The operating cost of batch-type furnace is a function of the load and the operatingconditions. Consideration of these factors leads us to a control scheme which minimizes the total fuel consumption and also satisfies the end-point temperature requirements.
In this paper, the mathematical model of a representative furnace is derived on the basis of a study of heat transfer relationships. The results computed from the mathematical model show a significant fuel saving when the optimum path is used rather than the conventional path. However there is some sacrifice of slab temperature uniformity. The control soheme, as designed, isessentially open-loop.

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As reported by some papers, the piping in the hydraulic servo of which length is unneglible compared to the propagation wave length of the hydraulic fluid plays the opposing roll at the high frequency range of the high speed electro-hydraulic servomechanisms. In this paper, the author considers the following parameters and proposes an approximate calculating method of the frequency response of the by draulic servo incorporating the piping with definite length; giving consideration to mass, rigidity, length, and the viscous resistance of the piping, and mass, bulk modulus and viscosity of the hydraulic fluid.
As the result of the calculation and some experiments, rather distinct peaks take place at the high frequency range of the frequency response of such a hydraulic servo.
These peaks give the abrupt chauge of the impedance seen from the servovalve side. The author also trys to explane squealing phenomena which occur sometimes in the high pressure hydraulic servo utilizing the theory presented here. These results will be shown in the continued papers some other time.

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Many papers on the dynamics of heat exchangers have been published and the dynamic response with input temperature change has been clarified. But the response with flow rate change is still hard to show analytically.
The author obtained the approximate step temperature response for parallel flow heat exchangers using Prof. Takahashi's graphical method. The experimental transient responses of counter-and parallel flow heat exchangers with flow rate change show good agreement with the graphical response.

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An approximate mathematical method is developed to evaluate integrated square error criteria of control systems. In this method the error response caused by a step reference input is approximated by a damped sinusoid. Close agreement is reported between the optimum gain adjustments given by the theory and the optimum points obtained by use of an analog computer. The theory is then modified and is applied to a control system which includes a gain switching, predicting a 20 to 30% improvement in performance, and is confirmed by an experiment on a pneumatic pressure process.

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