Control And Time Integration Algorithms For Real-time Hybrid Simulation

Seismic testing methodologies play a significant role in earthquake engineering dueto complexities of engineering materials and ground motion. Among available testingmethods, hybrid simulation is more appealing for its merits, e.g., evaluating dynamicresponses of large scale structures at lower cost. As a novel member of hybrid simu-lation, Real-time Hybrid Simulations (RHS), since its conception in1992, has shownits unique properties and capacity for testing complex structural components, especiallyrate-dependent ones.RHS often partitions the emulated structure into portions, which are then either nu-merically or physically simulated in real-time according to our knowledge of them. Inparticular, the critical nonlinear and/or rate-dependent parts are often physically modeledwithin a realistic real-time test, while the remainder parts are simultaneously evaluated bysolving diferential equations. Evidently, the challenge of these methods is to enforce thecoupling at the interface between portions via real-time loading and real-time computa-tion.Heretofore great development of RHS has been attained. This dissertation is devotedto developing RHS in two aspects, namely transfer system control and time integrationalgorithms. In detail, research work and findings are summarized as follows:The dissertation initially focuses on the implementation of a model-based controlstrategy–internal model control (IMC) and its comparison with the classic PID/PI controlon the lately conceived high performance test system-the TT1test system. The con-trol strategy of the electromagnetic actuators consists of three loops, namely one speedloop and two displacement loops. The outer displacement loop is regulated with IMC orPID/PI whilst the inner two loops with proportional control. In order to compare diferentcontrol strategies, realistic tests with swept sinusoidal waves and numerical simulationsconcentrating on robustness were carried out. Analysis showed that IMC is preferable forits robustness and its ease of implementation and online tuning. Both IMC and PID worksimilarly and well on the actuator which can be simplified into a first-order system plusdead time. In addition, RHS was performed and showed the favorable state of the system.In order to accurately compensate for a time-varying delay in RHS, online delayestimation methods were proposed and discussed based on a simplified actuator model.The model, consisting of a static gain and dead time, results in nonlinear relationships among diferent displacements. The estimation based on the Taylor series expansion wasfurther developed by introducing the recursive least square algorithm with a forgettingfactor. Then this scheme was investigated and assessed in pure simulations and RHSvia comparison with two other methods. Finally, the proposed scheme was identified tobe satisfactory in terms of its convergence speed, accuracy and repeatability and to besuperior to other methods.With the insight into the weakness of available compensation schemes in mind, twopolynomial delay compensation formulae considering the latest displacement and veloc-ity targets were proposed. Assessment and comparisons of the formulae by means offrequency response functions and stability analysis were carried out. In order to facilitatedelay compensation, another novel compensation scheme characterized by overcompen-sation and optimal feedback was conceived. Numerical simulations and realistic RHSwas performed to examine the proposed schemes. The analysis revealed that the pro-posed polynomial formulae exhibit smaller prediction errors and the second-order schemewith the LSRT2algorithm is endowed with a somewhat larger stability range. Moreover,the overcompensation scheme was concluded to have the ability of time-varying delayaccommodation, error reduction and sometimes stability improvement.With regard to time integration algorithms, this dissertation extends the equivalentforce control (EFC) method which is a method of RHS with implicit integrators to RHSon split mass systems. The EFC method for this problem was spectrally analyzed andwas found more satisfactory stability than some explicit integrator. Then larger controlerrors due to quadartically interpolated EF commands were recognized and treated witha proposed displacement correction. In view of the inherent feature of RHS–multiplequantities coupling at the interface, the correction was extended to simultaneously up-date displacement and acceleration. Spectral stability analysis and numerical simulationsdemonstrated that:(1) the correction can remove the constraint of zero-stability to themethod and reduce algorithmic dissipation;(2) it also works well for MDOF systems.Finally, an inter-field parallel algorithm for RHS, namely IPLSRT2, was developedand analyzed. This method was based on the Rosenbrock (LSRT2) method and a priorinter-filed parallel integrator–PLSRT2. The LSRT2with diferent stage sizes, velocityprojection and modified Jacobian evaluation were introduced to the algorithm in orderto avoid and/or weaken the disadvantages of the PLSRT2method, such as inefcientcomputation, displacement and velocity drifts, and complicated starting procedure. Ac-curacy analysis, spectral stability analysis, pure numerical simulations and realistic RHS were performed to investigate the properties of the IPLSRT2method. Compared with thePLSRT2method, this method exhibits pros and cons. In detail, the method loses the accu-racy order due to the velocity projection applied at all time steps. However, it can providemore accurate displacement and velocity results in common applications where a littlelarger time step is required. In some cases, the proposed method exhibits smaller phaseshifts and dissipation. Moreover, computation efciency in Subdomain A is improved andits implementation in real-time applications is simplified.