Improvements in Sparsity Promoting Estimator Design and Network Aware Controller Design for Wireless Structural Control

Abstract

Feedback control systems are an attractive approach to limit the structural response to large dynamics loading events such as wind and earthquakes. However, civil structures often contain too many degrees of freedom to measure all effectively when controlling the structure’s response. Previous work has shown that the Kalman filter can be used effectively to estimate the state response of structures from a limited set of measurements of the structure. Choosing a limited set of sensors from a larger sensor set poses a combinatorial problem. In light of this, we have devised a systematic method to determine a sparse set of measurements that have the largest impact on estimating the state of the structure. To avoid the use of a combinatorial search, we propose the addition of a sparsity promoting parameter and a penalty function to the optimization problem used to determine the Kalman gain. Promoting sparsity within the Kalman gain provides a method of removing sensors by setting the weight for a given sensor to zero which effectively removes the sensor’s measurements from the Kalman filter estimations. The use of wireless sensors in structural control has recently gained interest. How- ever, wireless sensors have an increased probability of packet error and longer communication delays in comparison with wired sensors. Using a sparse set of sensors has the added benefit of requiring fewer network resources, which allows for more efficient communication over wireless networks. Simulation results of a wireless feedback control of a 9 story structure show improved performance in limiting the structural response when using sensors placed according to the KFADMM in comparison to using the full sensor set. To further address the problem of packet loss and communication delays in wireless networks we examine an integrated model of the controller network and structure. Leveraging the integrated control model, we propose a controller capable of simultaneously controlling the network and structure. Preliminary simulation results indicate that the controller is able to effectively control both the network and structure by switching between sub systems within the controller network.