Takagi-Sugeno Fuzzy Control Based on Robust Stability Specifications

In the design of modern and classical control systems, the first step is establish a suitable mathematical model to describe the behavior of the controlled plant (Takagi & Sugeno, 1985; Ying et al., 1990). However, in practical situations, such a requirement is not feasible because in practical control systems the plants are always nonlinear systems, which makes this task analytically unfeasible for complex systems (Cetin &Demir, 2008; Dong et al., 2009; Park et al., 2007; Pelladra et al., 2009). This fact has motivated the use of fuzzy logic in the development of fuzzy model based control systems. In this context, The Fuzzy Systems have been widely used due to flexibility of its structure to incorporate linguistic information (knowledge expert) with numerical information (sensors and actuators measurements), as well as its functional efficiency as universal approximator capable of treat adequately uncertainties, parametric variations and nonlinearity of the plant to be controlled (Castro-Sitiriche et al., 2008; Cetin & Demir, 2008; Cheng et al., 2009; Ibrahim, 2003; Mishra et al., 2000; Park et al., 2007; Wen-Xu et al., 2009). Modeling is the task that simplifies a real system or complex reality with the aim of easing its understanding. In this sense, an effective approach to the identification of complex nonlinear systems is to partition the available data into subsets and approximate each subset by simple model. Fuzzy Clustering can be used as a tool to obtain a partitioning of experimental data where the transitions between the subsets are gradual rather than abrupt. The potential of fuzzy clustering algorithms to reveal the underlying structures in data can be exploited, not only for classification and pattern recognition in the available data, but also for the reduction of complexity in modeling and identification. One of the major applications of the model is the design of a controller for the true system. The ultimate goal of a control-system is to build a system that will work in the real environment. Since the real environment may change with time (parametric variations and nonlinearity) or operating conditions may vary (noise and disturbance), the control system must be able to withstand these variations (Petros & Sun, 1996). This fact has motivated, since 1980’s, the proposal of new methodologies for design of robust controllers. In this context, fuzzy systems have been widely used in robust controllers design (Barton, 2004; Serra & Boturra, 2006; Silva & Serra, 2009; Tanaka & Sugeno, 1993; Zhan, 2010). In this paper a robust fuzzy control design based on gain and phase margins specifications for nonlinear systems, in the continuous time domain, Takagi-Sugeno Fuzzy Control Based on Robust Stability Specifications 2