Ralph Berstecher

An adaptive fuzzy sliding-mode controller

This paper deals with a new adaptive fuzzy sliding-mode controller and its application to a robot manipulator arm. The theory for this approach and for the heuristics-based linguistic adaptation is presented, and a mathematical description is derived. Furthermore, an application of this adaptive controller for a two-link robot arm is shown. The obtained results show the high efficiency of the new controller type.

Direct Fuzzy Adaptation of a Fuzzy Controller

Abstract Sliding-mode fuzzy controllers are often used in an industrial environment because of their robustness. Nevertheless, the optimization of fuzzy controllers in general is difficult. By using fuzzy control principles for the definition of an adaptation algorithm, linguistically represented system knowledge as well as heuristic design principles can be considered and implemented in order to adapt the nonlinear input output characteristic of the sliding-mode fuzzy controller. The proposed linguistic adaptation strategy can be described analytically and classic Lyapunov theory is applied to prove convergence. Simulation results for an inverted pendulum with time-varying pendulum length illustrate the effectiveness of the adaptation algorithm.

Adaptive Sliding-Mode Control of the Absolute Gain

Abstract Nonlinear systems controlled by sliding-mode controllers exhibit robust behaviour towards model uncertainties and noise. However, the optimal estimation of the gain of the non-continuous control part remains an open problem. In general, one would tend to estimate a too large gain in order to reject all possible uncertainties, leading to an excessive control activity. Therefore, in this paper an adaptive sliding-mode controller automatically adjusting this gain is designed. No a priori knowledge about the estimation error is assumed. As a result, the gain approaches the optimal value. The adaptation is illustrated for a chaotic pendulum and the Duffing oscillator.

Construction of a linguistic adaptation law for a fuzzy sliding-mode controller

Fuzzy controllers are often used in the standard form of fuzzy sliding-mode controllers. The tuning of the numerous possible parameters of the fuzzy controller for optimal behaviour is difficult and time-consuming. Linguistically represented system knowledge as well as heuristic design principles of a control expert are expressed by fuzzy control principles, and are implemented in order to adapt the nonlinear input output characteristic of the fuzzy sliding-mode controller. Here, a detailed outline for the implementation of the linguistically defined adaptation law is given. Analysing the adaptation strategy, the adaptation algorithm itself proves to be of fuzzy sliding-mode controller type. Using Lyapunov theory, an analytic expression relating system uncertainties with parameter exactness is given. Simulation results for an inverted pendulum with time-varying pendulum length illustrate the effectiveness of the adaptation algorithm.

An adaptive fuzzy sliding-mode controller for a robot arm

Abstract This paper deals with a new adaptive sliding mode controller and its practical application to a robot manipulator arm. The theory for this new fuzzy sliding mode controller approach and for the heuristics-bayed linguistic adaptation is presented and a mathematical description is derived. Furthermore the application of this adaptive controller is shown for a simulated two-link robot arm and for the real time operation of a mobile three-link robot arm, respectively. The obtained results show the high efficiency of the new controller type.