Investigation Of V~2 Control Technique For Switching DC-DC Converters And Its Nonlinear Dynamics

As the electronic technology flourishes, the functions of various new electronic products are more and more perfect, and the requirement of better transient response and stability for power supply is increasingly demanded. Much attention has been paid on the V2 control of switching-mode power supply due to its fast load transient response. Previous research literatures on the V2 controlled switching converters are mainly focused on control principle, small-signal modeling, analysis of transient characterisitic and optimization of control method, and so on. Switching concerter is a kind of piecewise smooth and nonlinear time-varying systems which has specific nonlinear dynamic phenomena such as low-frequency fluctuation, subharmonic oscillation, period doubling bifurcation, border collision bifurcation and chaos. By using the theory of dynamics, the intrinsic nonlinear dynamics phenomena and its mechanism of V2 controlled switching converter are analyzed and revealed, which has a theoretical and practical significance for the parameter design of V2 controlled switching converter.The first-order equivalent discret map models of both peak V2 controlled and valley V2 controlled buck converters are established in this dissertation. Based on which, nonlinear characteristics and stabilities of peak and valley V2 controlled buck converters are performed by bifurcation diagram, Lyapunov exponent and state parameter space. The influences of ramp compensation on their dynamic behaviors and stabilities are also involved. In the view of the dynamics, the stable operation parameter ranges of the peak and valley V2 controlled buck converter are analyzed. For the stable operation, the duty cycle of peak V2 controlled buck converter must be below 0.5, while above 0.5 is needed for valley V2 controlled buck converter. Using ramp compensation technique, the stable operation area of V2 controlled buck converter can be extended, and its operation mode can be shifted from discontinuous conduction mode (DCM) to continuous conduction mode (CCM).The second-order accurate discrete map models of peak and valley V2 controlled buck converters are also established. Output voltage border, Jacobian matrix and eigenvalues are derived. Using the second-order accurate model, bifurcation diagram, eigenvalue trajectory, the maximum Lyapunov exponent, and Poincare map are adopted to analyze and compare the nonlinear dynamics and stabilities of peak and valley V2 controlled buck converters. The results indicate that the bifurcation characteristics of peak and valley V2 controlled buck converter in CCM are reverse when input voltage, reference voltage, and the proportional coefficient of error amplifier vary, where period-1 state of the converter enters into period-2 state after doubling bifurcation, and enters the CCM chaotic state after border collision bifurcation. The results also show that the same bifurcation characteristics exists in peak and valley V2 controlled buck converter in CCM when output capacitor and its equivalent series resistor (ESR) vary, where period-1 state of the converter enters into period-8 state after three times doubling bifurcation, and enters the CCM chaotic state after border collision bifurcation.Combinating the operation mode and output voltage ripple characteristics of boost converter, the V2 control method is firstly applied to boost converter in this dissertation. A detailed operation principle of valley V2 controlled boost converter is analyzed and the corresponding small-signal model is established. The control to output, input to inductor current, control to inductor current, input tooutput, and output impedance transfer functions are derived. Base on which, the analysis of frequency-domain characteristics and the comparison with valley current controlled boost converter are performed. The studies show that valley V2 controlled boost converter has faster input and load transient response speed than the valley current controlled boost converter.According to the derived boder voltage, the first-order equivalent discrete map model and the second-order accurate discrete map model of valley V2 controlled boost converter are established, and the corresponding Jacobian matrix and eigenvalues are also derived. Based on which, the nonlinear dynamic behaviors of valley V2 controlled boost converter are revealed. Taking the first-order equivalent model for example, the effect of ramp compensation on dynamic characteristics of valley V2 controlled boost converter is discussed. Using the first-order equivalent model, the research results show that valley V2 controlled boost converter and valley V2 controlled buck converter have the same stablity, the stable operation area of V2 controlled boost converter can also be extended by ramp compensation. Using the second-order accurate model, the research results show that the same bifurcation characteristicswith the variations of input valtage, output capacitor ant its ESR exists in between valley V2 controlled boost converter and valley V2 controlled buck converter. These results provide useful theoretical guidance for the circuit parameter design of valley V2 controlled boost converter.The corresponding time-domain simulation model and experimental platforms are built in this dissertation. Simulation and experimental results are given to verify theoretical analyses.