Using tensors to track earthquakes on hydraulic shaker tables

This paper presents a new method to design nonlinear, earthquake-tracking controls on the shaker table at the University of Notre Dame´s Structural Dynamics and Control/Earthquake Engineering Laboratory, by using symmetric tensor formulations of optimal nonlinear regulator design techniques. By means of a closed loop representation for the nonlinear optimal regulator problem, a compact and novel form of nonlinear regulator solution is obtained. Computer simulations show that the nonlinear controller provides much smaller tracking error on the shaker table than the linear controller, when mismatched reference command signals are used. For paired reference command signals, computed off-line in advance by direct inverse computation methods, both simulation and experimental results show that linear and nonlinear control can be used for tracking control of shaker table to a set of desired earthquake signals without redesigning the feedback loop control