Nonlinear signal-based control for single-axis shake tables supporting nonlinear structural systems

Nonlinear signal-based control (NSBC) is very powerful for controlling structural systems with parameter variations and has the advantage that the controllers can be designed using classical control theory and expressed by transfer functions. This report describes the first application of NSBC to shake table tests with nonlinear specimens and compares the performance of NSBC with that of a basic control approach that relies on the inverse transfer function of the controlled system. NSBC and the basic approach were numerically applied to shake table tests to excite a nonlinear single-degree-of-freedom system with earthquake acceleration motion, considering the nonlinear specimen characteristics and estimation errors associated with the table dynamics. NSBC achieved excellent control with near 100% accuracy, whereas the basic approach provided insufficient control. Although inaccurate estimation of the pure time delay in the controlled system causes instability at the practice of NSBC, proper design of the nonlinear signal feedback controller prevented instability. In experimental examinations, controllers for the two approaches were designed on the basis of the table dynamics with/without a specimen, which were preliminarily identified by performing tests using a random wave with small amplitude excitations. With no specimen present, both approaches yielded the expected acceleration motion on the table with high accuracy. However, with the specimen present, only NSBC successfully achieved excellent control of the shake table with near 100% accuracy, whereas the basic approach did not because of the specimen nonlinearity. These results numerically and experimentally demonstrate the efficiency and practicality of NSBC for shake tables supporting nonlinear structures.