Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters

A general critical condition of subharmonic oscillation in terms of the loop gain is derived. Many closed-form critical conditions for various control schemes in terms of converter parameters are also derived. Some previously known critical conditions become special cases in the generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme. Different control schemes share similar forms of critical conditions. For example, both V2 control and voltage mode control have the same form of critical condition. A peculiar phenomenon in average current mode control where subharmonic oscillation occurs in a window value of pole can be explained by the derived critical condition. A ripple amplitude index to predict subharmonic oscillation proposed in the past research has limited application and is shown invalid for a converter with a large pole.Comment: Submitted to an IEEE Journal on Dec. 23, 2011, and resubmitted to IEEE Transactions on Circuits and Systems-I on Feb. 14, 2012. My current six papers in arXiv have a common reviewe

Sliding mode control of reaction flywheel-based brushless DC motor with buck converter

AbstractReaction flywheel is a significant actuator for satellites’ attitude control. To improve output torque and rotational speed accuracy for reaction flywheel, this paper reviews the modeling and control approaches of DC–DC converters and presents an application of the variable structure system theory with associated sliding regimes. Firstly, the topology of reaction flywheel is constructed. The small signal linearization process for a buck converter is illustrated. Then, based on the state averaging models and reaching qualification expressed by the Lee derivative, the general results of the sliding mode control (SMC) are analyzed. The analytical equivalent control laws for reaction flywheel are deduced detailedly by selecting various sliding surfaces at electromotion, energy consumption braking, reverse connection braking stages. Finally, numerical and experimental examples are presented for illustrative purposes. The results demonstrate that favorable agreement is established between the simulations and experiments. The proposed control strategy achieves preferable rotational speed regulation, strong rejection of modest disturbances, and high-precision output torque and rotational speed tracking abilities

Nonlinear Analysis and Control of Interleaved Boost Converter Using Real-Time Cycle to Cycle Variable Slope Compensation

Switched-mode power converters are inherently nonlinear and piecewise smooth systems that may exhibit a series of undesirable operations that can greatly reduce the converter's efficiency and lifetime. This paper presents a nonlinear analysis technique to investigate the influence of system parameters on the stability of interleaved boost converters. In this approach, Monodromy matrix that contains all the comprehensive information of converter parameters and control loop can be employed to fully reveal and understand the inherent nonlinear dynamics of interleaved boost converters, including the interaction effect of switching operation. Thereby not only the boundary conditions but also the relationship between stability margin and the parameters given can be intuitively studied by the eigenvalues of this matrix. Furthermore, by employing the knowledge gained from this analysis, a real-Time cycle to cycle variable slope compensation method is proposed to guarantee a satisfactory performance of the converter with an extended range of stable operation. Outcomes show that systems can regain stability by applying the proposed method within a few time periods of switching cycles. The numerical and analytical results validate the theoretical analysis, and experimental results verify the effectiveness of the proposed approach

Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC-DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Nine examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.Comment: Submitted to an IEEE journal in 201

Study on Nonlinear Phenomena in Buck-Boost Converter with Switched-Inductor Structure

The switched-inductor structure can be inserted into a traditional Buck-Boost converter to get a high voltage conversion ratio. Nonlinear phenomena may occur in this new converter, which might well lead the system to be unstable. In this paper, a discrete iterated mapping model is established when the new Buck-Boost converter is working at continuous conduction current-controlled mode. On the basis of the discrete model, the bifurcation diagrams and Poincare sections are drawn and then used to analyze the effects of the circuit parameters on the performances. It can be seen clearly that various kinds of nonlinear phenomena are easy to occur in this new converter, including period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. Value range of the circuit parameters that may cause bifurcations and chaos are also discussed. Finally, the time-domain waveforms, phase portraits, and power spectrum are obtained by using Matlab/Simulink, which validates the theoretical analysis results

A design-oriented combined approach for bifurcation prediction in switched-mode power converters

In this brief, two different approaches are combined for studying the stability of a buck switching power dc-dc converter and for predicting its bifurcations. Instability indexes derived from both approaches are combined to get a complete design-oriented perspective of bifurcation analysis in terms of practical circuit parameter and to show the effect of each parameter on the system behavior. The first approach is based on the conventional Routh-Hurwitz criterion applied to the averaged converter dynamics, and it is suitable for detecting low-frequency oscillations but is unsuitable for predicting fast-scale period-doubling instabilities. Complementarily, the second approach considers the ripple component before the pulsewidth modulator to quantitatively predict the occurrence of subharmonic oscillations. The usefulness of the combined approach is shown by analytically deriving inequalities that compress the complete design space into simple instability indexes, which, used complementarily, allow a division of the design space into the different instability regions (both period-doubling or fast-scale instability, and Hopf or slow-scale instability). Comparison of the design-oriented complete map obtained combining both methods and their related stability indexes with the results obtained both from time-domain numerical simulations of the exact switched state equations, as well as the stability border obtained from discrete recurrent maps, corroborates the approach.Peer Reviewe

