The passivity property of dissipative mechanical structures has long been exploited in designing passive controllers that provide robust stability even in the presence of unmodeled dynamics of the system. For an input/output map of a flexible structure to be passive, collocation of the actuators and sensors is required and also the sensors should measure the velocity of the system. The so-called smart structures frequently have more sensors than actuators. Therefore, the passive controller can at best utilize only a subset of the sensors. In this paper we consider the design of a squaring down matrix which would render a system passive subject to some additional performance considerations. The problem of obtaining the synthesized passive output is cast as a set of linear matrix inequalities (LMIs) which can be efficiently solved by the LMI Toolbox in Matlab. We apply this procedure with the assumption that the sensors provide both displacement and velocity information which is generally not true. We show that the passive controllers can be implemented without the use of velocity information. By using synthesized passive outputs in addition to naturally occurring passive outputs, we obtain better system performance. We present experimental results involving a single flexible beam with torque input and hub angular position and strain gage outputs.
1997 American Control Conference, Albuquerque, NM, June, 1997.