✍ Scribed by L.T. Fan; Y.S. Hwang; C.L. Hwang
No coin nor oath required. For personal study only.
The basic form of Pontryagin's maximum principle which is a keystone of the modern optimal control theory is presented. The principle is applied to the determination of optimal control policies of several life support or environmental control systems.
Three concrete examples all of which are concerned with the temperature control of a life support system consisting of an air-conditioned cabin (the system proper) subject to an impulse heat disturbance and of a heat exchanger (the control element) are considered. The first example treats the case in which the time constant of the heat exchanger is negligible. The second example considers the case in which the time constant of the heat exchanger is not ignored. In the third example the optimal policy of the system where the flow of air in the cabin can be characterized by the two completely stirred tanks-inseries (2 CST's-in-series) model is studied. In this example, the time constant of the heat exchanger is again neglected. Procedures and computational approaches employed for obtaining the optimal control policies are given in detail.
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