Robust H∞ Control of Takagi–Sugeno Systems with Actuator Saturation

Producción CientíficaThe robust static output feedback control for continuous-time Takagi–Sugeno systems subject to actuator saturation is solved here, including H∞ performance guarantees. Based on a polytopic model of the saturation, sufficient conditions are proposed for designing these controllers in terms of Linear Matrix Inequalities. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved easily without requiring iterative algorithms or equality constraints, moreover, the output matrix of the considered system does not require to be full row rank. Finally, some examples are presented to show the validity of the proposed methodology

Robust Finite-Time Control for 2D Continuous-Continuous LTI Systems: New motivation and LMI Characterization

International audienceThis paper proposes a new condition for achieving robust finite-time stability (FTS) of two-dimensional (2D) linear systems in the continuous-continuous time-invariant setting. FTS is in its essence adapted to 2D systems since it ensures that, for a given bound on initial conditions, weighted norms of the vertical and horizontal state variables will not exceed a certain bound during a predefined time interval. On the basis of this concept a new and original control design problem, using the 2D FTS as a constraint, is proposed. In fact, a prominent parametric insensitive control design for LTI systems is recast here as an FTS control design for a specific 2D system. Moreover, the paper not only gives an extension of the 1D FTS concept to 2D systems but also proposes some extended LMI conditions, with a reduced conservatism, for achieving robust closed-loop FTS by means of a state-feedback. A numerical example is given to illustrate the effectiveness of the proposed conditions

LTI Descriptor Systems Admissibility under Structure Constraints: A Nonsmooth Newton Approach

International audienceThe paper deals with structured state feedback controllers design for linear time invariant (LTI) singular systems. New necessary and sufficient conditions for the existence of a structured state feedback guaranteeing the descriptor closed loop system admissibility is proposed by dint of linear quadratic (LQ) control theory. These conditions are presented in the form a system of matrix equations involving a non-smooth unconstrained equation. Keeping that in mind, the computation of the Clarke Jacobian of real symmetric matrix projection on semi-definite positives matrices’ cone, is used in order to solve the resulting system of matrix equations. Hence, local convergence of such non-smooth Newton like algorithm is proved. Based on this some numerical examples are presented to show the applicability of the proposed method

Descriptor Recurrent Neural Network Model and L2 gain Control Design for Systems with Dry Friction

International audienceThis paper presents a control design method for mechanical systems involving the Coulomb and Stribeck dry friction effects. The design method is based on a continuous-time recurrent neural network (RNN) descriptor model. The latter has the particularity of including a single nonlinearity verifying the well-known cone bounded condition. Hence, a nonlinear static feedback is proposed guaranteeing an efficient friction compensation and optimizing the ℒ 2 - gain of the closed-loop. The design procedure is recast as an optimization problem under LMI constraints that can be solved efficiently. The relevance of the proposed approach is confirmed through a didactic example

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Producción CientíficaThe stabilization of Takagi–Sugeno systems is solved here for the two-dimensional polynomial discrete case, by using the sum-of-squares approach. First, we provide a stabilization condition formulated in terms of polynomial multiple Lyapunov functions. Then, a non-quadratic stabilization condition is developed by applying relaxed stabilization technique. Both conditions can be used for design, by solving them using numerical tools such as SOSTOOLS. A numerical example illustrates the effectiveness of the results.Junta de Castilla y León y EU-FEDER (CLU 2017-09) y (UIC 233)Secretaría de Estado de Investigación, Desarrollo e Innovación (Grant. DPI2014-54530-R

Maximum Power Point Tracking of a Photovoltaic System Using State Feedback Gain Fuzzy Control

International audienc

Maximum Power Point Tracking of a Photovoltaic System Using State Feedback Gain Fuzzy Control

International audienc

Photovoltaic System's MPPT Under Partial Shading Using T-S Fuzzy Robust Control

International audienceThis paper deals with a T-S fuzzy robust control achieving maximum power point tracking (MPPT) for photovoltaic (PV) systems under partial shading situations. The aim is to track global maximum power point (GMPP). The T-S fuzzy robust control consists in an optimization approach that overcomes the well-known perturb and observe (P&O) technique drawbacks, such as the decreased tracking efficiency and transient oscillations. For this aim, a photovoltaic generator (PVG) with a DC-DC boost converter and battery energy storage devices are considered. The optimum trajectory is generated using a T-S fuzzy reference model, which must be followed to obtain optimal powerpoint. Solving a set of linear matrix inequalities (LMIs) yields the sought controller gains. A simulation is carried out to show that the tracking performance of the proposed T-S fuzzy robust control is assessed for various partial shading patterns. The results confirm that the T-S fuzzy robust H∞ control strategy ensures global MPP convergence. Furthermore, when compared to the existing solutions, simulations proved that it has better performances

Maximum Power Point Tracking of a Photovoltaic System Using State Feedback Gain Fuzzy Control

International audienceAn effective Maximum Power Point Tracking (MPPT) technique, that can be used in a variety of environmental conditions, is tackled with in this note. To this aim, an MPPT control based on a T-S fuzzy model is applied improving thus the performance and the efficiency of a solar photovoltaic (PV) generator. The nonlinear system's dynamics are embedded in a T-S fuzzy model. Sufficient criteria for designing such fuzzy control policy are presented in terms of linear matrix inequalities based on a quadratic Lyapunov function combined with some helpful slack variables (i.e. dilated quadratic LMI conditions). The proposed method reduces tracking time while overcoming the oscillation that usually appear near the maximum powerpoint. Besides, the simulation of a photovoltaic system using the proposed control policy demonstrates the efficiency of the approach even in the case of climate changes

Input–output stability and stabilisation conditions for discrete-time delayed fuzzy systems

International audienceThe problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method