Control and Time Integration Algorithms for Real-Time Hybrid Simulation

Seismic testing methodologies play a significant role in earthquake engineering due to complexities of engineering materials and ground motion. Among available testing methods, hybrid simulation is more appealing for its merits, e.g., evaluating dynamic responses of large scale structures at lower cost. As a novel member of hybrid simulation, Real-time Hybrid Simulations (RHS), since its conception in 1992, has shown its unique properties and capacity for testing complex structural components, especially rate-dependent ones. RHS often partitions the emulated structure into portions, which are then either numerically or physically simulated in real-time according to our knowledge of them. In particular, the critical nonlinear and/or rate-dependent parts are often physically modelled within a realistic real-time test, while the remainder parts are simultaneously evaluated by solving differential equations. Evidently, the challenge of these methods is to enforce the coupling at the interface between portions via real-time loading and real-time computation. Heretofore great development of RHS has been attained. This dissertation is devoted to developing RHS in two aspects, namely transfer system control and time integration algorithms. In detail, research work and findings are summarized as follows: The dissertation initially focuses on the implementation of a model-based control strategy –internal model control (IMC) and its comparison with the classic PID/PI control on the lately conceived high performance test system - the TT1 test system. The control strategy of the electromagnetic actuators consists of three loops, namely one speed loop and two displacement loops. The outer displacement loop is regulated with IMC or PID/PI whilst the inner two loops with proportional control. In order to compare different control strategies, realistic tests with swept sinusoidal waves and numerical simulations concentrating on robustness were carried out. Analysis showed that IMC is preferable for its robustness and its ease of implementation and online tuning. Both IMC and PID work similarly and well on the actuator which can be simplified into a first-order system plus dead 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 delay estimation 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 different displacements. The estimation based on the Taylor series expansion was further developed by introducing the recursive least square algorithm with a forgetting factor. Then this scheme was investigated and assessed in pure simulations and RHS via comparison with two other methods. Finally, the proposed scheme was identified to be satisfactory in terms of its convergence speed, accuracy and repeatability and to be superior to other methods. With the insight into the weakness of available compensation schemes in mind, two polynomial delay compensation formulae considering the latest displacement and velocity targets were proposed. Assessment and comparisons of the formulae by means of frequency response functions and stability analysis were carried out. In order to facilitate delay compensation, another novel compensation scheme characterized by overcompensation and optimal feedback was conceived. Numerical simulations and realistic RHS were performed to examine the proposed schemes. The analysis revealed that the proposed polynomial formulae exhibit smaller prediction errors and the second-order scheme with the LSRT2 algorithm is endowed with a somewhat larger stability range. Moreover, the overcompensation scheme was concluded to have the ability of time-varying delay accommodation, error reduction and sometimes stability improvement. With regard to time integration algorithms, this dissertation extends the equivalent force control (EFC) method which is a method of RHS with implicit integrators to RHS on split mass systems. The EFC method for this problem was spectrally analyzed and was found more satisfactory stability than some explicit integrator. Then larger control errors due to quadartically interpolated EF commands were recognized and treated with a proposed displacement correction. In view of the inherent feature of RHS –multiple quantities coupling at the interface, the correction was extended to simultaneously update displacement and acceleration. Spectral stability analysis and numerical simulations demonstrated that: (1) the correction can remove the constraint of zero-stability to the method and reduce algorithmic dissipation; (2) it also works well for MDOF systems. Finally, an inter-field parallel algorithm for RHS, namely IPLSRT2, was developed and analyzed. This method was based on the Rosenbrock (LSRT2) method and a prior inter-field parallel integrator–PLSRT2. The LSRT2 with different stage sizes, velocity projection and modified Jacobian evaluation were introduced to the algorithm in order to avoid and/or weaken the disadvantages of the PLSRT2 method, such as inefficient computation, displacement and velocity drifts, and complicated starting procedure. Accuracy analysis, spectral stability analysis, pure numerical simulations and realistic RHS were performed to investigate the properties of the IPLSRT2 method. Compared with the PLSRT2 method, this method exhibits pros and cons. In detail, the method loses the accuracy order due to the velocity projection applied at all time steps. However, it can provide more accurate displacement and velocity results in common applications where a little larger time step is required. In some cases, the proposed method exhibits smaller phase shifts and dissipation. Moreover, computation efficiency in Subdomain A is improved and its implementation in real-time applications is simplified.