Analysis of actuator delay compensation methods for real-time testing

Real-time testing is a useful technique to evaluate the performance of structural systems subjected to seismic loading. Servo-hydraulic actuators can introduce an inevitable delay when applying command displacements to a structure during a real-time test due to their inherent dynamics. Various compensation methods have been developed and applied in real-time testing to minimize the effect of actuator delay. This paper proposes an approach to analyze actuator delay compensation methods using an equivalent discrete transfer function. Discrete control theory is introduced and used to formulate the discrete transfer function in the frequency domain and the difference equation in the time domain for an actuator delay compensation method. The discrete transfer function is used to conduct frequency response analysis of the compensation method to provide insight into the expected performance of the compensation method by graphically illustrating the characteristics of the compensation method as a function of frequency of command displacement and the parameters for the compensator. The difference equation gives the form of the mathematical extrapolation in the time domain for the compensation method. Three popular compensation methods are selected to illustrate the proposed approach. Experiments with predefined sine sweep displacement and real-time hybrid simulations of a single-degree-of-freedom moment resisting frame with an elastomeric damper are conducted to experimentally validate the analysis of the selected compensation methods using the proposed approach.