The control of the ITER tokamak unstable vertical position is considered in the presence of actuator saturation. Linearised models of the ITER system all share the feature of a single unstable pole (attributable to the vertical instability) and a large number of stable poles. The aim of this work is to improve the existing controller in the sense of increasing the region of attraction while retaining the local performance around the origin. For second order systems with one unstable and one stable pole under saturated input, it has been shown that these requirements can be achieved using an additional nonlinear term in the existing linear control law. In this work, we discuss the extension to this nonlinear control law for higher order systems like the ITER tokamak. The validation of this new controller is done via simulations.