Thermonuclear controlled fusion is a promising answer to the current energy and climate issues, providing a safe carbon-free source of energy which is virtually inexhaustible. In magnetic confinement thermonuclear fusion based on tokamak reactors, hydrogen fuel in the state of plasma is confined using a system of external and self-generated magnetic fields. This thesis contributes to the development of magnetic confinement fusion research by applying techniques derived from control engineering to designing magnetic controllers for tokamak plasmas. Specifically, a new design for feedback control of plasma shape and position in the TCV tokamak is provided, and its efficacy is studied in dedicated simulations and experiments. Elongated plasmas lead to improved plasma performance in tokamaks, which is key to sustaining fusion conditions in reactors. The required magnetic field for shaping the plasma column however results in an unstable equilibrium that makes feedback control of the vertical plasma position mandatory. Active stabilization of the axisymmetric plasma vertical instability is a standard feature of elongated tokamaks and will be a fundamental feature in the ITER magnetic control system, since a loss of vertical control and the subsequent plasma disruption can lead to unacceptable heat loads on the plasma facing components. The TCV tokamak is the ideal benchmark for investigating the effect of plasma shaping on tokamak physics and performance, with its system of 16 independently powered poloidal field coils and a vessel with an elongated cross section. Shape and position control are coupled problems in TCV as they share the same poloidal field coils as actuators, requiring a multivariable approach to designing magnetic controllers. In this thesis, controller design for TCV is based on a model for the coupled plasma-vessel-coils electromagnetic dynamics: the RZIp model. In this axisymmetric model, the plasma current distribution is fixed but is free to move radially and vertically in the poloidal plane of a toroidal reference frame. An extension to this model is suggested, relaxing the assumption of rigid displacement in the radial direction to include plasma shape deformation and leading to a semi-rigid RZIp model which better fits numerical equilibria. An improvement to the existing algorithm for shape and position control in TCV is then proposed. In this new approach, tuning of the plasma position controller, in charge of vertical stabilization, can be performed independently of the shape controller, which itself acts on a stable system. Static decoupling is achieved and the shape controller is designed on the basis of an improved model for the plasma deformation, which includes the plasma contribution to the static magnetic flux perturbation. Simulations in closed loop with the RZIp model are provided to evaluate several optimized schemes. Finally, the vertical controller is optimized including the plasma dynamics as part of the controller design. Structured H-infinity, extending classical H-infinity to fixed-structure control systems, is applied to obtain a controller using all available coils for position control, and in particular a coil combination optimized for vertical stabilization. Closed-loop performance improvement is demonstrated in dedicated TCV experiments, confirming the simulation results and paving the way for the routine integration of the optimized position and shape controller in TCV discharges.