A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

Takagi-Sugeno Fuzzy Model Based Discrete Time Model Predictive Control for a Hypersonic Re-Entry Vehicle

In this thesis, we present a control algorithm for a hypersonic re-entry vehicle during a Martian aerocapture maneuver. The proposed algorithm utilizes a discrete-time model predictive control technique with a Takagi-Sugeno fuzzy model of the vehicle to control the re-entry vehicle along an arbitrary trajectory using bank angle modulation. Simulations using model parameters and initial conditions from a Martian aerocapture mission demonstrate the stability, performance, and robustness of the proposed controller

Synchronization of Discrete-Time Chaotic Fuzzy Systems by means of Fuzzy Output Regulation Using Genetic Algorithm

The synchronization of chaotic systems, described by discrete-time T-S fuzzy models, is treated by means of fuzzy output regulation theory. The conditions for designing a discrete-time output regulator are given in this paper. Besides, when the system does not fulfill the conditions for exact tracking, a new regulator based on genetic algorithms is considered. The genetic algorithms are used to approximate the adequate membership functions, which allow the adequate combination of local regulators. As a result, the tracking error is significantly reduced. Both the Complete Synchronization and the Generalized Synchronization problem are studied. Some numerical examples are used to illustrate the effectiveness of the proposed approach

Fuzzy-Model-Based (FMB) Control of a Spacecraft with Fuel Sloshing Dynamics

During the upper-stage separation and orbit injection, orbital control, and attitude maneuver, propellant slosh in partially-filled fuel tanks can cause dynamical instability or pointing errors. The spacecraft dynamics combined with propellant sloshing results in a highly nonlinear and coupled dynamic system that requires a complicated control law. This problem has been a long-standing concern for space missions. The purpose of this research is two fold. The first part is to investigate and develop nonlinear Takagi-Sugeno (T-S) fuzzy model-based controllers for a spacecraft with fuel sloshing considering the input constraints on the actuators. It includes i) a fuzzy controller/observer with a minimum upper-bound control input based on the parallel-distributed compensation (PDC) technique, ii) a fuzzy controller/observer based on the linear quadratic regulator (LQR) that uses the premises of the T-S model, and iii) a robust-optimal fuzzy-model-based controller/observer. The designed controllers are globally asymptotically stable and have a satisfactory performance and robustness. The second part of the research is to develop a mathematical model of a spinning spacecraft with fuel sloshing during high-g maneuvers. The equations of motion of a spacecraft with partially-filled multiple-tanks are derived using the Kane’s method. To do this, two spherical pendulums as an equivalent mechanical model of the fuel sloshing are adopted. The effect of the slosh model parameters on the spacecraft nutation angle is studied. The developed model is validated via several numerical simulations

Bi-level optimization based on fuzzy if-then rule

A bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of leader and follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time it is inconvenient to find the veracious relationship between the objective functions of leader, follower and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower, is composed by a block of fuzzy if-then rules. In order to analyze the model, A dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of leader as well as follower. Thus a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. To solve the final problem, we use the lingo software to find the optimal of objective function of follower first and using its solution we optimize the objective function of leader. A numerical example has been solved to signify the computational procedure.</p

Fuzzy Control Strategy for an Anaerobic Wastewater Treatment Process

In this paper, a fuzzy control strategy (FCS) for an anaerobic wastewater treatment process is proposed in order to reject large disturbances on input substrate allowing a high methane production. This strategy is composed of: i) a state observer, which is based on a principal components analysis (PCA) and Takagi-Sugeno (TS) algorithm; it is designed to estimate variables hard to measure: biomass and substrate, ii) proportional-integral (PI) controllers based on a combination of the L/A(logarithm/antilogarithm) and fuzzy approaches; these controllers have variable gains and are designed to regulate bicarbonate in the reactor by two control actions: a base supplying (binc) and dilution rate (D) changes, iii) a TS supervisor which detects the process state, selects and applies the most adequate control action, allowing a smooth switching between open loop and closed loop. Applicability of the proposed structure in a completely stirred tank reactor (CSTR) is illustrated via simulations. The obtained results show that the process works in open loop in presence of small disturbances. For large disturbances, the supervisor allows the control actions to be applied avoiding washout; after that, the process returns to open loop operation. In general, the FCS improves the performances of the anaerobic process and is feasible for application in real processes, since the control scheme shows a good compromise between efficiency and complexity