Passivity based controllers are used in structural control due to their inherent robustness properties. These controllers require sensor/actuator collocation. In this paper, we consider the design of a "squaring down" matrix which renders a system passive by using a linear combination of all collocated and non-collocated sensor/actuator pairs. The design uses experimental transfer functions and does not require the knowledge of the system model. The problem of finding the squaring down matrix is cast as a solution to a set of linear matrix inequalities (LMIs) subject to some additional performance considerations. The design procedure of the squaring down matrix assumes that velocity information is available from the sensors which is not generally the case. We show that the squaring down matrix can be implemented without the use of such velocity information. We provide experimental results gathered from the single link flexible beam setup in the C/sub La/MS laboratory at RPI to show that implementation of passive loops without velocity measurements provides very good results.
4th IEEE Conference on Control Applications, Albany, NY, Sept. 1995.