Large-signal Stability Research Articles

Hybrid One-Cycle Controller for Boost PFC Rectifier

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Discontinuous conduction mode and continuous conduction mode in the boost power factor controller rectifier design for constant-frequency operation are usually focused on separately and consider distinct controllers and respective tradeoffs. This paper proposes a <emphasis emphasistype="italic">hybrid one-cycle controller</emphasis> that presents a smooth mode transition inside one mains half-cycle. One-cycle control technique presents advantages such as operation with unity power factor (PF), large-signal stability, noise immunity, low cost, and simplicity. The proposed strategy allows operation in a large power range. </para>

Parametric oscillations in distributed power amplifiers

Parametric oscillations in high-efficiency distributed power amplifiers are analysed. Large-signal stability verification based on pole-zero identification is proposed in order to understand the origin of the instability and to choose the optimal value and place of the stabilisation resistor that ensures circuit stability while minimising degradation of circuit performance. The work is illustrated through the stabilisation of a three-stage high-efficiency LDMOS distributed power amplifier.

Large-signal stability analysis of solar array power system

A large-signal stability analysis of the solar array regulator system is performed to facilitate the design and analysis of a low-earth-orbit (LEO) satellite power system. The effective load characteristics of various control methods in the solar array regulator system, such as the constant power load, variable power load, constant voltage load, constant current load, and constant resistive load, are classified to analyze the large-signal stability. Then, using the state plane analysis technique, the large-signal behavior of the solar array system is portrayed and the stability of various equilibrium points is analyzed. Thus, this approach can be contributed to organize the optimal controller structure of the system by representing the relationship between the control method of the solar array regulator and the large-signal stability. For the verification of the proposed large-signal analysis, a solar array regulator system that consists of two 100 W parallel module buck converters has been built and tested using a real 200 W solar array.

A New Digital Control Algorithm to Achieve Optimal Dynamic Performance in DC-to-DC Converters

In this paper, a new control algorithm is proposed to achieve optimal dynamic performance for dc-to-dc converters under a load current change and for a given set of circuit parameters, such as the output inductor, output capacitor, switching frequency, input voltage, and output voltage. Using the concept of capacitor charge balance, the proposed algorithm predicts the optimal transient response for a dc-to-dc converter during a large signal load current change. During steady state operation, conventional current mode proportional-integral-derivative (PID) is used. During large signal transient conditions, the new control algorithm takes over. The equations needed to calculate the transient time and the required duty cycle series are presented. By using the proposed algorithm, the optimal transient performances, including the smallest output voltage overshoot/undershoot and the shortest recovery time, is achieved. In addition, since the large signal dynamic response of the power converter is successfully predicted, the large signal stability is guaranteed. Experimental results show that the proposed method produces superior dynamic performance over a conventional current mode PID controller.

Analysis and elimination of hysteresis and noisy precursors in power amplifiers

Power amplifiers (PAs) often exhibit instabilities leading to frequency division by two or oscillations at incommensurate frequencies. This undesired behavior can be detected through a large-signal stability analysis of the solution. However, other commonly observed phenomena are still difficult to predict and eliminate. In this paper, the anomalous behavior observed in a Class-E PA is analyzed in detail. It involves hysteresis in the power-transfer curve, oscillation, and noisy precursors. The precursors are pronounced bumps in the power spectrum due to noise amplification under a small stability margin. The correction of the amplifier performance has required the development of a new technique for the elimination of the hysteresis. Instead of a trial-and-error procedure, this technique, of general application to circuit design, makes use of bifurcation concepts to suppress the hysteresis phenomenon through a single simulation on harmonic-balance software. Another objective has been the investigation of the circuit characteristics that make the noisy precursors observable in practical circuits and a technique has been derived for their elimination from the amplifier output spectrum. All the different techniques have been experimentally validated.

Passivity-based integral control of a boost converter for large-signal stability

This paper presents a new integral control law for a boost converter that ensures the stability of large-signal operation. The integral controller is derived in two steps by means of passivity-based control theory. First, a static law, which ensures global stability, is obtained. Secondly, a combination of the storage function of this static law and a new positive semidefinite storage function results in a new integral control law. The proposed regulator satisfies the usual transient specifications and behaves robustly for parameter uncertainty. Global stability is guaranteed even if the duty cycle saturation is taken into account. Simulation and experimental results verify the theoretical predictions.

