Covariance Control Using Closed Loop Modeling for Structures 1

This paper presents a low order controller design method, using closed loop modeling plus covariance control, with application to the benchmark problem in structural control for the active mass drive system at the University of Notre Dame [1]. This method nds a satisfactory controller by iterating between closed loop modeling and covariance control. The closed loop modeling implies that the model used for model-based control design is extracted from the feedback system of the last iteration. Introduction It is well-known that the modeling and control are not independent problems [2], especially when the performance is stringent and the system is complex. Open loop modeling (identi cation, model reduction, etc.) may or may not provide a good model for control design. Civil structures are typically large and dynamically rich (complex systems with many vibrational modes). Wise use of the relatively large control energy and the limited control complexity demands a theory for synthesizing a simple controller to achieve relatively stringent performance. In this case, both structure-control interaction and model-control interaction are not negligible. In order to achieve stringent performances, we have to take those interactions into account. Combining closed loop modeling with covariance control [3,4] presents a way to incorporate those interactions. This combination iterates between the control design and plant model extraction from the previous closed loop system model. Due to the closed loop feature, this combination indirectly handles those di culties raised in structural control: spillover, limited control authority and modeling error. The benchmark problem in structural control [1] requires designing a compensator of limited complexity, based on a highdelity structure model, to achieve as stringent performance as possible. Hence the model-control interaction in the benchmark problem could be very strong, which implies that the combination of the closed loop modeling and control is demanded. Control Design Problem The active mass drive system at the University of Notre Dame described in [1] can be depicted by the block diagram shown in (a) of Fig. 1. Where  xg is the ground acceleration (modeling earthquake excitation), w represents the sensor noise. va and vs are signals used for modeling purpose. The system measurements are y = [y T 1  xg] T with y1 = [xm  xa1  xa2  xa3  xam ] T , xm;  xa1;  xa2 ;  xa3 and  xam have the same de nitions as in [1]. P is a high delity linear approximation of the actual plant, which includes Sponsored by NSF grant CMS-9403592 Structural Systems and Control Laboratory, Purdue University, West Lafayette, IN 47907.