Modeling, Control and Characterization of Aircraft Electric Power Systems

A study model of advanced aircraft electric power system (AAEPS) corresponding to B767 Aircraft is developed in the PSIM9 software environment. The performance characteristics of the system under consideration for large sharing of non-linear loads are studied. A comprehensive mathematical model describing system dynamics is derived where the GSSA technique is applied for reduced-order system approximation. The transient and steady-state performance of the hybrid PEM-FC/battery APU integrated to the aircraft electric network is analyzed while different loading scenarios are taken into account. In addition, dynamic bifurcation analysis is employed to characterize the systems stability performance under multi-parameters condition. Also, the power quality of the system is assessed under various loading configurations, and the effect of installing active/passive power filters (APF/PPF) on power quality of the system is investigated for a wide range of operating frequencies

Stability analysis and control of DC-DC converters using nonlinear methodologies

PhD ThesisSwitched mode DC-DC converters exhibit a variety of complex behaviours in power electronics systems, such as sudden changes in operating region, bifurcation and chaotic operation. These unexpected random-like behaviours lead the converter to function outside of the normal periodic operation, increasing the potential to generate electromagnetic interference degrading conversion efficiency and in the worst-case scenario a loss of control leading to catastrophic failure. The rapidly growing market for switched mode power DC-DC converters demands more functionality at lower cost. In order to achieve this, DC-DC converters must operate reliably at all load conditions including boundary conditions. Over the last decade researchers have focused on these boundary conditions as well as nonlinear phenomena in power switching converters, leading to different theoretical and analytical approaches. However, the most interesting results are based on abstract mathematical forms, which cannot be directly applied to the design of practical systems for industrial applications. In this thesis, an analytic methodology for DC-DC converters is used to fully determine the inherent nonlinear dynamics. System stability can be indicated by the derived Monodromy matrix which includes comprehensive information concerning converter parameters and the control loop. This methodology can be applied in further stability analysis, such as of the influence of parasitic parameters or the effect of constant power load, and can furthermore be extended to interleaved operating converters to study the interaction effect of switching operations. From this analysis, advanced control algorithms are also developed to guarantee the satisfactory performance of the converter, avoiding nonlinear behaviours such as fast- and slowscale bifurcations. The numerical and analytical results validate the theoretical analysis, and experimental results with an interleaved boost converter verify the effectiveness of the proposed approach.Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), and school of Electrical and Electronic Engineerin

Analysis and control of nonlinear phenomena in electrical drives

PhD ThesisElectrical motors are key to the growth of any modern society. In order to ensure optimal utilisation of the motors, the shaft speed and armature current must be controlled. Currently, the most efficient way of achieving both speed and current control in electrical motors is through power electronic switching, thus making the system both nonlinear and time varying. The combination of electric motors and control electronics is referred to as electric drives. Due to the inherent nonlinear nature of electrical drives, the system is prone to complex dynamical phenomena including bifurcations, chaos, co-existing attractors and fractal basin boundaries. The types of nonlinear phenomena that occur in some of the more common electrical drive systems, namely permanent magnet dc (PMDC) drives, series connected dc (SCDC) drives and switched reluctance motor (SRM) drives, are considered for analysis in this project. The nominal steady state behaviour of these drives is a periodic orbit with a mean value close to the reference value. But as some system parameters are being varied, the nominal orbit of the system referred to as the period-1 orbit, may lose its stability leading to the birth of new attracting orbit that is periodic, quasi-periodic or chaotic in nature. The most common technique for performing stability analysis of a periodic orbit is the Poincaré map approach, which has been successfully applied in DC-DC converters. This method involves reducing the continuous time dynamical system into a discrete time nonlinear iterative map and the periodic orbit into a fixed point. The stability of the periodic orbit then depends on the eigenvalue of the Jacobian matrix of the map evaluated at the fixed point. However, for some power electronic based system the nonlinear map cannot be derived in closed form due to the transcendental nature of the equation involved. In this project, the recently introduced Monodromy matrix approach is employed for the stability analysis of the periodic orbit in electrical drives. This method is based on Filippov’s method of differential inclusion and has been successfully applied in the stability analysis of periodic orbits in both low order and higher order DC-DC converters. This represents the first application of the technique in electrical drives. The Monodromy matrix approach involves computing the State Transition Matrix (STM) of the system around the nominal orbit including the STM at the switching manifold (sometimes referred to as the Saltation matrix). Also, by manipulating some of the parameters in the Saltation matrix, it is possible to control the instabilities and thus extend the system parameter range for nominal period-1 operation. The experimental validation of the nonlinear phenomena in a proportional integral (PI) controlled PMDC drive, which is absent in literature, is presented in this thesis. The system was implemented using dsPIC30F3010 which is a low cost and high performance digital signal controller.Petroleum Technology Development Fund (PTDF) of Nigeri