  Modern Tokamaks have evolved from the initial axisymmetric circular plasma
shape to an elongated axisymmetric plasma shape that improves the energy
confinement time and the triple product, which is a generally used figure of
merit for the conditions needed for fusion reactor performance. However, the
elongated plasma cross section introduces a vertical instability that demands a
real-time feedback control loop to stabilize the plasma vertical position and
velocity. At the Tokamak \`a Configuration Variable (TCV) in-vessel poloidal
field coils driven by fast switching power supplies are used to stabilize
highly elongated plasmas. TCV plasma experiments have used a PID algorithm
based controller to correct the plasma vertical position. In late 2013
experiments a new optimal real-time controller was tested improving the
stability of the plasma.
  This contribution describes the new optimal real-time controller developed.
The choice of the model that describes the plasma response to the actuators is
discussed. The high order model that is initially implemented demands the
application of a mathematical order reduction and the validation of the new
reduced model. The lower order model is used to derive the time optimal control
law. A new method for the construction of the switching curves of a bang-bang
controller is presented that is based on the state-space trajectories that
optimize the time to target of the system.
  A closed loop controller simulation tool was developed to test different
possible algorithms and the results were used to improve the controller
parameters.
  The final control algorithm and its implementation are described and
preliminary experimental results are discussed.
