Abstract: An example of utilizing the modern control theory is discussed in this paper. The controlled object is an electric furnace with two independent heating windings. Two thermocupls are used to measure the furnace temperature at two different, points. The tccuracy of controlling the temperatures of the upper and lower portion of the furnace is better. than 2C. The object is treated as a LQG system with two varirbles. The mathematical model consists of dynamic mathematical model, a Kalman filter, an optimum state feedback and the self adapting set point following computation. This control system has been used in controlling more thtn seventy similar furnaces with a small process-control computer.