Relaxed formulation of the design conditions for Takagi-Sugeno fuzzy virtual actuators

Abstract

The H ∞ norm approach to virtual actuators design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Using the second Ljapunov method, the design conditions are formulated in terms of linear matrix inequalities in adapted bounded real lemma structures. Related to the static output controller, and for systems under influence of single actuator faults, the design steps are revealed for a three-tank system plant.

Passivation blocks for fault tolerant control of nonlinear systems

“…Indeed, fault hiding consists in inserting a reconfiguration block (RB) between the faulty plant and the controller that corrects the sensor measurements and translates the control signals by control allocation provided by a controller that does not receive the information about the fault occurrence. Most of fault hiding applications deal with linear systems (Lunze & Steffen, 2006), although there are also applications for linear parameter varying (Quadros, Bessa, Leite, & Palhares, 2020;Rotondo, Cristofaro, & Johansen, 2018), Hammerstein-Wiener (Richter, 2011), piecewise affine (Richter, Heemels, Wouw, & Lunze, 2011), and Takagi-Sugeno fuzzy (Bessa, Puig, & Palhares, 2020;Filasová, Krokavec, & Liščinský, 2016) systems.…”

TS fuzzy reconfiguration blocks for fault tolerant control of nonlinear systems

“…Dynamic RBs are able to compensate for both the control signal from nominal controller applied to plant actuators; and the sensor measurements used by the controller. This is the main RB structure found in the literature [17,18] , although some variations also appear to handle the problem of fault hiding for nonlinear systems, e.g., VAs without sensor measurement compensation [19][20][21][22] , linear parameter-varying blocks [23][24][25][26][27][28][29][30] , adaptive blocks [31,32] , and Takagi-Sugeno system (TS) VAs [20,33] . Furthermore, special VA structures are used for FTC of specific classes of non-linear systems [12] , for instance, Hammerstein-Wiener [34,35] and Lur'e systems [36,37] .…”

“…To obtain the required sufficient conditions it is assumed that the nominal system is stable according to a Lyapunov function that is reused to induce the stability recovery of the faulty reconfigured system. In particular, the TS reconfiguration block proposed in this manuscript differs from the ones presented in [20,33] mainly because it can be generally employed as VS or VA. Furthermore, the proposed reconfiguration block is used to recover the stability of TS models with nonlinear consequent and a distributed version of the proposed reconfiguration block is used to recover the stability of networked TS systems.…”