抄録
In this paper is discussed the optimal flow-rate control problem of the counter current heat exchanger. This system is described by simultaneous partial differential equations of the first order. The control variable is the flow-rate of the heating fluid which appears bilinearly in the parameters of the equations. The performance index to be minimized is an integrated square error of the outlet temperature of the heated fluid. The initial and boundary conditions are assumed to be continuously differentiable with sufficiently small derivatives.
Such a problem is solved by applying the Maximum Principle for distributed parameter systems derived by Sirazetdinov. On the assumption that the outlet temperature of the heated fluid is able to reach and maintain the desired value, the pattern of optimal control is Bang-bang control Singular control.
The switching time for this pattern coincides with the time when the outlet temperature of the heated fluid attains the desired temperature. And the value of Singular control converges oscillatorily to the constant flow-rate for the stationary state with the new desired outlet temperature. The oscillation period is the residence time of the stationary state of the heated fluid.
The method of analysis of this paper is applicable to the more general distributed parameter system described by simultaneous partial differential equations of the first order.
