In recent years, there has been much interest in using the principle of dynamic substructuring as a framework for the testing of critical engineering components and systems. The most significant advantage of the method is that it can offer the opportunity to test full-size non-linear components within a laboratory environment. Such a test would be run in parallel with a real-time numerical simulation of the remaining part of the overall system to be emulated. Potentially, the most significant disadvantage of the method is the very high fidelity of control that is required, in order to achieve near-perfect synchronization of the test rig and the numerical model. This problem is further exacerbated by the presence of unknown and changing dynamic parameters, disturbances, and non-linearities in the test rig. The purpose of this paper is to lay a foundation for the linear control of dynamically sub-structured systems and, leading on from that, robust adaptive control via an extension to the adaptive minimal control synthesis (MCS) algorithm. Comparative simulation results from using the linear and adaptive control strategies are also included in the paper.

SUMMARYReal-time substructuring is a method of dynamically testing a structure without experimentally testing a physical model of the entire system. Instead the structure can be split into two linked parts, the region of particular interest, which is tested experimentally, and the remainder which is tested numerically. A transfer system, such as a hydraulic actuator or a shaking table, is used to impose the displacements at the interface between the two parts on the experimental substructure. The corresponding force imposed by the substructure on the transfer system is fed back to the numerical model. Control of the transfer system is critical to the accuracy of the substructuring process. A study of two controllers used in conjunction with the University of Bristol shaking table is presented here. A proof-of-concept one degree-of-freedom mass-spring-damper system is substructured such that a portion of the mass forms the experimental substructure and the remainder of the mass plus the spring and the damper is modelled numerically. Firstly a linear controller is designed and tested. Following this an adaptive substructuring strategy is considered, based on the minimal control synthesis algorithm. The deleterious e ect of oilcolumn resonance common to shaking tables is examined and reduced through the use of ÿlters. The controlled response of the experimental specimen is compared for the two control strategies.

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SUMMARYIn this paper we consider the concept of modelling dynamical systems using numerical-experimental substructuring. This type of modelling is applicable to large or complex systems, where some part of the system is di cult to model numerically. The substructured model is formed via the adaptive minimal control synthesis (MCS) algorithm. The aim of this paper is to demonstrate that substructuring can be carried out in real time, using the MCS algorithm. Thus, we reformulate the MCS algorithm into a substructuring form. We introduce the concepts of a transfer system, and carry out numerical simulations of the substructuring process using a coupled three mass example. These simulations are compared with direct simulations of a three mass system. In addition we consider the stability of the substructuring algorithm, which we discuss in detail for a class of second-order transfer systems. A numerical-experimental system is considered, using a small-scale experimental system, for which the substructuring algorithm is implemented in real time. Finally we discuss these results, with particular reference to the future application of this method to modelling large-scale structures subject to earthquake excitation.

Real-time hybrid testing is a promising technique for experimental structural dynamics, in which the structure under consideration is split into a physical test of key components and a numerical model of the remainder. The physical test and numerical analysis proceed in parallel, in real time, enabling testing of critical elements at large scale and at the correct loading rate. To date most real-time hybrid tests have been restricted to simple configurations and have used approximate delay compensation schemes. This paper describes a real-time hybrid testing approach in which non-linearity is permitted in both the physical and numerical models, and in which multiple interfaces between physical and numerical substructures can be accommodated, even when this results in very stiff coupling between actuators. This is achieved using a Newmark explicit numerical solver, an advanced adaptive controller known as MCSmd and a multi-tasking strategy. The approach is evaluated through a series of experiments on discrete mass-spring systems. Figure 14. System for MDOF multi-variate experiment with high coupling. not used in this test, ensuring a stiffer coupling overall. The resulting coupling stiffness is around 425 N/mm from actuator to actuator. The numerical substructure was kept of the same type.With such a stiff coupling between them, any attempt to make the motions of the actuators oppose each other will inevitably generate large interaction forces, making independent control of the two actuators extremely hard to achieve. In this test, excitation signals which caused opposing actuator motions could not be run with stability, due to the inability of the controller to adapt sufficiently quickly to the sudden change in force. However, when the two side excitations are in phase with each other, tests can be completed. The results presented are obtained with 3.5 mm sinusoidal frequency sweeps from 0 to 4 Hz on both actuators. The first modal resonance is swept The system identification tests have shown that the steady-state gains of the transfer system are unity, hence a = b. Writing a m = b m =â and a = b =â + a, where a is the discrepancy between the system identification and the actual transfer system dynamics coefficient values, the overall

Traditional shaking-table testing has been limited by the effectiveness of conventional fixed-gain algorithms used in their control. These algorithms are normally based on linear models of the shaking table and specimen, whose parameters are assumed to be fixed for the duration of the test. Although the influence of the specimen in the overall system dynamics can be partly removed by fine-tuning the linear controller, this process cannot deal with nonlinear effects and is limited in scope by the expertise of the operator.The minimal control synthesis (MCS) algorithm is a form of adaptive control, which was originally and successfully employed to cope with the nonlinear problems in the field of robotics. The MCS algorithm can tune the controller in real-time without any parametric knowledge of the system to be controlled. This paper describes how MCS has been incorporated within both analog and digital controllers for shaking tables and shows some of the results achieved on tables at the University of Bristol and at Athens Technical University. In both cases, the introduction of adaptive control has noticeably improved the performance of the shaking table, correcting errors by more than 5 dB in some experiments.

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