Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

This study examines the effectiveness of four different fuzzy logic controllers in self-balancing wheelchairs. The controllers under consideration are Type-1 Takagi-Sugeno-Kang (TSK) FLC, Interval Type-2 TSK FLC, Type-1 Mamdani FLC, and Interval Type-2 Mamdani FLC. A MATLAB-based simulation environment serves for the evaluation, focusing on key performance indicators like percentage overshoot, rise time, settling time, and displacement. Two testing methodologies were designed to simulate both ideal conditions and real-world hardware limitations. The simulations reveal distinct advantages for each controller type. For example, Type-1 TSK excels in minimizing overshoot but requires higher force. Interval Type-2 TSK shows the quickest settling times but needs the most force. Type-1 Mamdani has the fastest rise time with the lowest force requirement but experiences a higher percentage of overshoot. Interval Type-2 Mamdani offers balanced performance across all metrics. When a 2.7 N control input cap is imposed, Type-2 controllers prove notably more efficient in minimizing overshoot. These results offer valuable insights for future design and real-world application of self-balancing wheelchairs. Further studies are recommended for the empirical testing and refinement of these controllers, especially since the initial findings were limited to four-wheeled self-balancing robotic wheelchairs

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

Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions

Esta tesis considera un enfoque basado en Lyapunov para el análisis y control de sistemas no lineales cuyas ecuaciones dinámicas son reescritas como un modelo Takagi-Sugeno o uno polinomial convexo. Estas estructuras permiten resolver problemas de control mediante técnicas de optimización convexa, más concretamente desigualdades matriciales lineales y suma de cuadrados, que son eficientes herramientas desde un punto de vista computacional. Después de proporcionar una visión general básica del estado actual en el campo de los modelos Takagi-Sugeno, esta tesis aborda cuestiones sobre las funciones de Lyapunov por trozos, dependiente de parámetros e integral de línea, con las siguientes contribuciones: Un algoritmo mejorado para estimaciones del dominio de atracción de sistemas no lineales para sistemas de tiempo continuo. Los resultados se basan en funciones de Lyapunov por trozos, desigualdades matriciales lineales y argumentaciones geométricas; enfoques basados en conjuntos de nivel en la literatura previa se han mejorado significativamente. Una función Lyapunov generalizada dependiente de parámetros para la síntesis de controladores para sistemas Takagi-Sugeno. El enfoque propone una ley de control multi-índice que retroalimenta la derivada del tiempo de las funciones de membresía del modelo Takagi-Sugeno para anular los términos que causan localidad a priori en el análisis de Lyapunov. Una nueva función integral de Lyapunov para el análisis de estabilidad de sistemas no lineales. Estos resultados generalizan aquellos basados en funciones de Lyapunov integral de línea al marco polinomial; resulta que los requisitos de independencia del camino pueden ser anulados por una definición adecuada de una función Lyapunov con términos integrales.This thesis considers a Lyapunov-based approach for analysis and control of nonlinear systems whose dynamical equations are rewritten as a Takagi-Sugeno model or a convex polynomial one. These structures allow solving control problems via convex optimisation techniques, more specifically linear matrix inequalities and sum-of-squares, which are efficient tools from the computational point of view. After providing a basic overview of the state of the art in the field of Takagi-Sugeno models, this thesis address issues on piecewise, parameter-dependent and line-integral Lyapunov functions, with the following contributions: An improved algorithm to estimate the domain of attraction of nonlinear systems for continuous-time systems. The results are based on piecewise Lyapunov functions, linear matrix inequalities, and geometrical argumentations; level-set approaches in prior literature are significantly improved. A generalised parameter-dependent Lyapunov function for synthesis of controllers for Takagi-Sugeno systems. The approach proposed a multi-index control law that feeds back the time derivative of the membership function of the Takagi-Sugeno model to cancel out the terms that cause a priori locality in the Lyapunov analysis. A new integral Lyapunov function for stability analysis of nonlinear systems. These results generalise those based on line-integral Lyapunov functions to the polynomial framework; it turns out path-independency requirements can be overridden by an adequate definition of a Lyapunov function with integral terms.Aquesta tesi considera un enfocament basat en Lyapunov per a l'anàlisi i control de sistemes no lineals les equacions dinàmiques dels quals són reescrites com un model Takagi-Sugeno o un de polinomial convex. Aquestes estructures permeten resoldre problemes de control mitjançant tècniques d'optimització convexa, més concretament desigualtats matricials lineals i suma de quadrats, que són eines eficients des d'un punt de vista computacional. Després de proporcionar una visió general bàsica de l'estat actual en el camp dels models Takagi-Sugeno, aquesta tesi aborda qüestions sobre les funcions de Lyapunov per trossos, dependent de paràmetres i integral de línia, amb les següents contribucions: Un algoritme millorat per a estimar el domini d'atracció de sistemes no lineals per a sistemes de temps continu. Els resultats es basen en funcions de Lyapunov per trossos, desigualtats matricials lineals i argumentacions geomètriques; enfocaments basats en conjunts de nivell en la literatura prèvia s'han millorat significativament. Una funció Lyapunov generalitzada dependent de paràmetres per a la síntesi de controladors per a sistemes Takagi-Sugeno. L'enfocament proposa una llei de control multi-índex que retroalimenta la derivada del temps de les funcions de membres del model Takagi-Sugeno per anul·lar els termes que causen localitat a priori en l'anàlisi de Lyapunov. Una nova funció integral de Lyapunov per a l'anàlisi d'estabilitat de sistemes no lineals. Aquests resultats generalitzen aquells basats en funcions de Lyapunov integral de línia al marc polinomial; resulta que els requisits d'independència del camí poden ser anul·lats per una definició adequada d'una funció Lyapunov amb termes integrals.González Germán, IT. (2018). Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/101282TESI

