Optimized decentralized control of large scale systems

Xiao Qi Shi, Daniel E. Davison, Raymond H. S. Kwong, Edward J. Davison

Abstract: This paper presents a new optimal decentralized controller design method for solving the tracking and disturbance rejection problems for the class of large scale LTI systems, using only low order decentralized controllers. In particular, the class of large scale systems considered in this paper is described by the LTI model M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ÿ + M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> y + M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> y = Bu + Eω, where y is the output, u is the input, ω is an unknown constant disturbance, where e = y - y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</sub> is the tracking error in the system and y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</sub> is a constant given signal. To illustrate the type of results which can be obtained using the new optimal decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-Observer controller. In this case it is shown that the new decentralized controller obtained is orders of magnitude lower in dimension than the standard centralized LQR-Observer controller. The proposed controller also has the property that if a sensor/actuator failure occurs, the resulting system has certain fail-safe properties. The proposed optimal controller also has the property that it is strongly robust as compared to the standard centralized LQR-Observer controller. In particular, the proposed controller can have the property of being some 5 orders of magnitude more robust than the standard LQR-Observer controller. An illustration of the new decentralized controller design method is applied to a large flexible space structure (LFSS) system with 5 inputs and 5 outputs and of order 24.