Global stability analysis and stabilization of a class-E/F amplifier with a distributed active transformer

Power amplifiers (PAs) often exhibit instabilities giving rise to frequency divisions or spurious oscillations. The prediction of these instabilities requires a large-signal stability analysis of the circuit. In this paper, oscillations, hysteresis, and chaotic solutions, experimentally encountered in a high-efficiency class-E/F/sub odd/ PA with four transistors combined using a distributed active transformer, are studied through the use of stability and bifurcation analysis tools. The tools have enabled an in-depth comprehension of the different phenomena, which have been observed in simulation with good agreement with experimental results. The study of the mechanism generating the instability has led to a simplified equivalent circuit from which the optimum stabilization network has been determined. The network enables a global stabilization of the circuit for all the expected operating values of the amplifier bias voltage and input power. This has been achieved with negligible degradation of the amplifier performance in terms of drain efficiency and output power. The stable behavior obtained in simulation has been experimentally confirmed.

Sliding Mode Control of PFC Converter

The controllers in Power Factor Corrected (PFC) converters are conventionally designed in frequency or time domain using linearized model of the converter system. These controllers are not always adequate for PFC converters due to presence of hard nonlinearity in the system. Theoretically, linear feedback designs can only ensure stability and satisfactory operation under restrictive operating conditions for which the linearized model is valid. However, as the application base of PFC converters increases, the need for more robust control schemes becomes imperative. To this end, the sliding mode approach, described in this work, inherently addresses hard nonlinearity present in the PFC converters. The controller design and simulations results are presented and discussed in detail. As expected, the results show that sliding mode controller improves converter dynamics and large-signal stability without compromising on the intrinsic simplicity of the conventional control scheme. The sliding mode controller is found to be more robust and appropriate control scheme for PFC converters as compared to conventional linear controllers.

Transient stability assessment of systems comprising phase-shifting FACTS devices by direct methods

In this paper the concept of a control Lyapunov function is used to develop control strategies for thyristor-controlled phase-shifting transformers (TCPSTs). Two typical representatives of TCPSTs were chosen for consideration: a Quadrature Boosting Transformer (QBT) and a Phase Angle Regulator (PAR). For the case of the QBT we showed that the proposed control law can significantly improve the large signal stability in comparison to the control-law-based on the traditionally used injection model proposed in various references. Even if the system parameters are estimated very roughly, our proposed strategy gives better results than the ‘traditional’ strategy. Also, some novel energy functions, which consider the action of an optimally controlled TCPST in a single-machine infinite-bus (SMIB) system, are presented and validated by a numerical example.

Large-signal stability-oriented design of boost regulators based on a Lyapunov criterion with nonlinear integral

Exact nonlinear differential equations of boost pulsewidth modulation converters (either with hard-switching or soft-switching, in continuous and discontinuous conduction mode) are obtained, without using average approximations. An extended system of equations also contains the differential equation of the integrated error between the reference and the output voltage. A positive-definite Lyapunov function is defined, including in its expression a nonlinear integral of type Lurie. Sufficient conditions for the Lyapunov stability of the system are determined. Consequently, constraints on the feedback circuit parameters that assure the large-signal stability of the system are formulated. These constraints relate the parameters of the feedback circuit with the values of the power stage elements, load, switching frequency, steady-state duty-cycle. For different values of the steady-state duty-cycle, graphical boundaries which assure the large-signal stability for all the variation of the load are designed. Simulations and experiments confirm the stability of the design.

Linear State-Feedback Control of a Buck-Boost Converter Using Passivity Technique

This work presents the use of the passivity technique applied on a circuitorientedmodel of a switching buck-boost regulator including state-feedback. The procedure, which provides large-signal stability, is implemented for a control law that is a linear combination of the state variables of a buck-boost dc-dc converter. The converter's large-signal equivalent circuit is derived from the its bilinear description. The condition for stability is obtained by studying the condition for passivity of the resulting two-port. Considering stability, the saturation of the control signal is also taken into account. Once the large-signal stability has been guaranteed, the linear model of the converter and the root locus method are used to achieve proper values of the loop gain in order the desired transient response to be obtained. Simulations are in good agreement with analytical results

Linear state-feedback control of a boost converter for large-signal stability

The problem of stabilizing a boost regulator in large-signal situations using linear control laws is derived by means of a circuit-oriented procedure. After establishing a large-signal circuit model for the boost regulator including state-feedback, conditions for passivity in the resulting two-port are studied. As a consequence, a linear control law is derived, thus ensuring regulator global stability even if the control saturation is taken into account. Subsequently, a linear analysis is performed, in order to design the desired dynamics and robust behavior of the switching regulator. The nonlinear analysis shows that only one feedback gain is necessary, provided that the coordinates of the equilibrium point are known. The use of regulator root locus allows one to choose the proper value of this gain. Simulations and experimental results verify the analytical predictions.

A Subthreshold CMOS Continuous-Time Bandpass Filter with Large-Signal Stability

Continuous-time filters implemented in subthreshold CMOS have limited operating range. When processing real acoustic stimuli, input signals exceeding this range will occasionally be encountered. We compare the response of an RLC proto-type bandpass filter based on three transconductors to that of one based on four transconductors. It is found that, in response to large slowly varying input signals, the three-transconductor design tends toward oscillation whereas the four-transconductor design is stable. Simulation and chip measurements of a four-transconductor bandpass filter implemented in a 2-μm process verify these claims. The filter measures 117×416 μm^2, operates on ±1.25 V supplies, and consumes less than 20 nW when tuned to 1 kHz.

