Variable-Gain Controllers for Nonlinear Systems Using the T–S Fuzzy Model

Abstract

This correspondence proposes two novel control schemes with variable state-feedback gain to stabilize a Takagi-Sugeno (T-S) fuzzy system. The T-S fuzzy model is expressed as a linear plant with nonlinear disturbance terms in both schemes. In controller I, the T-S fuzzy model is expressed as a linear plant around a nominal plant arbitrarily selected from the set of linear subsystems that the T-S fuzzy model consists of. The variable gain then becomes a function of a gain parameter that is computed to neutralize the effect of disturbance term, which is, in essence, the deviation of the actual system dynamics from the nominal plant as the system traverses a specific trajectory. This controller is shown to stabilize the T-S fuzzy model. In controller II, individual linear subsystems are locally stabilized. Fuzzy blending of individual control actions is shown to make the T-S fuzzy system Lyapunov stable. Although applicability of both control schemes depends on the norm bound of unmatched state disturbance, this constraint is relaxed further in controller II. The efficacy of controllers I and II has been tested on two nonlinear systems.

Regulación Saturada con Ganancia Variable Derivativa de Robots Manipuladores

“…En Kumar et al (2006) se presentan dos nuevos controladores de ganancia variable demostrando estabilidad en el sentido de Lyapunov resolviendo la ecuación de Lyapunov. En el primer controlador se presenta un modelo difuso Takagi-Sugeno como una planta lineal, para el segundo controlador se presentan varios subsistemas lineales que son localmente estabilizados.…”

Unbounded regulators with variable gains for a direct-drive robot manipulator

“…Two variable-gain controllers were presented in [14]. The first fuzzy controller is designed in order to cancel the effects of variable disturbance which is, in essence, the deviation of the actual system dynamics from the nominal plant as the system traverses a specific trajectory.…”

An Indirect Adaptive Fuzzy Control Scheme for a Class of Nonlinear Systems

“…Subsequent works [12,13] follow a similar approach with emphasis being given to relaxing the condition for stability and controller design. In another approach, variable gain controllers have been proposed [14] which relaxed the constraint imposed by a fixed gain state feedback controller [15]. Latterly, various fuzzy observer based Manuscript received August 29, 2014; revised February 12, 2015; accepted May 22, 2015.…”

“…Two major steps in the T-S fuzzy model based controller design are first, identifying the local linear models, and second, designing an appropriate controller for the global system. In the literature, the local model parameters are identified either by linearizing the nonlinear system dynamics or from the input-output data set using a fuzzy neural network [14]. The controller design issue boils down to finding out a stability condition so that a convex combination of local linear controllers can stabilize the overall system [12,14].…”