of the output voltage require a larger external ramp to stabilize digital constant-on-time V2 control while suffers only a little bit of damping performance. One simple method for measuring control-to-output transfer functions in digital constant-on-time V2 control is presented. The experimental results verify the small-signal analysis except for the high frequency phase difference which reveals the delay effects in the circuit. Load transient experimental results prove the proposed design guideline for digital constant on-time V2 control. As a conclusion, the characteristics of analog and digital constant-on-time V2 control structures are examined and design guidelines are proposed for ramp compensations based on the factorized small-signal model. The analysis and design guideline are verified with simplis simulation and experimental results. / Master of Science

This thesis focuses on the study, implementation and improvement of a digital controller for a power factor correction (PFC) converter. The development of the telecommunications industry and the Internet demands reliable, cost-effective and intelligent power. Nowadays, the telecommunication power systems have output current of up to several kilo amperes, consisting of tens of modules. The high-end server system, which holds over 100 CPUs, consumes tens of kilowatts of power. For mission-critical applications, communication between modules and system controllers is critical for reliability. Information about temperature, current, and the total harmonic distortion (THD) of each module will enable the availability of functions such as dynamic temperature control, fault diagnosis and removal, and adaptive control, and will enhance functions such as current sharing and fault protection. The dominance of analog control at the modular level limits system-module communications. Digital control is well recognized for its communication ability. Digital control will provide the solution to system-module communication for the DC power supply. The PFC converter is an important stage for the distributed power system (DPS). Its controller is among the most complex with its three-loop structure and multiplier/divider. This thesis studies the design method, implementation and cost effectiveness of digital control for both a PFC converter and for an advanced PFC converter. Also discussed is the influence of digital delay on PFC performance. A cost-effective solution that achieves good performance is provided. The effectiveness of the solution is verified by simulation. The three level PFC with range switch is well recognized for its high efficiency. The range switch changes the circuit topology according to the input voltage level. Research literature has discussed the optimal control for both range-switch-off and range-switch-on topologies. Realizing optimal analog control requires a complex structure. Until now optimal control for the three-level PFC with analog control has not been achieved. Another disadvantage of the three-level PFC is the output capacitor voltage imbalance. This thesis proposes an active balancing solution to solve this problem. / Master of Science