Contributions to nonlinear system modelling and controller synthesis via convex structures

Esta tesis discute diferentes metodologías de modelado para extraer mejores prestaciones o resultados de estabilidad que aquéllas que el modelado convencional basado en sector no-lineal de sistemas Takagi-Sugeno (también denominados cuasi-LPV) es capaz de producir. En efecto, incluso si las LMIs pueden probar distintas cotas de prestaciones o márgenes de estabilidad (tasa de decaimiento, $\mathcal H_\infty$, etc.) para sistemas politópicos, es bien conocido que las prestaciones probadas dependen del modelo elegido y, dado un sistema no-lineal, dicho modelo politópico no es único. Por tanto, se presentan exploraciones hacia cómo obtener el modelo que es menos perjudicial para la medida de prestaciones elegida. Como una última contribución, mejores resultados son obtenidos mediante la extensión del modelado politópico Takagi-Sugeno a un marco de inclusiones en diferencias cuasi-convexas con planificación de ganancia. En efecto, una versión sin planificación de ganancia fue propuesta por un equipo de investigadores de la Universidad de Sevilla (Fiaccini, Álamo, Camacho) para generalizar el modelado politópico, y esta tesis propone una version aún más general de algunos de dichos resultados que incorpora planificación de ganancia.This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield. Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented. As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.Aquesta tesi discuteix diferents metodologies de modelatge per extreure millors prestacions o resultats d'estabilitat que aquelles que el modelatge convencional basat en sector no-lineal de sistemes Takagi-Sugeno (també anomenats quasi-LPV) és capaç de produir. En efecte, fins i tot si les LMIs poden provar diferents cotes de prestacions o marges d'estabilitat (taxa de decaïment, $\mathcal H_\infty$, etc.) per a sistemes politòpics, és ben conegut que les prestacions provades depenen del model triat i, donat un sistema no-lineal, el dit model politòpic no és únic. Per tant, es presenten exploracions cap a com obtenir el model que és menys perjudicial per a la mesura de prestacions triada. Com una darrera contribució, millors resultats són obtinguts mitjançant l'extensió del modelatge politòpic Takagi-Sugeno a un marc d'inclusions en diferències quasi-convexes amb planificació de guany. En efecte, una versió sense planificació de guany va ser proposada per un equip d'investigadors de la Universitat de Sevilla (Fiaccini, Álamo, Camacho) per a generalitzar el modelatge politòpic, i aquesta tesi proposa una versió més general d'alguns d'aquests resultats que incorpora planificació de guany.Robles Ruiz, R. (2018). Contributions to nonlinear system modelling and controller synthesis via convex structures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/100848TESI

Integrating Servo-Pneumatic Actuator with Ball Beam System based on Intelligent Position Control

The purpose of this paper is to design a controller that can control the position of the cylinder pneumatic stroke. This work proposes two control approaches, Proportional-Integral-Derivative Fuzzy Logic (Fuzzy-PID) controller and Proportional-Derivative Fuzzy Logic (PD-Fuzzy) controller for a Servo-Pneumatic Actuator. The design steps of each controller implemented on MATLAB/Simulink are presented. A model based on position system identification is used for the controller design. Then, the simulation results are analyzed and compared to illustrate the performance of the proposed controllers. Finally, the controllers are tested with the real plant in real-time experiment to validate the results obtained by simulation. Results show that PD-Fuzzy controller offer better control compared to Fuzzy-PID. A Pneumatic Actuated Ball & Beam System (PABBS) is proposed as the application of the position controller. The mathematical model of the system is developed and tested simulation using Feedback controller (outer loop)-PD-Fuzzy controller (inner loop). Simulation result is presented to see the effectiveness of the obtained model and controller. Results show that the servo-pneumatic actuator can control the position of the Ball & Beam system using PD-Fuzzy controller

