This report describes the procedure of the design and simulation of a Kalman
observer for control of the vertical plasma position in TCV. The design of the
observer is based on knowledge of a linearised system representation of the tokamak
with its surrounding active poloidal eld coil systems and vessel wall. One
of the pillars for this linearised system are the circuit equations for the plasma
with its surroundings. Other important components of the model are the vertical
and radial force balance equations. Together these equations lead to a state
space representation with 19 active coil voltages as inputs and 95 measurements
as outputs. The measurements consist of the 19 active coil currents obtained
from current transducers inside the coils, 38 poloidal eld loops which measure
the local magnetic
ux and 38 magnetic eld probes that measure the magnetic
eld at the probe location. Due to the elongated plasma form the vertical
plasma position is an unstable variable that needs to be controlled. With the
obtained state space model a Proportional Derivative controller is designed that
stabilizes the vertical plasma position. The input for the PD controller is the
vertical plasma position. The plasma position cannot be measured directly and
has to be reconstructed using an observer. Currently this plasma position is being
reconstructed using a static least-squares observer that uses a priori system
equilibrium knowledge. This observer however is very sensitive for measurement
noise. For high noise levels the estimated vertical position from the observer has
a noisy character where the absolute value of the time derivative is very high.
Since this is an input for the controller the reconstruction has to be improved.
Here the dynamic observer comes into play.
These observers reconstruct states using the measurement outputs, the system
inputs and system knowledge. A dynamical observer system is constructed
which has the state estimates as its own states. When designed appropriately
the state estimates asymptotically converge to the true state values. However,
when the system contains noise, the design of the dynamical observer system becomes
more dicult. The Kalman observer is an dynamical observer designed
using a method that accounts for the noise characteristics and the resulting
observer optimally reconstructs the system states. Simulation of this Kalman
observer indeed shows a good state reconstruction and appropriate control of
the vertical plasma position