Design of a parallel distributed fuzzy LQR controller for double-pendulum-type overhead cranes

One of the common industrial structures that are used widely in many harbors and factories and buildings is overhead crane. Overhead cranes are usually operated manually or by some conventional control methods. In this paper, we propose a hybrid controller includes both position regulation and anti-swing control. According to Takagi-Sugeno fuzzy model of an overhead crane, a fuzzy controller designed with parallel distributed compensation and Linear Quadratic Regulation. With the Takagi-Sugeno fuzzy modeling, the nonlinear system is approximated by the combination of several linear subsystems in the corresponding fuzzy state space region. Then by constructing a linear quadratic regulation subcontroller according to each linear subsystem, a parallel distributed fuzzy LQR controller is designed. Further, the stability of the overhead crane with the parallel distributed fuzzy LQR controller is discussed. Simulation results illustrated the validity of the proposed control algorithm and it is compared with a similar method parallel distributed fuzzy controller.