Design and Tuning of Distributed Importance-Based Fuzzy Logic Controller for Two-Link Rigid-Flexible Manipulator

Abstract

Fuzzy logic control has been widely used in many industrial processes due to its computationally efficient and robust characteristics. In many applications, verbalization of expert-knowledge can be easily used to design a fuzzy logic controller (FLC). On the other hand, other applications with many variables and complex mathematical model offer challenges to fuzzy logic control. Multi-link flexible manipulators belong to this category. An earlier work, [1], presented a distributed importance-based FLC for a single-link flexible manipulator. This paper extends this idea to a two-link rigid-flexible manipulator that moves in a vertical plane where the gravity field is active. The structure of the proposed controller is based on evaluating the importance degrees of the variables of the system, over its range of operation, to consider the coupling effects between the rigid and the flexible links. Variables with higher importance degrees are grouped together while variables with lesser importance degrees may be deleted to simplify the design of the controller. After determining the importance degrees of the variables, a distributed controller composed of four two-input one-output FLC’s is created. Unlike the single-link flexible manipulator, the fuzzy rules of the distributed FLC for the two-link rigid-flexible manipulator cannot be written by an expert based on intuition and observation of the inertial system due to the complexity of the manipulator and the coupling effect of its variables. To solve this problem, an importance-based linear controller that has the same input-output structure as that of distributed importance-based FLC is constructed to help write the fuzzy rules of the distributed FLC. Fuzzy rules of the distributed FLC are then selected to mimic the performance of the corresponding linear controllers. To compare the performance of the distributed importance-based FLC with that of importance-based linear controller, these two controllers are tuned using nonlinear programming by varying the gains of the importance-based linear controller and the parameters of membership functions of the variables in the distributed importance-based FLC. Robustness of each of the controllers after tuning is tested by varying the payload of the manipulator. The two importance-based controllers are simulated and compared.