Friction compensation in TP model form - Aeroelastic wing as an example system

The aim of this paper is to fit the friction compensation problem in the field of modern polytopic and Linear Matrix Inequality (LMI) based control design methodologies. The paper proves that the exact Tensor Product (TP) type polytopic representations of most commonly utilized friction models such as Coulomb, Stribeck and LuGre exist. The paper also determines and evaluates these TP models via a TP model transformation. The conceptual use of the TP model of the friction is demonstrated via a complex control design problem of a 2D aeroelastic wing section. The paper shows how the friction model and the model of the aeroelastic wing section can be merged and transformed to a TP type polytopic model - by TP model transformation - whereupon LMI based control performance optimization can immediately be executed to yield an observer based output feedback control solution to given specifications. The example is evaluated via numerical simulations. © 2015, Budapest Tech Polytechnical Institution. All rights reserved

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

Transition Between TS Fuzzy Models and the Associated Convex Hulls by TS Fuzzy Model Transformation

One of the primary objectives underlying the extensive 20-year development of the TS Fuzzy model transformation (originally known as TP model transformation) is to establish a framework capable of generating alternative Fuzzy rules for a given TS Fuzzy model, thereby manipulating the associated convex hull to enhance further design outcomes. The existing methods integrated into the TS Fuzzy model transformation offer limited capabilities in deriving only a few types of loose and tight convex hulls. In this article, we propose a radically new approach that enables the derivation of an infinite number of alternative Fuzzy rules and, hence, convex hulls in a systematic and tractable manner. The article encompasses the following key novelties. Firstly, we develop a Fuzzy rule interpolation method, based on the pseudo TS Fuzzy model transformation and the antecedent Fuzzy set rescheduling technique, that leads to a smooth transition between the Fuzzy rules and the corresponding convex hulls. Then, we extend the proposed concept with the antecedent Fuzzy set refinement and reinforcement technique to tackle large-scale problems characterized by a high number of inputs and Fuzzy rules. The paper also includes demonstrative examples to illustrate the theoretical key steps, and concludes with an examination of a real complex engineering problem to showcase the effectiveness and straightforward execution of the proposed convex hull manipulation approach