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1

LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials

Sánchez Marcelino, Bernal Miguel

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

275--283

EN

This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

2

An LMI-based heuristic algorithm for vertex reduction in LPV systems

Sanjuan Adrián, Rotondo Damiano, Nejjari Fatiha, Sarrate Ramon

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

725--737

EN

The linear parameter varying (LPV) approach has proved to be suitable for controlling many non-linear systems. However, for those which are highly non-linear and complex, the number of scheduling variables increases rapidly. This fact makes the LPV controller implementation not feasible for many real systems due to memory constraints and computational burden. This paper considers the problem of reducing the total number of LPV controller gains by determining a heuristic methodology that combines two vertices of a polytopic LPV model such that the same gain can be used in both vertices. The proposed algorithm, based on the use of the Gershgorin circles, provides a combinability ranking for the different vertex pairs, which helps in solving the reduction problem in fewer attempts. Simulation examples are provided in order to illustrate the main characteristics of the proposed approach.

3

Supervisory fault tolerant control of the GTM UAV using LPV methods

Péni T., Vanek B., Szabó Z., Bokor J.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

117--131

EN

A multi-level reconfiguration framework is proposed for fault tolerant control of over-actuated aerial vehicles, where the levels indicate how much authority is given to the reconfiguration task. On the lowest, first level the fault is accommodated by modifying only the actuator/sensor configuration, so the fault remains hidden from the baseline controller. A dynamic reallocation scheme is applied on this level. The allocation mechanism exploits the actuator/sensor redundancy available on the aircraft. When the fault cannot be managed at the actuator/sensor level, the reconfiguration process has access to the baseline controller. Based on the LPV control framework, this is done by introducing fault-specific scheduling parameters. The baseline controller is designed to provide an acceptable performance level along all fault scenarios coded in these scheduling variables. The decision on which reconfiguration level has to be initiated in response to a fault is determined by a supervisor unit. The method is demonstrated on a full six-degrees-of-freedom nonlinear simulation model of the GTM UAV.

4

Robust quasi-LPV model reference FTC of a quadrotor UAV subject to actuator faults

Rotondo D., Nejjari F., Puig V.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

7--22

EN

A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.

5

Fault-tolerant control strategy for actuator faults using LPV techniques: application to a two degree of freedom helicopter

Montes de Oca S., Puig V., Witczak M., Dziekan Ł.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 1

161-171

EN

In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.

6

An LPV pole-placement approach to friction compensation as an FTC problem

Patton R. J., Chen L., Klinkhieo S.

International Journal of Applied Mathematics and Computer Science

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2012

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Vol. 22, no. 1

149-160

EN

The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves pole-placement within suitable LMI regions, guaranteeing both stability and performance of a multi-fault LPV estimator employed within an FTC structure. The proposed design strategy is illustrated using a nonlinear two-link manipulator system with friction forces acting simultaneously at each joint. The friction forces, regarded as a special case of actuator faults, are estimated and their effect is compensated within a polytope controller system, yielding a robust form of active FTC that is easy to apply to real robot systems.

7

Gain-scheduled state-feedback control for active cancellation of multisine disturbances with time-varying frequencies

Heins W., Ballesteros P., Bohn C.

Mechanics and Control

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2011

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Vol. 30, no. 3

127-137

EN

The paper presents a discrete-time LTV controller for the rejection of harmonic disturbances with time-verying based on a state-augmented observer-based state-feedback controller with a time-verying internal model and a scheduled state-feed back gain. The control design method is based on quadratic stability for LPV systems. The design is carried out in discrete time and the controller can easily be implemented on real-time hardware.

PL

W pracy przedstawiono dyskretny regulator LTV do eliminacji składowych harmonicznych zakłóceń. Wprowadzony regulator bazuje na sprzężeniu od zmiennych stanu z zależnym od czasu wewnętrznym modelem. Konstrukcja regulatora wykorzystuje własności stabilności układów LPV. Regulator został opisany równaniami dyskretnymi i może być łatwo zaimplementowany w układach czasu rzeczywistego.