Antonio Javier Barragán

A methodology to design stable nonlinear fuzzy control systems

The stability of nonlinear systems has to be investigated without making linear approaches. In order to do this, there are several techniques based on Lyapunov’s second method. For example, Krasovskii’s method allows to prove the sufficient condition for the asymptotic stability of nonlinear systems. This method requires the calculation of the Jacobian matrix. In this paper, an equivalent mathematical closed loop model of a multivariable nonlinear control system based on fuzzy logic theory is developed. Later, this model is used to compute the Jacobian matrix of a closed loop fuzzy system. Next, an algorithm to solve the Jacobian matrix is proposed. The algorithm uses a methodology based on the extension of the state vector. The developed algorithm is completely general: it is independent of the type of membership function that is chosen for building the fuzzy plant and controller models, and it allows the compound of different membership functions in a same model. We have developed a MATLAB’s 1 function that implements the improved algorithm, together with a series of additional applications for its use. The designed software provides complementary functions to facilitate the reading and writing of fuzzy systems, as well as an interface that makes possible the use of all the developed functions from the MATLAB’s environment, which allows to complement and to extend the possibilities of the MATLAB’s Fuzzy Logic Toolbox. An example with a fuzzy controller for a nonlinear system to illustrate the design procedure is presented. The work developed in this paper can be useful for the analysis and synthesis of fuzzy control systems.

A general methodology for online TS fuzzy modeling by the extended Kalman filter

HighlightsWe present an online fuzzy modeling methodology based on the extended Kalman filter.This methodology can work with noise, is very efficient and completely general.The model can be obtained in a recursive way only based on input-output data.There are no restrictions in the type of membership functions used.Membership functions can even be mixed in the antecedents of the rules. This paper presents an online TS fuzzy modeling general methodology based on the extended Kalman filter. The model can be obtained in a recursive way only based on input-output data. The methodology can work online with the system, properly in the presence of noise, is very efficient computationally and completely general. It is general in the sense theorically there are no restrictions neither in the number of inputs nor outputs, neither in the type nor distribution of membership functions used (which can even be mixed in the antecedents of the rules). Some examples and comparisons with other online fuzzy identification models from signals are provided to illustrate the skill of the online identification of the proposed methodology.

Variable Structure Control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed. The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model. A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven infront of disturbances and noise effects.

Control borroso multivariable basado en heurística. un caso práctico: grúa porta contenedores

In this work, the design of a fuzzy controller based on heuristic is introduced: the knowledge of the plant and the incorporation of the knowledge of an expert (crane operator) allow automating the process of load containers to ships. The plant (container crane) is a nonlinear complex system that, in respect of its fuzzy control, is formed like a multivariable system with 2 input variables and 5 output variables. The advantage of this design methodology is that there is no need to know the mathematical plant model. Simulations display that the closed loop system performance is satisfactory.

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

Graphical abstractFLC-VSC for multivariable nonlinear systems is presented. The main contribution of this work is the development of new functions for chattering elimination without sacrificing invariant properties (Figs. 1 and 2 represent the temporal evolution of s1 and s2 before applying the proposed algorithm and Figs. 3 and 4 after applying the proposed algorithm respectively). Fig. 5 shows fuzzy sets of the switching surface. Fig. 6 shows the transient response of a two-link robot model. Display Omitted HighlightsA fuzzy based variable structure control for multivariable nonlinear systems is presented.A generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, is proposed.The weighting parameters approach is used to optimize local and global modelling capability of T-S fuzzy model.The global stability of the controlled system is guaranteed.A fuzzy switching function is added as an additional fuzzy variable. In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.

Fuzzy optimal control for double inverted pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

Suboptimal Recursive Methodology for Takagi-Sugeno Fuzzy Models Identification

When there is no one mathematical model of the system it is necessary to use modeling techniques based on input–output data (Lopez-Baldan et al. 2002). This process is critical in control systems, since both, system analysis (Garcia-Cerezo et al. 1994; Gordillo et al. 1997; Andujar et al. 2006; Aroba et al. 2007; Al-Hadithi et al. 2007; Jimenez et al. 2009; Andujar and Barragan 2010) and controller design (Wang et al. 1996; Andujar and Bravo 2005; Andujar et al. 2009), require to obtain a model as accurate as possible.

New Concepts for the Estimation of Takagi-Sugeno Model Based on Extended Kalman Filter

This chapter describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi-Sugeno (TS) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that TS identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the TS method because this type of membership function has been widely used during the last two decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of TS identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of TS fuzzy model. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original TS model. Simulation results indicate the potential, simplicity, and generality of the algorithm. In this chapter we prove that these algorithms converge very fast, thereby making them very practical to use.

Integration of Sensors, Controllers and Instruments Using a Novel OPC Architecture

The interconnection between sensors, controllers and instruments through a communication network plays a vital role in the performance and effectiveness of a control system. Since its inception in the 90s, the Object Linking and Embedding for Process Control (OPC) protocol has provided open connectivity for monitoring and automation systems. It has been widely used in several environments such as industrial facilities, building and energy automation, engineering education and many others. This paper presents a novel OPC-based architecture to implement automation systems devoted to R&D and educational activities. The proposal is a novel conceptual framework, structured into four functional layers where the diverse components are categorized aiming to foster the systematic design and implementation of automation systems involving OPC communication. Due to the benefits of OPC, the proposed architecture provides features like open connectivity, reliability, scalability, and flexibility. Furthermore, four successful experimental applications of such an architecture, developed at the University of Extremadura (UEX), are reported. These cases are a proof of concept of the ability of this architecture to support interoperability for different domains. Namely, the automation of energy systems like a smart microgrid and photobioreactor facilities, the implementation of a network-accessible industrial laboratory and the development of an educational hardware-in-the-loop platform are described. All cases include a Programmable Logic Controller (PLC) to automate and control the plant behavior, which exchanges operative data (measurements and signals) with a multiplicity of sensors, instruments and supervisory systems under the structure of the novel OPC architecture. Finally, the main conclusions and open research directions are highlighted.

Stable Fuzzy Control System by Design

The control problem is closely linked to the concept of stability. So much so these concepts are linked, it makes no sense to talk about control systems if these are not stable. When it is desired to design a control system for a nonlinear plant is desirable, and sometimes necessary, do not use linear approximations; since the loss of information that this implies, may cause the resulting system not be stable, or be very locally.