The existence of a non-zero neutron electric dipole moment (nEDM) would violate parity and time-reversal symmetry. Extensions to the Standard Model predict the nEDM to be 10^{-26} -- 10^{-28} e·cm. The current best upper limit is 3.0x10^{-26} e·cm. The nEDM experiment at TRIUMF is aiming to improve the precision of the measurement to the 10^{-27} e·cm level. The experiment requires a very stable (< pT) and homogeneous (< nT/m) magnetic field (B_0) within the measurement cell.

This thesis concerns the development of active magnetic shielding to stabilize the external magnetic field by compensation coils using a prototype active magnetic shield at The University of Winnipeg. Experimental results are compared with simulations of the behaviour of the active magnetic compensation system. The quasi-static magnetic behavior of the system, including the effect of the passive magnetic shields, is included in this simulation using finite element analysis (FEA). These results are then used to create a full time-dependent simulation of the multi-dimensional feedback system response. A major challenge faced in the development of the system was a slow current response, even though the magnetic response was rapid. This is now understood to be due to having too much freedom in assigning the currents in the system. Reducing the degrees of freedom in the coil system, as an alternate strategy to Tikhonov regularization, solved this problem in a way that hasn't been previously discussed in the literature. Several recommendations are made to improve the performance in future realizations of the system at TRIUMF.