Abstract: A furnace 1 runs while repeating a cycle in which the furnace inside temperature varies along a preset pattern of temperature change with time under the control of a primary controller 12, and adjustment input r being applied to an enlarged system including the furnace 1 and the controller 12 is renewed at the end of each cycle of operation, based partly on output from a dual system with respect to the enlarged system, so as to reduce error between the preset temperature and the furnace inside temperature in the next cycle. The temperatures of heaters 2 of the furnace 1 are controlled by a secondary controller 35, and the set values at the input of the secondary controller 35 are given by output signals (.tau.) from the primary controller 12 which responds to the furnace inside temperatures (y). The order of the dual system is reduced, and the renewal of the adjustment input r is quickened.

Abstract: A temperature control apparatus of a learning type for a furnace which runs repetitively with a certain operating pattern of temperature change with time. The apparatus has a dual system model with respect to an enlarged system consisting of the furnace and its controller. For each cycle of the repetition of the certain operating pattern, adjustment input (r) is calculated by using the dual system model and the error between the preset temperature values (r) for the pattern and the actual inside temperatures (y) of the furnace, which adjustment input (r) is applied to the enlarged system to cause the inside temperatures (y) to track the preset temperature values (r). After each cycle of operation, the adjustment input (r) is renewed using the latest value of the above error.