This paper introduces the ship dynamic positioning (DP) control problem, details a non-linear multivariable simulation model for a floating production, storage and offloading (FPSO) vessel and proposes a new model-free linear method for rapid tuning of the DP multivariable PID controllers. Three existing model free tuning methods are compared for their performance and stability properties and a procedure is developed for rapid tuning of DP control systems. Controller structures are discussed and the methods are applied to the simulation model at an operating point, thereby justifying the use of linear tuning techniques. It is shown that some of the methods are appropriate and that it is straightforward to produce a controller of acceptable performance within the thruster input constraints of the ship. Simulation results are presented and analysed. The proposed methods are particularly useful for the cases where an adaptive DP control system is required to meet the desired performance.