Robust constrained stabilization of a boost DC-DC converter with Lyapunov-based control and piecewise-linear Lyapunov functions

Abstract

In this paper we describe a new methodology for designing robust and efficient state-feedback control laws for a switched-mode boost DC-DC power converter. The proposed design is adopting the so-called Lyapunov-based control law and attempts to solve the robust constrained stabilization problem under large parameter variations. With the methodology proposed static or switching state-feedback control laws are generated so that a number of further key issues are addressed, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, robustness to supply voltage variations, set-point and load changes. The control design procedure is based on the generation of controlled invariant polytopes (safety domains) using piecewise-linear Lyapunov functions. The proposed technique is numerically evaluated using the exact switched model of the converter.

Optimal switching Lyapunov‐based control of power electronic converters

“…These results justify the usefulness of using optimal switching gains: even static optimal laws with one or two switching points achieve very satisfactory responses at the whole operating range and under the most demanding situations (startup transients). More detailed experimentation in a wider operating region as well as a larger number of switchings suggested that the results obtained with only one or two switchings are comparable with the results with four switchings in . Hence, only few switchings are enough to get most of the benefit of improved performance and reduced complexity of the control law.…”

“…We consider the boost DC–DC converter used in with nominal parameter values L = 1.5 mH , C = 10 μF , R = 40Ω, V in = 5 V , V ref = 10 V and a wide range of operating conditions, i.e. V ref ∈ [8, 10] V, V in ∈ [3.5, 6.5] V, R ∈ [20, 80]Ω, which result in d ss ∈ [0.1875, 0.65].…”

“…The problem of designing robust wide‐range Lyapunov‐based control laws for this converter has been studied recently in . In a design methodology for selecting λ has been introduced.…”

“…Although this approach is not new and similar ideas have been used in the literature (see e.g. [21][22][23]), this work shows that this framework is particularly flexible when combined with the Lyapunov-based control paradigm, offering a straightforward design procedure which enjoys general applicability and involves minimal analytical calculations.…”

“…Because there is no dependence of the initial conditions on λ, zero initial conditions ỹ(0) may be assumed. For a fixed λ, the new state vector ỹ(t) may be calculated by integration forward in time on the basis of its nonlinear differential equation (21).…”