Robust Regulation of a Power Flow Controller via Nonlinear Integral Action

Abstract

This paper considers a robust output setpoint tracking problem for a m-terminal power flow controller (PFC) for meshed DC micro-grids. The PFC is a power electronics device used to control the power flow at a node in the meshed grid, and may act as a DC circuit breaker. The system is modelled by state-space bilinear dynamics coupled with a polynomial output. In the proposed design, the plant is first extended with an integral action processing the regulation error. The cascaded model composed of the plant and the integrator is then stabilised using a saturated state-feedback law, designed with a forwarding approach. An anti-windup function is added to cope with transient saturations. A tuning method is proposed to set the controller gains along the available degrees of freedom with respect to a cost function. The stability of the closed-loop is guaranteed for any compact set of initial conditions and for small parametric variations around the nominal set-point. Experiments have been carried out and these properties are successfully assessed on a tenth-scale experimental setup.

Incremental Stabilization of Cascade Nonlinear Systems and Harmonic Regulation: A Forwarding-Based Design

“…for each t ≥ 0, χ → X (χ, t) is a contraction), see [1], [4]. The open-loop system (1) is in the so-called feedforward (or cascade) form, for which forwarding-based control techniques have been developed for equilibrium stabilization purposes ([19]- [22], [30]). Practical examples of systems in this form are the diskinertia pendulum in [22] or the TORA system [31].…”

Stabilization for a Class of Positive Bilinear Systems

“…For stabilization of a bilinear system, it is standard in the literature to assume some open-loop stability (see e.g. [10], [11], [13]- [15], [17], [19], [20]). In the case of the heat exchanger (1), A+Bu * is Hurwitz for all u * > 0 as confirmed in Section V. Thus, we impose the same assumption as [10], [11], [17], [19], [20], i.e., there exists u * ≥ 0 such that A+ m i=1 B i u * i is Hurwitz 1 .…”

“…[10], [11], [13]- [15], [17], [19], [20]). In the case of the heat exchanger (1), A+Bu * is Hurwitz for all u * > 0 as confirmed in Section V. Thus, we impose the same assumption as [10], [11], [17], [19], [20], i.e., there exists u * ≥ 0 such that A+ m i=1 B i u * i is Hurwitz 1 . Then, for fixed u * , the system (3)…”

“…To increase robustness, our objective is to design a state feedback controller. Differently from [10]- [20], we take advantage of positivity and max-separable functions for control design. In [21], [22], stabilization of positive bilinear systems by static controllers are considered only when b i = 0, i = 1, .…”

“…Although there are numerous results on stabilization of bilinear systems, e.g. [10]- [20], positivity has not been incorporated except for a special case without additive terms [21], [22]. It is worth emphasizing that none of [10]- [22] employs a max-separable Lyapunov function for stabilizing control design.…”