With the fast development of information technology (IT) industry, the demand and market volume for off-line power supplies keeps increasing, especially those for desktop, flat-panel TV, telecommunication, computer server and datacenter. An off-line power supply normally consists of electromagnetic interference (EMI) filter, power factor correction (PFC) circuit and isolated DC/DC converter. Isolated DC/DC converter occupies more than half of the volume in an off-line power supply and takes the most control responsibilities, so isolated DC/DC converter is the key aspect to improve the overall performance and reduce the total cost for off-line power supply. On the other hand, of all the power supplies for industrial applications, those for the data center servers are the most performance driven, energy and cost conscious due to the large electricity consumption. The total power consumption of today's data centers is becoming noticeable. Moreover, with the increase in cloud computing and big data, energy use of data centers is expected to continue rapidly increasing in the near future. It is very challenging to design isolated DC/DC converters for datacenters since they are required to provide low-voltage high-current output and fast transient response. The LLC resonant converters have been widely used as the DC-DC converter in off-line power supplies and datacenters due to its high efficiency and hold-up capability. Using LLC converters can minimize switching losses and reduce electromagnetic interference. Almost all the high-end offline power supplies employs LLC converters as the DC/DC converter. But there are three major challenges in LLC converters. Firstly, the control characteristics of the LLC resonant converters are very complex due to the dynamics of the resonant tank. This dissertation proposes to implement a special LLC control method, state-trajectory control, with a low-cost microcontroller (MCU). And further efforts have been made to integrate all the state-trajectory control function into one MCU for high-frequency LLC converters, including start-up and short-circuit protection, fast transient response, light load efficiency improvement and SR driving. Secondly, the transformer in power supplies for IT industry is very bulky and it is very challenging to design. By pushing switching frequency up to MHz with gallium nitride (GaN) devices, the magnetics can be integrated into printed circuit board (PCB) windings. This dissertation proposes a novel matrix transformer structure and its design methodology. On the other hand, shielding technique can be employed to suppress the CM noise for PCB winding transformer. This dissertation proposes a novel shielding technique, which not only suppresses CM noise, but also improves the efficiency. The proposed transformer design and shielding technique is applied to an 800W 400V/12V LLC converter design. Thirdly, the LLC converters have sinusoidal current shape due to the nature of resonance, which has larger root mean square (RMS) of current, as well as larger conduction loss, compared to pulse width modulation (PWM) converter. This dissertation employs three-phase interleaved LLC converters to reduce the circulating energy by inter-connecting the three phases in certain way, and proposed a novel magnetic structure to integrated three inductors and three transformers into one magnetic core. By pushing switching frequency up to 1MHz, all the magnetics can be implemented with 4-layer PCB winding. Additional 2-layer shielding can be integrated to reduce CM noise. The proposed magnetic structure is applied to a 3kW 400V/12V LLC converter. This dissertation solves the challenges in analysis, digital control, magnetic design and EMI in high-frequency DC/DC converters in off-line power supplies. With the academic contribution in this dissertation, GaN devices can be successfully applied to high-frequency DC/DC converters with MHz switching frequency to achieve high efficiency, high power density, simplified but high-performance digital control and automatic manufacturing. The cost will be reduced and the performance will be improved significantly. / Ph. D. / With the fast development of information technology (IT) industry, the demand and market volume for off-line power supplies keeps increasing, especially those for desktop, flat-panel TV, telecommunication, computer server and datacenter. The total power consumption of today’s data centers is becoming noticeable. Moreover, with the increase in cloud computing and big data, energy use of data centers is expected to continue rapidly increasing in the near future. The efficiency of off-line power supplies is very critical for the whole human society in order to reduce the total electricity consumption. And the cost is also a key driving force for the development of novel technology in off-line power supplies due to the large market volume. An off-line power supply normally consists of electromagnetic interference (EMI) filter, power factor correction (PFC) circuit and isolated DC/DC converter. Isolated DC/DC converter occupies more than half of the volume in an off-line power supply and takes the most control responsibilities, so isolated DC/DC converter is the key aspect to improve the overall performance and reduce the total cost for off-line power supply. Among all the DC/DC converter topologies, the LLC resonant converters have been most widely used as the DC/DC converter due to its high efficiency and hold-up capability. But there are three major challenges in LLC converters. Firstly, the control characteristics are very complex due to the dynamics of the resonant tank. To achieve good control performance, very complex and expensive digital controller has to be employed. Secondly, the magnetic components are very bulky, and it is expensive to manufacture them. Thirdly, there is circulating energy in LLC converters due to the nature of resonance, which increases the total loss. To solve these challenges, this dissertation proposes to implement a special control method, state-trajectory control, with a low-cost microcontroller (MCU). All the control functions can be integrated into one simple, low-cost MCU to replace the previous complex and expensive controller. By pushing switching frequency up to MHz with next generation power devices, this dissertation proposes a novel magnetics structure that can be integrated into printed circuit board (PCB) windings to achieve low-cost and automatic manufacturing. Furthermore, this dissertation employs three-phase interleaved LLC converters topology to reduce the circulating energy, and proposed a novel magnetic structure to integrated three inductors and three transformers into one magnetic core with simple 4-layer PCB winding. All the proposed technologies have been verified on hardware prototypes, and significant improvements over industrial state-of-art designs have been demonstrated. To sum up, this dissertation solves the challenges in analysis, digital control, magnetic design and EMI in DC/DC converters for off-line power supplies. With the academic contribution in this dissertation, the cost can be reduced due to the simplified control and automatic manufactured magnetics, and the efficiency can be improved with proper utilization of next generation power devices. This dissertation will improve future DC/DC converter for IT industrial in the three most important aspects of efficiency, power density and cost.

The optimal estimation theory of the Wiener-Kalman filter is extended to cover the situation in which the number of memory elements in the estimator is restricted. A method, based on the simultaneous diagonalisation of two symmetric positive definite matrices, is given which allows the weighted least square estimation error to be minimised. A control system design method is developed utilising this estimator, and this allows the dynamic controller in the feedback path to have a low order. A 12-order once-through boiler model is constructed and the performance of controllers of various orders generated by the design method is investigated. Little cost penalty is found even for the one-order controller when compared with the optimal Kalman filter system. Whereas in the Kalman filter all information from past observations is stored, the given method results in an estimate of the state variables which is a weighted sum of the selected information held in the storage elements. For the once-through boiler these weighting coefficients are found to be smooth functions of position, their form illustrating the implicit model reduction properties of the design method. Minimal-order estimators of the Luenberger type also generate low order controllers and the relation between the two design methods is examined. It is concluded that the design method developed in this thesis gives better plant estimates than the Luenberger system and, more fundamentally, allows a lower order control system to be constructed. Finally some possible extensions of the theory are indicated. An immediate application is to multivariable control systems, while the existence of a plant state estimate even in control systems of very low order allows a certain adaptive structure to be considered for systems with time-varying parameters.

