Dynamics, control and real-time issues related to substructuring techniques: application to the testing of isolated structure systems

Abstract

This article presents the designs of output-based adaptive and numerical-substructure-based controllers for the testing of a base-isolated substructured system. The linear numerical-substructure-based controllers, which are developed using state-space and transfer-function methods and a higher-order actuator model, are introduced in order to address new substructured eigenvalue techniques in relation to testing stability and accuracy. An output-based framework for the synthesis of new adaptive substructuring controllers and for the associated stability proof is discussed, based upon an ad hoc reference model concept. Implementation studies favourably verify the proposed control and analysis strategies, showing that the adaptive controller effectively compensates for time-varying and unwanted parameters within the actuator systems, and using the substructured eigenvalue can explicitly predict the testing performance in advance. In addition, the results also indicate that a feedforward controller incorporating closed-loop control schemes could be disadvantageous if the numerical substructure contains the dynamic parameters, which possibly may yield slow substructured eigenvalues.

Dynamic and numerical issues relating to the control robustness of dynamically substructured systems

“…Stable and fast substructured eigenvalues enhance the synchronisation accuracy. However, if Σ N1 contains a low‐damping and large‐mass component, resulting in slow eigenvalues, the forward and feed‐forward control action will not be enough, as shown in Figure 11 of and Figure (c) of . In this case, the feedback term K en must be included to improve the robustness.…”

“…With the substitution of Eqn into Eqn , the forward and feed‐forward gains are determined as Assuming that the G TS parameters are known exactly, the design of Eqn ensures the homogeneous nature of the error dynamics as follows In the presence of parameter variations within the G TS dynamics, the use of the feedback term, K en , enhances the closed‐loop stability and robustness. Here, linear robust pole placement was used to determine K en , while optimal H ∞ or adaptive strategies can be considered if needed . The solution of Eqns and , showing that the control design is independent of the Σ 2 parameters, reflects the NB strategy.…”

“…In the presence of parameter variations within the G TS dynamics, the use of the feedback term, K en , enhances the closed-loop stability and robustness. Here, linear robust pole placement [19] was used to determine K en , while optimal H ∞ or adaptive strategies can be considered if needed [14,20]. The solution of Eqns (22) and (23), showing that the control design is independent of the Σ 2 parameters, reflects the NB strategy.…”

“…The N-SSLSC performance can be initially and explicitly quantified by substructured eigenvalues [14,15], as determined via the plant matrix of the error dynamics. For example, the substructured eigenvalue of the MSD DSS is given by the plant matrix in Eqn (20) or (23).…”

“…The framework of was modified in , where the Σ N and Σ P parts were explicitly separated, allowing the state‐space technique and uncertainty analysis to be performed. In comparison with the modifications in , introduced a new numerical‐substructure‐based (NB) framework to tailor DSS controllers . As shown in Figure (b), the dotted‐line Σ 2 block is treated as unknown in the NB control design.…”