Fuzzy time optimal control of crane load

A linear time varying state equation is developed for hoisting and lowering operations of a crane system model. After showing that bang-bang control is time optimal and the number of switchings is limited, a set of new control variables, that is a set of switching times, is defined. Through parametrization of switching times, a set of fuzzy control variables are extracted and a simple iterative switching time update scheme is devised to find a set of time optimal switching times. The amounts of switching times adjustment are determined by a set of fuzzy rules and corresponding fuzzy control. For distance control a lookup table is generated by trying different distance indices, collecting the data, and incorporating an interpolation algorithm.