Les travaux de cette thèse portent sur l’analyse de stabilité et la synthèse de commandes robustes pour les systèmes linéaires à commutation en temps discret avec des incertitudes polytopiques et des incertitudes sur la loi de commutation. On considère des lois de commutations arbitraires et on montre que l’utilisation des fonctions de Lyapunov commutées dépendant de paramètres permet de déterminer des critères de stabilité et de stabilisation robuste moins conservatifs. Ensuite, des conditions de stabilité robuste pour les systèmes en temps discret avec une loi de commutation incertaine sont présentées en termes de temps minimum de séjour. Les résultats obtenus s’avèrent utiles dans le contexte de la commande numérique des systèmes continus en présence d’imprécisions sur les instants d’échantillonnage et d’application des commandes. Nous montrons comment une modélisation à base d’évènements permet de ramener le problème original à un problème spécifique aux systèmes à commutation avec des incertitudes polytopiques. Les résultats sont étendus au cas des systèmes à commutation continus commandés par des correcteurs numériques / This PhD thesis is dedicated to the study of robust stability analysis and control synthesis for discrete time uncertain switching systems under arbitrary switching. Polytopic uncertainties are considered. We show that Lyapunov functions that depend on the uncertain parameter and that take into account the structure of the system may be used in order to reduce the conservatism related to uncertainty problems. Next, we consider the case of discrete time switched systems that are stabilized by a switched state feedback for which the switching signal may be temporary uncertain. Dwell time conditions for stability analysis of such systems are given. These results are usefull in the context of continuous time are stabilized via a computer when uncertainties occur on the sampling and actuation events. We present a new event based discrete-time model and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system. The methodology is extended to the case of switched system

Digital control needs discrete time models, but conversion from continuous time, fed by a zero order hold, to discrete time introduces sampling zeros which are outside the unit circle, i.e. non-minimum phase (NMP) zeros, in the majority of the systems. Also, some systems are already NMP in continuous time. In both cases, the inverse problem to find the input required to maintain a desired output tracking, produces an unstable causal control action. The control action will grow exponentially every time step, and the error between time steps also grows exponentially. This prevents many control approaches from making use of inverse models. The problem statement for the existing stable inverse theorem is presented in this work, and it aims at finding a bounded nominal state-input trajectory by solving a two-point boundary value problem obtained by decomposing the internal dynamics of the system. This results in the causal part specified from the minus infinity time; and its non-causal part from the positive infinity time. By solving for the nominal bounded internal dynamics, the exact output tracking is achieved in the original finite time interval. The new stable inverses concepts presented and developed here address this instability problem in a different way based on the modified versions of problem states, and in a way that is more practical for implementation. The statements of how the different inverse problems are posed is presented, as well as the calculation and implementation. In order to produce zero tracking error at the addressed time steps, two modified statements are given as the initial delete and the skip step. The development presented here involves: (1) The detection of the signature of instability in both the nonhomogeneous difference equation and matrix form for finite time problems. (2) Create a new factorization of the system separating maximum part from minimum part in matrix form as analogous to transfer function format, and more generally, modeling the behavior of finite time zeros and poles. (3) Produce bounded stable inverse solutions evolving from the minimum Euclidean norm satisfying different optimization objective functions, to the solution having no projection on transient solutions terms excited by initial conditions. Iterative Learning Control (ILC) iterates with a real world control system repeatedly performing the same task. It adjusts the control action based on error history from the previous iteration, aiming to converge to zero tracking error. ILC has been widely used in various applications due to its high precision in trajectory tracking, e.g. semiconductor manufacturing sensors that repeatedly perform scanning maneuvers. Designing effective feedback controllers for non-minimum phase (NMP) systems can be challenging. Applying Iterative Learning Control (ILC) to NMP systems is particularly problematic. Incorporating the initial delete stable inverse thinkg into ILC, the control action obtained in the limit as the iterations tend to infinity, is a function of the tracking error produced by the command in the initial run. It is shown here that this dependence is very small, so that one can reasonably use any initial run. By picking an initial input that goes to zero approaching the final time step, the influence becomes particularly small. And by simply commanding zero in the first run, the resulting converged control minimizes the Euclidean norm of the underdetermined control history. Three main classes of ILC laws are examined, and it is shown that all ILC laws converge to the identical control history, as the converged result is not a function of the ILC law. All of these conclusions apply to ILC that aims to track a given finite time trajectory, and also apply to ILC that in addition aims to cancel the effect of a disturbance that repeats each run. Having these stable inverses opens up opportunities for many control design approaches. (1) ILC was the original motivation of the new stable inverses. Besides the scenario using the initial delete above, consider ILC to perform local learning in a trajectory, by using a quadratic cost control in general, but phasing into the skip step stable inverse for some portion of the trajectory that needs high precision tracking. (2) One step ahead control uses a model to compute the control action at the current time step to produce the output desired at the next time step. Before it can be useful, it must be phased in to honor actuator saturation limits, and being a true inverse it requires that the system have a stable inverse. One could generalize this to p-step ahead control, updating the control action every p steps instead of every one step. It determines how small p can be to give a stable implementation using skip step, and it can be quite small. So it only requires knowledge of future desired control for a few steps. (3) Note that the statement in (2) can be reformulated as Linear Model Predictive Control that updates every p steps instead of every step. This offers the ability to converge to zero tracking error at every time step of the skip step inverse, instead of the usual aim to converge to a quadratic cost solution. (4) Indirect discrete time adaptive control combines one step ahead control with the projection algorithm to perform real time identification updates. It has limited applications, because it requires a stable inverse.

