Fusion power may be seen as the energy of the future in the sense that it composes a potentially clean, cheap and unlimited power source that would reduce the worldwide dependency on non-renewable energies. Nevertheless, while nowadays the fusion reaction process itself has been achieved, significant net power has not yet been obtained, since the generated plasma needs to remain in particular pressure and temperature conditions. For this purpose, the plasma has to be confined. To do so, one of the solutions is to use a fusion reactor device that creates magnetic fields in a toroidal chamber, called Tokamak reactor. The main issue of Tokamak reactors is the presence of plasma instabilities, which provoke the fusion reaction decay and, in consequence, a reduction in the pulse duration. To maintain this pulse duration as long as possible, the use of robust and fast controllers is mandatory due to the unpredictability and the small time constant of the plasma behavior. In this context, this article focuses on improving the controllability of the plasma current, a relevant control variable, crucial during the plasma heating and confinement processes. In particular, two new robust control schemes based on sliding surfaces, namely, a Sliding Mode Controller (SMC) and a Supertwisting Controller (STC) are presented and applied to the plasma current control problem. In order to test the validity and goodness of the proposed controllers, their behavior is compared to that of the traditional PID schemes applied in these systems, using the RZIp model for the TCV (Tokamak a Configuration Variable) reactor. The obtained results are very promising, leading to consider these controllers as strong candidates to improve the performance of the PID-based controllers usually employed in this kind of systems.