which helps achieve better robustness properties. A recent advance, representing a breakthrough in the computational aspects of this mathematical technique, is the paper by Doyle et al, 1989. 2) The Structured Singular Value (also called p or mu) analysis. This theory combined with H- infmity theory results in the so-called mu-synthesis approach. Here, explicit modeling of the dynamic and parametric uncertainty of the system is provided, so that the control design is satisfactory for a set of models in the neighborhood of a nominal model. Only physically meaningful uncertainty is considered (structured uncertainty description) to avoid conservativeness in the design. For the fundamental theoretical basis of this technique and its application to the control of LSS[GJ Balas, 1990, GJ Balas et al, 1989].. Algorithms for these methods have already been developed and implemented in various control- aided-design software packages (MATLAB™ among others). Further research in these areas that will greatly enhance our capability of predicting and controlling behavior of the large space solar power program structures, will involve research in both improved system identification (modeling) methods for uncertain systems and large-scale computational schemes for all these "robust control" techniques. Control of Large Space Structures: A Reduced Order Model (ROM)/Residual Mode Filter (RMF) Design Concept During the design of any control system for a Large Space Structure (LSS) possibly containing an infinite number of modes, there is usually a constraint on the number of frequencies a certain design can accommodate. This is a phenomenon usually caused by the lack of computer speed to compute the necessary gains for the large number of modes associated with Distributed Parameter Systems (DPS). To get around this limitation. Reduced Order Models (ROM), which contain only some of the modes of vibration of the actual system (n modes) are employed during the control law and observer design of the control system. Figure 9.1 shows the closed loop with matrix A being the model of the structure, matrix B being the input matrix, matrix C being the output and matricies Ln, Kn and Gn being gain matricies within the controller. Unfortunately, in the closed-loop with the controller, some of the modes not directly included in the ROM design become unstable (q modes), although some of them do not (r modes). This problem of Controller Structure Interaction (CSI) is easily solved with the introduction of a parallel set of frequency-locking filters or Residual Mode Filters (RMF), equal in number to the number of q modes [Balas, 1988, Davidson 1990, Ouyang, 1987]. These filters can be added after the original ROM based controller has been designed, and produce very little degradation of designed performance while yielding acceptable stability margin for the closed-loop operation. In general, this ROM/RMF design allows for low order control of very large systems (the limit has not yet been found, i.e. distributed parameter systems are in infinite dimension space) and has been successfully employed experimentally and computationally [Reisenauer, 1990, Balas and Quan, 1989],
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