Abstract not available

The main goal of this thesis is to develop an active thermal management control scheme for multi-phase current mode buck converters in order to improve the long term reliability of the converters. A thermal management unit (TMU) with independent linear compensators for the thermal loops is incorporated into the existing digital controller to regulate the current through each phase so that equal temperature distribution is achieved across all phases. A lumped parameter thermal model of the multi-phase converter is built as the basis of the TMU. MATLAB simulation results are used to verify the TMU concept. Experimental results from a digitally controlled 12 V to 1 V, 50 A, 250 kHz four-phase peak current mode buck converter demonstrate the effectiveness of the proposed thermal management technique in the presence of uneven air flow. The steady-state performance, dynamic transient load performance, effect of gate drive voltage and efficiency measurements are investigated and discussed.

The main goal of this thesis is to develop an active thermal management control scheme for multi-phase current mode buck converters in order to improve the long term reliability of the converters. A thermal management unit (TMU) with independent linear compensators for the thermal loops is incorporated into the existing digital controller to regulate the current through each phase so that equal temperature distribution is achieved across all phases. A lumped parameter thermal model of the multi-phase converter is built as the basis of the TMU. MATLAB simulation results are used to verify the TMU concept. Experimental results from a digitally controlled 12 V to 1 V, 50 A, 250 kHz four-phase peak current mode buck converter demonstrate the effectiveness of the proposed thermal management technique in the presence of uneven air flow. The steady-state performance, dynamic transient load performance, effect of gate drive voltage and efficiency measurements are investigated and discussed.

Distributed generation that utilizes 5-10kW Solid Oxide Fuel Cells requires power electronics to optimize the overall system efficiency while reducing the cost. The Adaptive Energy Zero-Voltage-Switching Phase-Shift-Modulated Full-Bridge (AE-ZVS-PSM-FB) topology meets these criteria under all loading conditions, but suffers from complexity associated with an analog control implementation. This thesis presents a novel Look-Up-Table (LUT) based digital controller required for such converter. The applied design approach also reduces the design time and controller requirements, which in turn decreases the overall system cost. Steady-state analysis for the AE-ZVS-PSM-FB converter is performed using a piece-wise equivalent circuit model. This analysis is used to verify the LUT concept that forms the basis for the proposed LUT-based digital controller. The proposed LUT-based digital control algorithm is developed and verified using Field Programmable Gate Array (FPGA) Logic platform. Design procedures and operational function under steady state and step change conditions are presented. Simulation results demonstrate the LUT concept in the AE-ZVS-PSM-FB converter, and the simplicity of the proposed LUT-based digital controller in producing the expected switching sequence. Simulation results were also produced showing successful dynamic response of LUT-based digital controller interconnected with the converter under different operating conditions. A Xilinx FPGA demonstration board was used to generate experimental switching sequence results to demonstrate the simplicity of the proposed controller. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2007-09-25 10:26:39.909