Design and analysis of a regulated peak-power tracking system

A regulated peak-power tracking (RPPT) system for space power application is proposed. Large-signal stability analysis is provided to understand the main four different modes of operations of the system, as well as the mode transitions. A simple and effective control scheme for the system is also proposed. Small-signal analysis is performed thereafter to provide design optimization, and the predictions are verified by computer simulations.

A new methodology for the stability analysis of large-scale power electronics systems

A new methodology is proposed to investigate the large-signal stability of interconnected power electronics systems. The approach consists of decoupling the system into a source subsystem and a load subsystem, and stability of the entire system can be analyzed based on investigating the feedback loop formed by the interconnected source/load system. The proposed methodology requires two stages: 1) since the source and the load are unknown nonlinear subsystems, system identification, which consists of isolating each subsystem into a series combination of a linear part and a nonlinear part, must be performed; and 2) stability analysis of the interconnected system is conducted thereafter based on a developed stability criterion suitable for the nonlinear interconnected source-load model. Applicability of the methodology is verified through the stability analysis of a typical power electronics system.

Design of feedback gain vector of two-state basic PWM multifeedback regulators for large-signal stability

A method for determining boundaries on the feedback gains in a switching regulator with multiple feedback, in order to ensure stability for large changes in the load values, is developed. Using an original approach for time-domain analysis, a large-signal, nonlinear, discrete-time model of the closed-loop converter is obtained; the model's equations are expressed in disturbances of the state variables due to disturbance in the load. The first step toward a global stability design is to find the constraint that ensures local stability around the operating point: the nonlinear terms (products of disturbances) are neglected in the model, the z-transform is applied to the linearized equations, and the condition that the eigenvalues are situated inside the unit circle is imposed. The nonlinear model, including the nonlinearity of the pulsewidth modulation (PWM), due to possible saturation, is then considered. A new constraint in terms of feedback gains is found in order to ensure that one and only one real equilibrium point (i.e., the quiescent operating point) exists. Putting together the constraints, boundaries on the feedback gains are found. The method is developed for converters containing two reactive elements, operating in continuous conduction mode. An example of a boost converter with inductor current and output voltage feedback is presented in detail. The large-signal stability of the design is checked by using the state-plane portrait and time-domain simulation.

Large-signal stability and spectrum characterization of a medium power HBT using active load-pull techniques

Large-signal stability and spectrum characterizations of a half-watt HBT at 2 GHz for a class AB bias point are reported. Constant power, constant power-added efficiency, constant current gain contours, and second and third harmonic generation level contours over the whole Smith chart are presented. The characterization setup is an automated high power, multi-harmonic, active load-pull system that is based on six-port techniques and frequency discrimination using a controlled band pass YIG filter. >

Large signal analysis of switching regulators employing adaptive gain current injected control

The large signal stability and transient response of a buck-boost programmable switching regulator employing adaptive gain current injected control (CIC) are investigated. The stability of the regulator is analysed studying the equilibrium points of the system. The type of the equilibrium points is determined by the linearized about the equilibrium point state space averaged model of the regulator. The linearized model is used also for proper initial selection of the feedback coefficients. The transient responses of the buck-boost programmable switching regulator employing normal and adaptive gain current injected controls are compared. It is found that the adaptive gain CIC improves the dynamics of the regulator working at different operating conditions. The simulation runs are verified experimentally. >

Large-signal stability analysis of spacecraft power processing systems

The authors present a comprehensive large-signal stability analysis of a solar-array power system. The stability of the equilibrium points of a system with a typical nonlinear load characteristic is analyzed. Employing state-plane analysis techniques, the dynamic behavior of the system from an arbitrary initial condition is characterized, and the region of the desired stable operation is identified. The stability and transient response of the system operation near the solar array's maximum power point are evaluated. The dynamic response of the spacecraft power system operating in the shunt mode and battery-discharge mode is analyzed. >

Unified large-signal stability and noise theory for synchronised oscillators

A unified model is developed which is capable of analysing large-signal performance, stability, and noise of synchronised oscillators under rather general conditions. The passive circuitry is arbitrary; the active subnetwork may in principle contain one-port or two-port devices with or without harmonic content. However, only one-port devices operating at a single frequency are treated explicitly. The active device is modelled by its describing function (i.e. its effective admittance) with respect to both carrier and noise signals. The noise analysis directly leads to a new stability criterion, which clearly shows the restrictions and even failure of the hitherto-used criteria. These results are proved by measurements. Finally, the application of the nonlinear theory to the analysis of multiple-device oscillators is illustrated by results.