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Three new synthesis methods for an efficiency optimized speed-control system for a separately excited dc motor system are proposed on the basis of an improved optimal regulator theory. Controllable losses, such as copper losses, iron losses, power converter losses, etc., are approximately represented by a square of the armature current and the field current. In the first method, the losses are included in a particular quadratic performance index to be minimized. In the second method, optimal ratio of the armature current and the field current giving the minimum losses is analytically derived and the speed-control system attaining the optimal ratio is synthesized. In the third method, optimal ratio of the armature-impressed voltage and the field-impressed voltage giving the minimum losses is again analytically derived and the optimal speed-control system is synthesized. Maximum efficiency of the machine system is attained by adopting these methods.