Full power scale back-to-back power converter PMSG wind turbine system, with direct-drive configuration, is an attractive solution, particularly for off-shore wind energy applications. For such systems,(nonlinear) direct control, which requires neither a modulation process nor cascaded linear controllers, but will operate the system at very high control dynamics, is a very promising control class. In this work, we reviewed and experimentally assessed the classical(C-), the duty-optimal(DO-), the ripple-reduced(RR-) and the multi-vector direct model predictive torque control(MV-DMPTC) solutions to deal with the generator side control of grid-tied full power scale back-to-back power converter PMSG wind turbine systems. Their theoretical background, realizations and control performances are presented and discussed. The realizations and experimental assessments of all the discussed control approaches are carried out with a fully FPGA based real-time controller, at a lab-constructed test-bench. The resource usage and implementation complexity are provided. Comprehensive evaluation results are given at the end.