State-plane analysis techniques are employed to study the voltage stepup energy-storage dc-to-dc converter. Within this framework, an example converter operating under the influence of a constant on-time and a constant frequency controller is examined. Qualitative insight gained through this approach is used to develop a conceptual free-running control law for the voltage stepup converter which can achieve steady-state operation in one on/off cycle of control. Digital computer simulation data are presented to illustrate and verify the theoretical discussions presented.As the field of power electronics has evolved and matured, increasingly more attention has been given to analyzing, simulating, and understanding the principles of operation of the highly nonlinear power-processing subnetworks which often are the building blocks of modern power electronics equipment. In recent years, considerable success has been realized in this endeavor. There now are available a variety of mathematical analyses and computer simulation techniques which enable detailed quantitative examinations of particular power inverter and converter configurations [1]- [12] . In addition to applying such quantitative techniques and approaches, it often is useful to examine complex nonlinear networks in a qualitative manner for the purpose of enhancing a conceptual visualization of the system nonlinearities. It is the nonlinearities which usually are the principal cause of difficulty in analyzing and understanding the system behavior, but, at the same time, they are usually the keystone for successful circuit operation. One such qualitative approach to the study of nonlinear networks and systems which enables a useful visualization of overall system behavior is the phase-plane or, more generally, the statespace approach [13]. This paper presents a study of the voltage stepup dc-to-dc energy-storage converter, a highly nonlinear power electronics network, which employs such a state-space approach as a means for revealing considerable qualitative insight into the fundamental behavior of this converter in both steady-state and transient operation. As a demonstration of how this theoretical insight can be used, a new conceptual converter control law is developed which can, in theory, achieve steady-state operation within one "on/off' switching cycle, regardless of the system's initial state or operating conditions. After introducing the particular dc-to-dc converter configuration which is used throughout the paper to illustrate this approach, a general discussion of converter behavior as it can be characterized in the state plane is presented. Particular attention is given to observing how the system behavior changes when subjected to changes in system parameters or externally imposed operating conditions. This technique is then employed to portray the transient step-load-change response of an example converter functioning under the influence of two commonly used controller configurations; specifically, a constant on-time controller and a constant f...

Mathematical representations of a state-plane switching boundary employed in a state-trajectory con trol law for dc-to-dc converters are derived. Several levels of approximation to the switching boundary equations are presented, together with an evaluation of the effects of nonideal operating characteristics of converter power stage components on the shape and location of the boundary and the behavior of a system controlled by it.Digital computer simulations of dc-to-dc converters operating in conjunction with each of these levels of control are presented and evaluated with respect to changes in transient and steady-state performance. 70-PESC 77 RECORDVOLTAGE STEP-UP CURRENT STEP-UP CURRENT-OR-VOLTAGE STEP-UP J: 1 0 ι rc " V* ι·» VA Λ / Λ / !_Λ-Λ Λ / χ--Fig, 1. Graphical summary of the conceptual development of a state-trajectory control law for dc-to-dc converters. Scale factors for the time waveforms 1n (F) are, in normalized units per major division: ιχ-Ν» 1.0/div, VQ-N and VQ-N» 0.005/div for the voltage step-up and current-or-voltage step-up converters; VQ-N and V 0-N> 0.002/div for the current step-up converter.PESC 77 RECORD-71

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