Convex hull manipulation does matter in LMI based observer design, a TP model transformation based optimisation (original) (raw)

Convex hull manipulation based control performance optimization: Case study of impedance model with feedback delay

2012 IEEE 10th International Symposium on Applied Machine Intelligence and Informatics (SAMI), 2012

This paper deals with the topic of qLPV state-space model based control design in which LMIs are used to optimize the multi-objective control performance. In this paper we investigate how the manipulation convex hull of the polytopic model influences the control performance which is derived by LMIs. We examine these influences through the control design of the two dimensional aeroelastic system's example. First we define various TP type polytopic model representations of a wing section whose vertices define different convex hulls. In the second step we investigate how these models lead to different control performances.

Determination of the stability parameter space of a two dimensional aeroelastic system, a TP model-based approach

2010

This paper falls in the topic of qLPV state-space model based control design in which LMIs are used to optimize the multi-objective control performance. In this paper we investigate how the convex hull of the polytopic model influences the feasibility of the LMI based control design and the resulting control performances. We examine these influences through the control design of the two dimensional aeroelastic system's example. First we define various TP type polytopic model representations of a wing section whose vertices define different convex hulls. In the second step we investigate how these models lead to different control performances.

Polytope LPV estimation for non-linear flight control

IFAC Proceedings Volumes, 2011

The current study is motivated by the need to implement the linear based model-based fault detection and isolation (FDI) methodology onto the nonlinear aircraft system directly. The nonlinear model is expressed in the linear parameter varying (LPV) manner and the corresponding LPV FDI estimator can be developed through the combination of the polytopic FDI estimators developed on each system vertex. The proposed design strategy is applied to the nonlinear longitudinal motion of a UAV aircraft (Machan) with different faults acting on the elevator actuator and wind turbulence affecting the vertical force.

Tensor product type polytopic LPV modeling of aeroelastic aircraft

2018 IEEE Aerospace Conference

In order to improve fuel efficiency, future aircraft will have reduced weight and increased wingspan. Such aircraft require active control systems to suppress ASE effects. ASE systems are often modeled in the grid based linear parametervarying (LPV) framework, which captures the parameter varying dynamics. The controller is generally synthesized by solving Linear Matrix Inequalities (LMIs) for the LPV model. Selecting the grid density for such control synthesis approach requires special attention. On the one hand, a too coarse grid might not capture the parameter variation of the dynamics accurately enough. On the other hand, solving LMIs for too dense grid can lead to numerical issues and computational cost. This is usually relaxed by synthesizing the controller for a coarser grid and the stability and performance are verified for a denser grid. A possible remedy for this drawback of grid-based LPV models is polytopic LPV representation. In such case the LMIs need to be solved only for the vertex systems of the convex polytopic hull. Various types of convex polytopic models can be obtained by Tensor Product (TP) model transformation. The aim of the paper is to derive polytopic models for ASE vehicles and to apply these models for flutter suppression control design. The goal is to have a small number of vertex systems and sufficient accuracy while keeping the conservativeness of polytopic modeling low. The aircraft under consideration is the mini MUTT (Multi Utility Technology Testbed) vehicle. Based on the polytopic representation a stabilizing state feedback controller and observer is synthesized. The effectiveness of the resulting control design is verified through numerical simulations.

Fixed-Order Controller Design for Polytopic Systems Using LMIs

IEEE Transactions on Automatic Control, 2000

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex innerapproximation of the whole non-convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all stabilizing fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with some LMIs. These LMIs can be used for robust pole placement of polytopic systems.

A novel control-oriented multi-affine qLPV modeling framework

2010

This paper proposes a framework for selecting affinely parametrized quasi Linear Parameter Varying (qLPV) model structures that facilitates solutions to specific control design tasks encountered in vehicle dynamics applications. Moreover it facilitates the selection of the scheduling variables and provides a framework to decide whether the controller performance can be improved by introducing some estimated parameters as scheduling variables, i.e., if some adaptive strategy is needed or not. The proposed scheme is an iterative process: in every step a suitable model transformation is applied to generate a finite element convex polytopic representation in order to obtain a qLPV model. Then the LMI feasibility of a robust control objective is verified, which is closely related to the original control task. This step provides a selection criterion that sorts out the suitable models from a finite set of model candidates generated by the iterative method.

Fixed-order controller design for state space polytopic systems by convex optimization

IFAC Proceedings Volumes (IFAC-PapersOnline), 2013

In this paper, a new method for fixed-order controller design of systems with polytopic uncertainty in their state space representation is proposed. The approach uses the strictly positive realness (SPRness) of some transfer functions, as a tool to decouple the controller parameters and the Lyapunov matrices and represent the stability conditions and the performance criteria by a set of linear matrix inequalities. The quality of this convex approximation depends on the choice of a central state matrix. It is shown that this central matrix can be computed from a set of initial fixed-order controllers computed for each vertex of the polytope. The stability of the closed-loop polytopic system is guaranteed by a linear parameter dependent Lyapunov matrix. The results are extended to fixed-order H ∞ controller design for SISO systems.

Polytopic Observers for LPV Discrete-Time Systems

Lecture Notes in Control and Information Sciences, 2013

The main goal of this work is to give a general treatment on observer synthesis for LPV systems in the framework of Linear Matrix Inequalities. A special Parameter Dependent Lyapunov Function, called poly-quadratic Lyapunov function, is considered. It incorporates the parameter variations for LPV systems with polytopic parameter dependence and allows to guarantee a so-called poly-quadratic stability which is sufficient to ensure Global Asymptotic Stability. The concept of polytopic observers is introduced. A LMI-based method for the synthesis of this type of observers is proposed. The case when LPV systems are subjected to disturbances or when the parameter is known with a bounded level of uncertainty is further addressed. Conditions to guarantee performances like Input-to-State Stability (ISS), bounded peak-to-peak gain and L2 gain are given. The design of polytopic Unknown Input Observers both in the deterministic and in the noisy or uncertain cases is also presented. Finally, two illustrative examples dealing with polytopic observers for chaos synchronization and air path management of a turbocharged Spark Ignition engine are detailed.

LMI-based Multiobjective Optimization and Control of Flexible Aircraft Using VCCTEF

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2015

This paper considers the control of coupled aeroelastic aircraft model with Variable Camber Continuous Trailing Edge Flap (VCCTEF) system. The relative motion between two adjacent flaps is constrained and this actuation constraint problem is converted into an output covariance constraint problem, and therefore can be formulated using linear matrix inequalities (LMIs). A set of LMI conditions is derived for the design of an observer-based dynamic output feedback controller for VCCTEF configured aeroelastic aircraft model. The proposed controller is then applied to the NASA Generic Transport Model (GTM) for simulation, and the results demonstrate the efficacy of the proposed approach.