PROOF COPY [EM/2003/023636] 004503QEM PROOF COPY [EM/2003/023636] 004503QEM Nonlinear System Modeling and Velocity Feedback Compensation for Effective Force Testing Jian Zhao, S.M.ASCE 1 ; Carol Shield, M.ASCE 2 ; Catharine French, M.ASCE 3 ; and Thomas Posbergh 4 Abstract: Effective force testing (EFT) is a test procedure that can be used to apply real-time earthquake loads to large-scale structural models. The implementation of the EFT method requires velocity feedback compensation for the actuators in order to apply forces accurately to test structures. Nonlinearities in the servosystem have a significant impact on the velocity feedback compensation and test results when large flow demands are present, which can be caused by large structural velocities and/or large forces applied to the test structure. This paper presents a nonlinear servosystem model, upon which a nonlinear compensation scheme is proposed. The model and compensation scheme are experimentally verified. The results indicate that the proposed model accurately describes the servosystem behavior, and with the nonlinear velocity feedback compensation, real-time dynamic testing can be conducted using the EFT method. DOI: XXXX CE Database subject headings: Dynamic tests; Simulation models; Earthquakes; Structural response; Velocity; Damping. Introduction Computer simulation has been widely used in evaluating control algorithms for seismic mitigation with passive or semiactive damping devices; however, the accuracy of the results depends on the characterization of the energy dissipation components. Hence real-time dynamic testing is necessary for assessing the behavior of structures employing velocity dependent devices under seismic loadings. A shake table is often used to simulate the dynamic effects of earthquakes on structural models. However, structures tested on shake tables typically have to be scaled down due to limited table capacities. At smaller scales, structural details such as connections cannot be represented realistically, and energy dis- sipation of structural control devices may not be demonstrated accurately. Effective force testing (EFT) is a dynamic test procedure to apply real-time earthquake loads to large-scale structures that can be simplified as lumped mass systems. In an EFT test, the test structure is anchored to a stationary base, and dynamic forces are applied by hydraulic actuators to the center of each story mass of the structure. The force to be imposed (effective force) is the product of the structural mass and the ground acceleration record, and thus is independent of the structural properties such as stiff- ness and damping, and their changes during the test. Motions measured relative to the ground are equivalent to the response that a structure can develop relative to a moving base as in a shake table test or an earthquake event. The development and implementation of EFT has been under- way at the University of Minnesota since 1996. Early direct ap- plication of the EFT method on a linear elastic structural model indicated that the actuator was not able to apply forces accurately near the natural frequency of the test structure (Dimig et al. 1999). The concept of natural velocity feedback (i.e., the interac- tion between the actuator piston velocity and the actuator control) identified by Dyke et al. (1995) was used to explain the problem: the actuator is controlled by a servovalve through hydraulic flow under pressure, and the differential pressure inside the actuator chambers causes the force applied to the test structure. The actua- tor chamber volumes change due to the actuator piston in motion with the structure, resulting in unwanted chamber pressure varia- tion. Standard proportional-integral-derivative (PID) controllers are unable to compensate for the pressure variation, thus causing force-tracking errors. Velocity feedback compensation can solve this problem and make the successful implementation of EFT possible (Shield et al. 2001). In the solution, the effect of the natural velocity feedback is compensated by modifying the command to the servovalve. The chamber volume change to be compensated is determined as the product of the measured piston/structure velocity and the pis- ton area. The compensation signal is convolved with the inverse of the forward system dynamics, and then added to the force command. The modified command signal compensates for the effect of the piston motion after going through the forward dy- namics. The compensation is independent of the structural prop- erties (i.e., damping and stiffness) and their changes during a test. Previous implementation of the EFT method (e.g., Timm 1999) was limited to tests with small hydraulic demands, for which the servovalve operated in the linear range of its behavior. For tests with large flow demands, nonlinearities of the servosys- tem can have significant impact on the performance of the veloc- ity feedback compensation (Zhao et al. 2003a, b). The servosys- tem nonlinearities become significant when a test involves large 1 Research Associate, Dept. of Civil Engineering, Iowa State Univ., Ames, IA 50011. E-mail: zhao0058@iastate.edu 2 Professor, Dept. of Civil Engineering, Univ. of Minnesota, Minneapolis, MN. E-mail: cfrench@umn.edu 3 Associate Professor, Dept. of Civil Engineering, Univ. of Minnesota, Minneapolis, MN. E-mail: ckshield@umn.edu 4 Associate Professor, Dept. of Electrical and Computer Engineering, Univ. of Minnesota, Minneapolis, MN. E-mail: posbergh@umn.edu Note. Associate Editor: Eric N. Landis. Discussion open until August 1, 2005. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on October 13, 2003; approved on May 11, 2004. This paper is part of the Journal of Engineering Mechan- ics, Vol. 131, No. 3, March 1, 2005. ©ASCE, ISSN 0733-9399/2005/3- 1–XXXX/$25.00. JOURNAL OF ENGINEERING MECHANICS © ASCE / MARCH 2005 / 1 PROOF COPY [EM/2003/023636] 004503QEM