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.