Analytic derivation and evaluation of a state-trajectory control law for DC-to-DC converters

Abstract

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

Closed-loop design and time-optimal control for a series-capacitor buck converter

“…To realize the required switching sequence, the first task is to map the behavior of the state-variables with respect to the new loading conditions [19]- [20], then the required switching sequence can be derived from the possible trajectories of the state-variable. The state equations for state-1 can be expressed as: …”

Near time-optimal transient response in DC-DC buck converters taking into account the inductor current limit

“…4, in order to better illustrate the physical meaning of (6). In particular, a goal is to verify that the load steps that can be handled with N = 2 switching actions are all and only those that satisfy (6). To this purpose, and referring to Fig.…”

“…which is equivalent to (6) for N min = 2. Equation (11) identifies all and only the transients which can be handled through a two-switch action like the one shown in Fig.…”

“…An application example, shown in Fig. 1, is represented by Point-of-Load (PoL) DC-DC converters, where various non-linear time-optimal control (TOC) methods have been introduced in order to significantly improve step-load transient responses [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In its simplest form, the TOC responds to a step load change with a single, properly timed on/off or off/on switching action, after which the output voltage deviation is fully recovered.…”

“…In its simplest form, the TOC responds to a step load change with a single, properly timed on/off or off/on switching action, after which the output voltage deviation is fully recovered. Recent works in this field make use of the switching surface approach [5][6][7][8][9][10][11][12][13][14][15] in order to determine the optimal switching sequence, while continuous-time digital signal processing has been successfully exploited in [1] in order to implement a charge balance-based TOC algorithm.…”