Representing the model of impedance controlled robot interaction with feedback delay in polytopic LPV form: TP model transformation based approach

The aim of this paper is to transform the model of the impedance controlled robot interaction with feedback delay to a Tensor Product (TP) type polytopic LPV model whereupon Linear Matrix Inequality (LMI) based control design can be immediately executed. The paper proves that the impedance model can be exactly represented by a finite element TP type polytopic model under certain constrains. The paper also determines various further TP models with different advantages for control design. First, it derives the exact Higher Order Singular Value Decomposition (HOSVD) based canonical form, then it performs complexity trade-off to yield a model with less number of components but rather effective for LMI design. Then the paper presents various different types of convex TP model representations based on the non-exact model in order to investigate how convex hull manipulation can be performed on the model. Finally the presented models are analyzed to validate the accuracy of the transformation and the resulting TP type polytopic LPV models. The paper concludes that these prepared models are ready for convex hull manipulation and LMI based control design

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

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