Matrix Inequality Based Control Design Research Articles

Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model

AbstractThe tensor‐product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state‐space models to the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models, a type of polytop models, for linear matrix inequality based controller design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the parameter‐varying state‐space model. In this paper we propose a modified TP model transformation that leads to considerable reduction of the computation. The key idea of the method is that instead of transforming the whole system matrix at once in the whole parameter space, we decompose the problem and perform the transformation element wise and restrict the computation to the subspace where the given element of the model varies. The modified TP model transformation can readily be executed in higher dimensional cases when the original TP model transformation fails. The effectiveness of the new method is illustrated with numerical examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

COMPLEXITY RELAXATION OF THE TENSOR PRODUCT MODEL TRANSFORMATION FOR HIGHER DIMENSIONAL PROBLEMS

ABSTRACTThe Tensor Product (TP) model transformation method was proposed recently as an automated gateway between a class of non‐linear models and linear matrix inequality based control design. The core of the TP model transformation is the higher order singular value decomposition of a large sized tensor, which requires high computational power that is usually outside of a regular computer capacity in cases of higher dimensionality. This disadvantage restricts the utilization of the TP model transformation to models having smaller dimensionality. The aim of this paper is to propose a computationally relaxed version of the TP model transformation. The paper also presents a 6 dimensional example to show the effectiveness of the modified transformation.

Linear matrix inequality based controller design with feedback linearisation: application to power systems

A control scheme for the design of damping controllers for power systems is presented. The scheme is based on the combination of two powerful control design techniques, namely the linear matrix inequality (LMI) technique and the direct feedback linearisation (DFL) technique. It is shown that the DFL technique can cancel nonlinearities in the power system model, thus, reducing the uncertainty in the LMI design. The obtained results show that the proposed controller provides smooth control actions and a fast transient response, and is highly suited for the problem of electromechanical oscillation damping in power systems.