Béla Takarics

Tensor-Product-Model-Based Control of a Three Degrees-of-Freedom Aeroelastic Model

Active control of aeroelasticity has been in the focus of aerospace and control engineering for several decades. An introduction to this topic can be found in [1]. This paper largely focuses on the three degrees-of-freedom (DoF) Nonlinear Aeroelastic Test Apparatus (NATA) model. The NATA model with unsteady aerodynamics was presented in [2, 3] and several active controllers were developed in [4 14]. LPV control of an improved three DoF aeroelastic model is discussed in [15]. The aim of this paper is to propose a control design strategy to stabilize the improved 3 DoF NATA model presented in [15], as well as to stabilize the NATA model with nonlinear friction. It is assumed that only the free stream velocity and the pitch angle are measurable, thus an output feedback control structure is applied. The control design considers the following performance requirements: asymptotic stability, decay rate and constraint on the control signal, which are formulated in terms of Linear Matrix Inequalities (LMIs). The proposed control design strategy has two main steps. First, the quasi linear parameter varying (qLPV) NATA model is transformed into Tensor Product (TP) type polytopic form via TP model transformation ([16 18]). LMI based control design is applied to the TP type polytopic form in the second step, which yields in stabilising controller and observer via optimising the control performance. Besides resulting in a stabilising control solution to the 3 DoF NATA model, it is shown that

Aeroelastic wing section control via relaxed tensor product model transformation framework

A study was conducted to demonstrate aeroelastic wing section control via relaxed tensor product model transformation framework. The investigations focused on the three-degree-of-freedom (3-DOF) nonlinear aeroelastic test apparatus (NATA) model. The study also revisited the parallel distributed compensation (PDC) framework-based control solution of the 3-DOF NATA model in the case where the model was extended to incorporate friction. It presented a new general theoretical control design framework based on tensor product (TP) model transformation. The proposed framework was capable of a significant complexity reduction of quasi-linear parameter-varying (QLPV) models, including numerical and theoretical for linear matrix inequality (LMI)-based control design. The proposed control design framework was applied for active stabilization of the 3-DOF aeroelastic wing section as an extension of the design method.

TP Model-based Robust Stabilization of the 3 Degrees-of-Freedom Aeroelastic Wing Section

Active stabilisation of the 2 and 3 degrees-of-freedom (DoF) aeroelastic wind sections with structural nonlinearities led to various control solutions in the recent years. The paper proposes a control design strategy to stabilise the 3 Dof aeroelastic model. It is assumed that the aeroelastic model has uncertain parameters in the trailing edge dynamics and only one state variable, the pitch angle is measurable, therefore, robust output feedback control solution is derived based on the Tensor Product (TP) type convex representation of the aeroelastic model. The control performance requirements include robust asymptotic stability and constraint on the l2 norm of the control signal. The control performance requirements are formulated in terms of Linear Matrix Inequalities (LMIs). As the first step of the proposed strategy, the TP type model is obtained by executing TP transformation. As the second step, LMI based control design is performed resulting in controller and observer solution defined with the same polytopic structure as the TP type model. The validation and evaluation of the derived control solutions is based on numerical simulations.

Parallel Distributed Compensation based sector sliding mode control of Takagi-Sugeno type polytopic models

The main contribution of this paper is a new sliding mode design methodology for nonlinear systems, which utilizes the Parallel Distributed Compensation based multi-objective LMI control design for Takagi-Sugeno type polytopic representations of qLPV models. It is partially extension and combination of the classical optimal manifold design for linear (or linearized) system and sector sliding mode control. This new approach enables a systematic design and decomposition of optimal sliding sector by the High Order Singular Value Decomposition based canonical description of a wide class of nonlinear systems. This brings the advantages of the LMI based control design to the field of sliding mode control. The effectiveness of the methodology is validated by simulation results.

Robust Grid Point-Based Control Design for LPV Systems via Unified TP Transformation

The paper considers a general approach for linear parameter varying (LPV) control. The approach is based on polytopic representation of the LPV system. First, a grid point based control design is applied for a set of linearized models of the LPV system. The design is based on linear time invariant (LTI) techniques. Such control design allows a larger flexibility in the controller structure than the conventional parallel distributed compensation (PDC) based polytopic control. The LPV controller is obtained by linear interpolation between the LTI controllers. The paper proposes linear matrix inequality (LMI) based convex optimization for robustness analysis of the resulting controller. The approach requires the plant and the controller to be defined by a common polytopic structure. It is proposed to obtain this common structure via unified TP model transformation. A simple numerical example shows the efficiency of the proposed control design approach.

TP type polytopic modelling of the Bergman minimal model of the diabetes mellitus

The paper investigates the possibility of the Tensor Product (TP) type polytopic modelling of the quasi Linear Parameter Varying (qLPV) model formulation of the Bergman minimal model with the aim to fit the model to the modern polytopic and Linear Matrix Inequality (LMI) based control design methodologies. The paper proofs that the Higher Order Singular Value Decomposition (HOSVD) based canonical form as an exact TP type polytopic representation of the Bergman minimal model exist. The paper also determines and evaluates this TP model via TP model transformation. Various convex hulls for the Bergman minimal model were systematically constructed by TP model transformation enabling convex hull manipulation based optimisation in LMI-based control design.

TP model transformation based sliding mode control design for nonlinear systems

The main contribution of this paper is a new sliding mode design for nonlinear systems. This method is based on Tensor Product Model Transformation. It is partially extension and combination of the classical optimal manifold design for linear (or linearized) system and sector sliding mode control. This new approach enables a systematic design and decomposition of optimal sliding sector by the High Order Singular Value Decomposition (HOSVD)-based canonical description of a wide class of nonlinear systems. Two design examples and experimental results of a DSP-controlled single-degree-of-freedom motion-control system are presented.

Telemanipulation without Physical Contact in the Intelligent Space

This paper presents a telemanipulation system, where the operators movement is transmitted to the slave site not in a mechanical way, as in case of a real master device, but by image processing. The virtual master device uses cameras as sensors, subtracts the background from the images, and recognizes the skin colour of the operator in real time. The 3D position of the operators hand is determined by stereo vision and it becomes traceable by the colour of the skin.