Application of Sparse Feedback Control Strategies to Civil Structures

Abstract

Modern structural control systems use centralized, wired sensor feedback to impart counter forces based on measurement of the response. However, centralized systems can be sensitive to sensor failure, controller failure, and the reliability of sensor links. The recent study of wireless control systems has encouraged decentralized control approaches to overcome wireless structural control challenges, including limiting the wireless communication required and the associated slow sampling rate and time delays in the control system. Decentralized control offers the additional advantages of multiple independent controllers and small subsets of measurement feedback. Previous decentralized structural control algorithms, both Ad-Hoc and Heuristic, enforce a spatial sparsity pattern during the design, which is assumed \textit{a priori}. Therefore, the optimal feedback structure is not considered in the design. This work explores a decentralized optimal LQR design algorithm (LQRSP) where the sparsity of the feedback gain is incorporated into the objective function. The control approach is compared to previous decentralized control techniques on 5- and 20-Story control benchmark structures fitted with active or semi-active systems. Additionally, the sparsity and control requirements are compared to centralized designs to gain insight on the overall performance of sparse feedback systems. The LQRSP program and its additional parameters are explored more fully to make informed control decisions, further enhancing the decentralized control design. The optimal sparse feedback design offers the best balance of performance, measurement feedback, and control effort, while clearly highlighting important feedback control measurements. Additionally, the feedback structure identified is not easily identifiable \textit{a priori} in the reduced order model of the 20-story structure, highlighting the significance of particular measurements in this feedback framework. To bridge the gap between simulation and reality, the LQRSP design is extended to a discrete time simulation system to incorporate wireless transmission time as well as sensor and estimation noise. A 5-Story specimen with semi-active control devices is designed for a uniaxial shake table for future physical testing of various centralized and decentralized control algorithms during seismic excitations.