Abstract
In this paper, we study the optimal design of dual mode feedback control systems using a state observer and a relay element.
In the usual design of the dual mode optimal control systems, the sigular mode is realized by the stable silding motion of a relay whose switching surface is constructed by the state feedback law. In addition, the same surface is used as the switching surface for the bang-bang mode in the whole space.
But in practical situations, only the input and the output of the system are available for the design, and the state feedback cannot be realized in general. Hence, it is necessary to depend on the state observer for the construction of the switching surface, and there arise many problems owing to the adoption of the state observer which are to be studied in this paper.
First, sufficient conditions for the stable sliding motion of the relay and the global asymptotic stability of the system are given. Secondly, the loss of the performance index compared with the optimal system is calculated, and it is shown that the theory of optimal observers is applicable to our problem.
Finally, after the discussion on the optimal selection of the initial state of the observer, we propose to apply the, optimal design procedure of linear compensators to our problem, regarding the observer in the feedback loop as a compensator. Our method of design is illustrated by an example of a pure inertia system. The analysis of this example shows that the “optimal” feedack coefficient is not optimal according to our method.
