Presenting two original studies, this report is intended to show our philosophy in conducting research on the theory of optimal automatic control systems in the past four years. Owing to its technical nature, most of the pages of this report are used in explaining the two studies. One of them is concerned with a second order oscillating plant having a negative feedback loop with a linear compensation. The natural frequency and the damping coefficient of the plant are though to vary within a range. The role of the feedback loop compensation is to keep the natural frequency and the damping coefficient of the closed loop system within some specified margin, making the whole system insensitive to some variation of the plant's main parameters. The synthesizing procedure is the same as the Wiener's optimum filter determination. The performance index are augmented the squares of the control signals and dynamic sensitivity functions.
The second study is to give insensitive characteristics to the linear regulator system in spite of small changes of its plant parameter. In this case the so-called good characteristic of the linear regulator, for instance, the perfect state feedback configuration is assumed to be maintained to be the same as the given regulator's characteristics. For this purpose we must be permitted to make some small changes of plant structure. But, fortunately, we know that there are many systems whose performance index values and the control laws are the same as those of the given linear regulator system. These systems are called equivalent systems. We developed the theory to find a system in the equivalent systems which has better characteristics with respect to the sensitivity and which represents the given regulator system as near as possible. Two examples are shown to clarify the obtained results.
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