Decentralized pole placement using polynomial matrix fractions

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Virginia Polytechnic Institute and State University

As the dimension and the complexity of large interconnected systems grow, so does the necessity for decentralized control. One of the interesting challenges in the field of decentralized control is the arbitrary pole placement using output feedback. The feasibility of this problem depends solely on the identification of the decentralized fixed modes. As a matter of fact, if the system is free of fixed modes, then by increasing the controller’s order, any arbitrary closed loop poles can always be assigned. Due to this fact, reducing the controller’s order constitutes another interesting challenge when dealing with decentralization.

This research describes the decentralized pole placement of linear systems. It is assumed that the internal structure of the system is unknown. The only access to the system is from a number of control stations. The decentralized controller consists of output feedback controllers each built at a control station.

The research can be divided into two parts. In the first part, conditions for fixed modes existence as well as realization and stability of the overall system under decentralization are established using polynomial matrix algebra. The second part deals with the solution of decentralized pole placement problem, in particular, finding a decentralized controller which assigns some set of desired poles. The solution strategy is to reduce the controller’s order as much as possible using mathematical programming techniques. The idea behind this method is to start with a low order controller and then attempt to shift the poles of the closed loop system to the desired poles.