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This thesis presents a simulation of the control system for Laser Guide Star (LGS) wavefront sensing of the Narrow Field Infrared Adaptive Optics System (NFIRAOS) which will be the Adaptive Optics (AO) system on the Thirty Meter Telescope. The control system is multirate and combines data from multiple sources, both natural and artificial, to provide wavefront correction. Artificial guide stars are generated by exciting atoms in the mesospheric sodium (Na) layer. The characteristics of the Na layer have been examined; its variability, altitude and thickness will lead to false atmospheric turbulence measurements by AO systems integrated with Extremely Large Telescopes. A periodically updated constrained matched filter algorithm has been implemented in the control system simulation in order to gauge its ability to mitigate these effects. The control system has also been implemented on the University of Victoria LGS Test Bench which reproduces wavefront measurements as they will be made by several of the wavefront sensors of NFIRAOS. The simulation has provided insight into the stability of the proposed control system and allowed necessary improvements to be made. It has been shown to meet the requirements of stability over long term with fast convergence. The matched filter algorithm has been shown to effectively reject the Na layer fluctuations both in simulation and on the test bench.