Stable and robust fuzzy control for uncertain nonlinear systems

Author name used in this publication: F. H. F. LeungAuthor name used in this publication: P. K. S. Tam2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

High dimentional neural fuzzy controller for nonlinear systems

De nos jours, la théorie de contrôle joue un rôle significatif dans presque tous les domaine de la science et de l'ingénierie. Les contrôleurs linéaires PID sont les applications principales de la théorie de contrôle, et ils se basent sur les systèmes de contrôle simples. Mais beaucoup de vrais systèmes possèdent des caractéristiques non-linéaires. Dans la pratique, il est nécessaire de faire beaucoup de linéarisations. Quand nous employons le contrôleur classique dans un système non-linéaire fortement complexe, les difficultés augmentent exponentiellement. Pour éviter les imperfections, on peut employer des contrôleurs flous. Le contrôleurs flous se basent sur le système de connaisance. Ce sont des outils importants dans le domaine de l'automatique. Ils possèdent beaucoup plus d'avantages que les contrôleurs classiques"PID", mais ils ont besoin d'experts pour concevoir les règles de base. La limite principale des contrôleurs flous est la difficulté d'établir les règles de base. Maintenant, beaucoup de recherches sont consacrées à la fusion des réseaux de neurones et de systèmes flous dans une nouvelle structure (les réseaux de neuro-floue). Cette approche combine les avantages de deux paradigmes puissants dans une capsule simple, et fournit un cadre puissant pour extraire des règles floues des données numériques. Cependant, cette technologie n'est pas parfaite. Il reste quelques difficultés: beaucoup de règles floues sont nécessaires, les algorithmes sont complexes et la fiabilité est basse (Par exemple, pour un même modèle ou fonction, les résultats dépendent des ensembles d'apprentissage). Pour éviter les difficultés, ce mémoire présente une nouvelle méthode, appelée"inférence neuro-floue de haute-dimension". L'idée fondamentale de cette méthode proposé est de considérer chaque donné dans ce système comme point avec la haute dimension. Chaque dimension d'entrée sera traitée en même temps dans les mêmes sous-ensembles de haute dimension. L'algorithme proposé a été examiné sur différentes applications, et les résultats ont été comparés aux données éditées sur trois problèmes de repère. Cet algorithme est simple à employer, et les résultats expérimentaux prouvent que le nombre de faisceaux exigés est inférieur à ceux rapportés dans la littérature. L'exactitude de rendement est bonne dans beaucoup d'applications

Forkloader Position Control for A Mini Heavy Loaded Vehicle using Fuzzy Logic-Antiwindup Control

This paper presents a proposed integrated Takagi-Sugeno-Kang (TSK) type Fuzzy Logic control (TSK-FLC) with Antiwindup elements for a forkloader position control of a Mini Heavy Loaded Forklift Autonomous Guided Vehicle (MHeLFAGV). The study was carried out by modeling TSK-FLC as a close-loop control for the each axis of the fork-lift’s movement. The degree of membership is designed with reference to the system response, in which ultrasonic sensor with 1cm resolution is used. Moreover, the rule base is determined and optimized to deal with microcontroller processing speed. In order to cater for the windup phenomenon, a proportional and integrated antiwindup elements are integrated into the TSK-FLC model. This control strategy consumes less memory and is expected to increase the time response of the control system. The experiment and analysis is done on the actual forkloader unit of MHeLFAGV system. The experiment was done on the vertical axis motion since horizontal motion will have the same characteristic pattern of implementation and characteristic of tuning. The experiment shows that the proposed integrated TSK-FLC with antiwindup elements is able to speed up the time response of the system and eliminate the overshoot as well as oscillation on the forkloader movement

Forkloader Position Control for A Mini Heavy Loaded Vehicle using Fuzzy Logic-Antiwindup Control

This paper presents a proposed integrated Takagi-Sugeno-Kang (TSK) type Fuzzy Logic control (TSK-FLC) with Antiwindup elements for a forkloader position control of a Mini Heavy Loaded Forklift Autonomous Guided Vehicle (MHeLFAGV). The study was carried out by modeling TSK-FLC as a close-loop control for the each axis of the fork-lift’s movement. The degree of membership is designed with reference to the system response, in which ultrasonic sensor with 1cm resolution is used. Moreover, the rule base is determined and optimized to deal with microcontroller processing speed. In order to cater for the windup phenomenon, a proportional and integrated antiwindup elements are integrated into the TSK-FLC model. This control strategy consumes less memory and is expected to increase the time response of the control system. The experiment and analysis is done on the actual forkloader unit of MHeLFAGV system. The experiment was done on the vertical axis motion since horizontal motion will have the same characteristic pattern of implementation and characteristic of tuning. The experiment shows that the proposed integrated TSK-FLC with antiwindup elements is able to speed up the time response of the system and eliminate the overshoot as well as oscillation on the forkloader movement. 

Fuzzy Modeling by Active Learning Method

Non