A method of controlling an operating temperature of a first combustion zone of a combustor of a rotary machine includes determining a current operating temperature and a target operating temperature of a first combustion zone using a digital simulation. The method further includes determining a derivative of the current operating temperature with respect to a current fuel split using the digital simulation. The fuel split apportions a total flow of fuel to the combustor between the first combustion zone and a second combustion zone. The method also includes calculating a calculated fuel split that results in a calculated operating temperature approaching the target operating temperature. The method further includes channeling a first flow of fuel to the first combustion zone and a second flow of fuel to the second combustion zone.