A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft

Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system

[EN] In this paper, a systematic methodology to design fuzzy Takagi-Sugeno observers and controllers will be used to estimate the angular positions and speeds, as well as to stabilise an experimental mechanical system with 3 degrees of freedom (fixed quadrotor). Takagi-Sugeno observers and controllers are compared to observers and controllers based on the linearized model, both designed with the same optimization criteria and design parameters. Experimental results confirm that Takagi-Sugeno models and observers behave similarly to linear ones around the linearization point, but have a better performance over a larger operating range, as intuitively expected.The work of Zs. Lendek was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-RU-TE-2011-3-0043, contract number 74/05.10.2011. Spanish authors are grateful to grants DPI2011-27845-C02-01 (A. Sala), DPI2011-27845-C02-02 (R. Sanchis), DPI2011-28507-C02-01 (P. Garcia) from Spanish Government, and PROMETEOII/2013/004 (A. Sala, P. Garcia) from Generalitat Valenciana.Lendek, Z.; Sala, A.; García Gil, PJ.; Sanchis Llopis, R. (2013). Experimental application of Takagi-Sugeno observers and controllers in a nonlinear electromechanical system. Control Engineering and Applied Informatics. 15(4):3-14. http://hdl.handle.net/10251/150453S31415

Robust fault diagnosis of proton exchange membrane fuel cells using a Takagi-Sugeno interval observer approach

In this paper, the problem of robust fault diagnosis of proton exchange membrane (PEM) fuel cells is addressed by introducing the Takagi-Sugeno (TS) interval observers that consider uncertainty in a bounded context, adapting TS observers to the so-called interval approach. Design conditions for the TS interval observer based on regional pole placement are also introduced to guarantee the fault detection and isolation (FDI) performance. The fault detection test is based on checking the consistency between the measurements and the output estimations provided by the TS observers. In presence of bounded uncertainty, this check relies on determining if all the measurements lie inside their corresponding estimated interval bounds. When a fault is detected, the measurements that are inconsistent with their corresponding estimations are annotated and a fault isolation procedure is triggered. By using the theoretical fault signature matrix (FSM), which summarizes the effects of the different faults on the available residuals, the fault is isolated by means of a logic reasoning that takes into account the bounded uncertainty, and if the number of candidate faults is more than one, a correlation analysis is used to obtain the most likely fault candidate. Finally, the proposed approach is tested using a PEM fuel cell case study proposed in the literature.Peer ReviewedPostprint (author's final draft

Takagi-Sugeno fuzzy observer for a switching bioprocess : sector nonlinearity approach

Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT)

Integrated design of fault-tolerant control for nonlinear systems based on fault estimation and T-S fuzzy modelling

This paper proposes an integrated design of faulttolerant control (FTC) for nonlinear systems using Takagi-Sugeno (T-S) fuzzy models in the presence of modelling uncertainty along with actuator/sensor faults and external disturbance. An augmented state unknown input observer is proposed to estimate the faults and system states simultaneously, and using the estimates an FTC controller is developed to ensure robust stability of the closed-loop system. The main challenge arises from the bi-directional robustness interactions since the fault estimation (FE) and FTC functions have an uncertain effect on each other. The proposed strategy uses a single-step linear matrix inequality formulation to integrate together the designs of FE and FTC functions to satisfy the required robustness. The integrated strategy is demonstrated to be effective through a tutorial example of an inverted pendulum system (based on robust T-S fuzzy designs)

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM)