Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

Using the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.Web of Science71110

PSO BASED TAKAGI-SUGENO FUZZY PID CONTROLLER DESIGN FOR SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR

A permanent magnet synchronous motor (PMSM) is one kind of popular motor. They are utilized in industrial applications because their abilities included operation at a constant speed, no need for an excitation current, no rotor losses, and small size. In the following paper, a fuzzy evolutionary algorithm is combined with a proportional-integral-derivative (PID) controller to control the speed of a PMSM. In this structure, to overcome the PMSM challenges, including nonlinear nature, cross-coupling, air gap flux, and cogging torque in operation, a Takagi-Sugeno fuzzy logic-PID (TSFL-PID) controller is designed. Additionally, the particle swarm optimization (PSO) algorithm is developed to optimize the membership functions' parameters and rule bases of the fuzzy logic PID controller. For evaluating the proposed controller's performance, the genetic algorithm (GA), as another evolutionary algorithm, is incorporated into the fuzzy PID controller. The results of the speed control of PMSM are compared. The obtained results demonstrate that although both controllers have excellent performance; however, the PSO based TSFL-PID controller indicates more superiority

Parallel distribution compensation PID based on Takagi-Sugeno fuzzy model applied on egyptian load frequency control

This paper presents a new technique for a Takagi-Sugeno (TS) fuzzy parallels distribution compensation-PID'S (TSF-PDC-PID'S) to improve the performance of Egyptian load frequency control (ELFC). In this technique, the inputs to a TS Fuzzy model are the parameters of the change of operating points. The TS Fuzzy model can definite the suitable PID control for a certain operating point. The parameters of PID'S controllers are obtained by ant colony optimization (ACO) technique in each operating point based on an effective cost function. The system controlled by the proposed TSF-PDC-PID’S is investigated under different types of disturbances, uncertainty and parameters variations. The simulation results ensure that the TSF-PDC-PID'S can update the suitable PID controller at several operating points so, it has a good dynamic response under many types of disturbances compared to fixed Optimal PID controller

Optimal Fuzzy Model Construction with Statistical Information using Genetic Algorithm

Fuzzy rule based models have a capability to approximate any continuous function to any degree of accuracy on a compact domain. The majority of FLC design process relies on heuristic knowledge of experience operators. In order to make the design process automatic we present a genetic approach to learn fuzzy rules as well as membership function parameters. Moreover, several statistical information criteria such as the Akaike information criterion (AIC), the Bhansali-Downham information criterion (BDIC), and the Schwarz-Rissanen information criterion (SRIC) are used to construct optimal fuzzy models by reducing fuzzy rules. A genetic scheme is used to design Takagi-Sugeno-Kang (TSK) model for identification of the antecedent rule parameters and the identification of the consequent parameters. Computer simulations are presented confirming the performance of the constructed fuzzy logic controller

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228