Multivariable algebraic loops in linear anti-windup implementations

IET Control Theory & Applications

2016

We develop new robust synthesis procedures for directionality compensation for linear exponentially stable multivariable plants incorporating both plant uncertainties and input saturations. The control structure is similar to those of anti-windup controls but requires the online solution of a low-order convex optimization. The condition for the existence of a compensator can be expressed as a feasibility problem involving a set of linear matrix inequalities (LMIs). We demonstrate the effectiveness of the design compared to several schemes using a highly ill-conditioned benchmark simulation example.

Section: Main Result: Lmi-based Synthesismentioning

confidence: 99%

Section: Multivariable Algebraic Loop and Well-posednessmentioning

confidence: 99%

Section: Simulation Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust synthesis for directionality compensation

Adegbege¹,

IET Control Theory & Applications

2016

“…We show that many existing anti-windup designs correspond to particular implementations of the algebraic loop. Some preliminary results have been presented in [1,3]; here we provide formal proofs of the two main results (Proposition 5 and Proposition 7). In addition we include simulation results which demonstrate both the simplicity of on-line implementation of LCP solvers and the benefits offered by such a generalized framework.…”

Section: Introductionmentioning

confidence: 87%

A framework for multivariable algebraic loops in linear anti-windup implementations

Adegbege

2017

Automatica

This brief paper addresses the implementation and well-posedness aspects of multivariable algebraic loops which arise naturally in many anti-windup control schemes. Using the machinery of linear complementarity problems, a unified framework is developed for establishing well-posedness of such algebraic loops. Enforcing well-posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti-windup design stage. Several existing anti-windup implementations appear as special cases of the unified framework presented in this brief paper.

Robust stability analysis for barrier-based equation-free multi-linear model predictive control

Petsagkourakis

Chemical Engineering Research and Design

Theodoropoulos

2019

On-line optimization strategies such as model predictive control (MPC) have been widely used to compute control actions for a range of complex industrial systems. Barrier based MPC has recently been introduced, bringing together theory and algorithms for analysing the stability of linear models, however such models may not describe complex systems dynamics adequately. Multi-model linear MPC configurations can be used as a more reliable solution as piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately. Additionally, model order reduction can be applied to large-scale distributed systems, to reduce their dimensionality, jeopardising however their closed-loop stability. As a result, there is a clear need for an input to output stability analysis for closed loop systems under unstructured uncertainty when multi-model barrier MPC is utilized. In this work, we combine equation-free model reduction with integral quadratic constraints (IQCs) for the stability analysis of large-scale closed-loop systems under unstructured uncertainties, including model approximation errors and nonlinearities, including MPC. An illustrative example is used to elucidate the proposed methodology.