The plasma vertical position system in a tokamak device can be open-loop unstable with time-varying dynamics, such that the instability increases with system dynamical changes. Time-varying unstable dynamics makes the plasma vertical position a particularly difficult one to control with traditional fixed-coefficient controllers. A self-tuning technique offers a new solution of the plasma vertical position control problem by an adaptive control approach. Specifically, the self-tuning controller automatically tunes the controller parameters without an a priori knowledge of the system dynamics and continuously tracks dynamical changes within the system, thereby providing the system with auto-tuning and adaptive tuning capabilities. An overview of the self-tuning methods is given, and their applicability to a simulation of the Joint European Torus (JET) vertical plasma position system is illustrated. Specifically, the applicability of pole-assignment and generalized predictive control self-tuning methods to the vertical plasma position system is demonstrated.