Analysis and design of quadratically bounded QPV control systems

© 2019. ElsevierA nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

Automated generation and comparison of Takagi-Sugeno and polytopic quasi-LPV models

In the last decades, gain-scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non-linear systems. Among the approaches proposed in the literature, the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms have proved to be successful in dealing with the different trials that the analyzer, or the designer, of a gain-scheduled control system has to face. Despite the strong similarities between the two paradigms, research on LPV and TS systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them. However, in recent works, some clues that there is a very close connection between LPV and TS worlds have been presented. The present paper openly addresses the presence of strong analogies between LPV and TS models, in an attempt to establish a bridge between these two worlds, so far considered different. In particular, this paper addresses the modeling problem, presenting two methods for the automated generation of LPV and TS systems, and introducing some measures in order to compare the obtained models. A mathematical example is used to illustrate the proposed methods.This work has been funded by the Spanish Ministry of Science and Technology through the projects CICYT SHERECS (Ref. DPI2011-26243) and CICYT ECOCIS (Ref. DPI2013-48243-C2-1-R), by the European Commission through contract i-Sense FP7-ICT-2009-6-270428, by UPC through the grant FPI-UPC E-01104, by AGAUR through the contracts FI-DGR 2013 (Ref. 2013FIB00218) and FI-DGR 2014 (Ref. 2014FI_B1 00172), and by the DGR of Generalitat de Catalunya (SAC group Ref. 2014/SGR/374). The work was also supported by the National Science Centre in Poland under the grant 2013/11/B/ST7/01110.Peer Reviewe

Robust unknown input observer for state and fault estimation in discrete-time Takagi-Sugeno systems

In this paper, a robust unknown input observer (UIO) for the joint state and fault estimation in discrete-time Takagi-Sugeno (TS) systems is presented. The proposed robust UIO, by applying the H-infinity framework, leads to a less restrictive design procedure with respect to recent results found in the literature. The resulting design procedure aims at achieving a prescribed attenuation level with respect to the exogenous disturbances, while obtaining at the same time the convergence of the observer with a desired bound on the decay rate. An extension to the case of unmeasurable premise variables is also provided. Since the design conditions reduce to a set of linear matrix inequalities that can be solved efficiently using the available software, an evident advantage of the proposed approach is its simplicity. The final part of the paper presents an academic example and a real application to a multi-tank system, which exhibit clearly the performance and effectiveness of the proposed strategy.Postprint (author's final draft

A necessary and sufficient condition for total observability of discrete-time linear time-varying systems

This paper deals with the total observability problem of discrete-time linear time-varying systems. In particular, a review and suitable analysis of the state-of-the-art of this emerging area are provided. Subsequently, the total observability problem of discrete-time linear time-varying systems is transformed into the one of checking the rank of a convex sum of matrices. As a result, a new total observability test is proposed, along with a suitable computational strategy. The final part of this paper shows examples regarding observability analysis that clearly exhibit the benefits of using the proposed approach.Postprint (published version

A practical test for assessing the reachability of discrete-time Takagi-Sugeno fuzzy systems

This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the teachability analysis can be performed efficiently using the proposed approach.This paper provides a necessary and sufficient condition for the reachability of discrete-time Takagi-Sugeno fuzzy systems that is easy to apply, such that it constitutes a practical test. The proposed procedure is based on checking if all the principal minors associated to an appropriate matrix are positive. If this condition holds, then the rank of the reachability matrix associated to the Takagi-Sugeno fuzzy system is full for any possible sequence of premise variables, and thus the system is completely state reachable. On the other hand, if the principal minors are not positive, the property of the matrix being a block P one with respect to a particular partition of a set of integers is studied in order to conclude about the reachability of the Takagi-Sugeno system. Examples obtained using an inverted pendulum are used to show that it is easy to check this condition, such that the teachability analysis can be performed efficiently using the proposed approach.Postprint (author's final draft

Development of a Fault-Tolerant Control with MATLAB and its application to the Twin-Rotor System

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holderThe main objective of this paper is to present the MATLAB block-set that can be used for faulttolerant control of linear-parameter varying systems. In particular, the introductory part of the paper presents a theoretical background regarding the fault identification and control strategy. Subsequently, it is shown how to implement these theoretical results in Matlab/Simulink. The final part of the paper presents the experimental study regarding the twin-rotor system, which confirms the effectiveness of the developed tool.Postprint (published version

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

Predictive fault tolerant control for LPV systems using model reference

The present work proposes a Fault Tolerant Control (FTC) methodology for non-linear discrete-time systems that can be modeled as Linear Parameter Varying (LPV) systems. The proposed approach relies on the modeling of faults as additional scheduling parameters of the LPV model for the controlled system and it uses a triple loop architecture. The inner control loop is designed by means of the standard H2/H1 control methodologies based on Linear Matrix Inequalities (LMIs). The design takes into account a prespecified set of faults and the ranges of their magnitudes that are wanted to be tolerated and it assumes the availability of on-line fault estimations provided by a Fault Detection and Isolation (FDI) module. The resulting controller tries to compensate the system faults in order to maintain a satisfactory closed-loop dynamic performance, but it does not take into account possible system input and state constraints associated to actuator saturation and other physical limitations. Thus, an intermediate control loop determines the actual compensation feasibility using set invariance theory. And, when it is needed, it applies suitable additive predictive control actions that enlarge the invariant set, trying to assure that the current state remains inside the enlarged invariant set. Finally, an outer loop implements a model reference control that allows reference tracking. The use of the proposed FTC methodology is illustrated through its application to the well-known quadruple tank system benchmark.Peer ReviewedPostprint (published version