Stable fuzzy control for a class of nonlinear systems

Abstract

The paper investigates the construction of fuzzy controllers for a class of nonlinear systems. Our approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a linguistic manner. The proposed method enables the designer systematically to derive the rule base of the control. We implement the scheme to both tracking and stabilizing control for a two-link rigid robot and overhead crane load swing. Numerical tests show the feasibility of the proposed control scheme.

An Adaptive Fuzzy Sliding Mode Control Scheme for Robotic Systems

“…Initially, the arm is assumed at rest, i.e. tests, the learning rates were adjusted as 1 [15,1.5] T   and 2 [45,6] T  …”

“…have been itiated as ˆ[ 300, 100] T E    . As mentioned earlier, the sign (6) an been replaced by the saturation function with…”

“…The control system has been initiated with the same initial conditions (i.e. e and e  ) followed did with respect to the AFSMC, the sign function in (6) has been replaced by the saturation function. The gain K of the hitting controller gain in (6) (10) were selected as follows: ˆ5 M I whic  h means that it is a time-independent matrix and 0.5 0 2 0 0.5 1…”

“…Payload changes and/or its exact position in the end effector are examples of uncertainties. The control methodologies that can be used are ranging from classical adaptive control and robust control to the new methods that usually combine good properties of the classical control schemes to fuzzy [1,2], genetic algorithms [3], neuro-fuzzy [4,5] and neural network [6] based approaches. Classical adaptive control of manipulators requires a precise mathematical model of the system's dynamics and the property of linear parameterization of the system's uncertain physical parameters [7].…”

“…Examples are numerous; see [13] for instance. While non-adaptive fuzzy control has proven its value in some applications [1,2,14], it is sometimes difficult to specify the rule base for some plants, or the need could arise to tune the rule-base parameters if the plant changes. This provides the motivation for adaptive fuzzy control, where the focus is on the automatic on-line synthesis and tuning of fuzzy controller parameters.…”