Compensation of Actuator Delay and Dynamics for Real-time Hybrid Structural Simulation

Compensation of delay and dynamic response of servo-hydraulic actuator is critical to the stability and accuracy of hybrid experimental and numerical simulations of the seismic response of structures. In this study, current procedures for compensation of actuator delay are examined and improved procedures are proposed. The proposed procedures need little or no a priori information about the behavior of the test specimen. In addition, a simple approach is introduced for online estimation of system delay and actuator command gain, thus eliminating the need for system calibration before a simulation. The effectiveness of these compensation procedures is verified analytically, numerically and experimentally. Energy error measures resulting from actuator tracking errors are compared to the overall energy input from the excitation. The reduction in added artificial energy due to experimental errors is used to demonstrate the improved accuracy in the simulation obtained from using the proposed procedures. An extrapolation procedure, alternative to the widely-used polynomial extrapolation in fast hybrid testing is proposed based on the same numerical integration procedures used to solve the equation of motion. This procedure is shown to result in smaller amplitude and phase errors. Introduction Real-time testing of substructures or hybrid simulation is an efficient method for assessment of the dynamic and possibly rate-dependent behavior of structural systems subjected to earthquake excitations. The method separates a structure into physical (experimental) and numerical substructures, only requiring the experimental simulation of parts of the structure that are difficult to model. In a displacement controlled hybrid simulation, the displacements computed by the numerical model are applied to the physical specimen, and the resisting force is measured and fed back into the numerical model, as shown in Figure 1. It is essential for the stability and accuracy of the simulation to make corrections and compensation on the signals being transmitted among numerical and experimental substructures, as otherwise, the errors may cumulate during the simulation, and make the simulation unreliable, or even unstable. Figure 1. Overall block diagram of a displacement controlled hybrid simulation. Hybrid simulation of structures has been the subject of vast research body in recent years, partially due to the development of NEES which provides researchers with advanced tools for hybrid simulations, including real-time testing, shake table substructures (Reinhorn, Sivaselvan et al. 2004), and geographically distributred substructures (Stojadinovic, Mosqueda et al. 2006). Earlier studies (Mahin and Shing 1985; Thewalt and Mahin 1987; Mahin, Shing et al. 1989) explored the capabilities of the , m m d r c d Integrator / Simulation Correction / Compensation Correction / Compensation Experiment Analysis Signal Generation D/A PID Controller Servo-valve Actuator Hydraulic Supply Specimen Transducers A/D