Design and simulation of a Kalman filter for a rigid plasma electromagnetic model on TCV

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