Low-Gain Stabilizers for Linear-Convex Optimal Steady-State Control

TL;DR

This paper introduces low-gain stabilizer designs for linear- convex optimal control problems, providing explicit formulas and LMI methods, with applications demonstrated in power system frequency regulation.

Contribution

It offers new, fully constructive low-gain stabilizer designs for optimal steady-state control, enhancing robustness and explicit gain computation methods.

Findings

Explicit controller formulas derived

LMI-based gain computation methods provided

Validated through power system frequency control example

Abstract

We consider the problem of designing a feedback controller which robustly regulates an LTI system to an optimal operating point in the presence of unmeasured disturbances. A general design framework based on so-called optimality models was previously put forward for this class of problems, effectively reducing the problem to that of stabilization of an associated nonlinear plant. This paper presents several simple and fully constructive stabilizer designs to accompany the optimality model designs from [1]. The designs are based on a low-gain integral control approach, which enforces time-scale separation between the exponentially stable plant and the controller. We provide explicit formulas for controllers and gains, along with LMI-based methods for the computation of robust/optimal gains. The results are illustrated via an academic example and an application to power system frequency control.