Robust Predictive Control for Structures Under Damage Condition

Abstract

M ODEL-BASED predictive control approaches have attracted much attention in both academia and industry due to their relatively simple time-domain formulation and good performance [1]. Among these methods, generalized predictive control (GPC) [2], which combines the process of system identification and the process of predictive control design, has received widespread acceptance and has been successfully applied to various test beds [3,4]. A version of the GPC procedure was developed at NASA Langley Research Center (LaRC) for efficient computation and unknown disturbance rejection [3,4]. A fundamental issue about GPC is its robustness to model uncertainty. Current GPC techniques do not incorporate the identified damage and the quantifiedmodel uncertainty in the control design process. A robustness predictive control approach with the incorporated model uncertainty was recently developed for the application to the benchmark active controls technology (BACT) wind-tunnel model [5]. The integration of the identified damage into GPC is one major issue addressed in this Note. Aircraft structural damage and component damage can cause unwanted aerodynamic effects and may lead to a catastrophic structural failure of the flight vehicle [5]. If these anomalies can be identified, they can be used as input to an adaptive control system to properly adjust and accommodate these conditions. During the flight, aircraft structural damagemay continue to grow after damage occurs, and so it is important to design a controller that can accommodate more severe damage than the initially identified one. One important issue addressed in this study is the performance and stability of the designed controller under various levels of damage. The aeroelastic flutter of a flight vehicle is a dynamic instability associated with the interaction of aerodynamic, elastic, and inertial forces [6]. Flutter can lead to a catastrophic structural failure of the flight vehicle. Recently, flutter suppression techniques have been investigated on the BACT wind-tunnel model [7–9], which was developed by the researchers at LaRC to address the flutter problem. In this Note, the developed approaches will be demonstrated by application to the BACTwindtunnel model with time-varying dynamic pressure andMach number under damage. The main accomplishment of this Note is the development of a predictive control design process capable of including the identified structural damage and the quantifiedmodel uncertainty, which can be applied to online aircraft flutter suppression with damage under changing flight conditions. The integration of the identified damage into GPC is one major issue addressed in this study. This approach has four fundamental steps in the design process. The first step is to perform online system identification to compute output prediction matrices to map input–output data from different periods of time. The second step is to use singular value decomposition [10] to characterize and quantify parameter uncertainties of the identified output prediction matrices, which are identified directly from online input/output data [4] under various flight conditions. The third step is to identify the damage type and intensity by comparing the changes of the elements of the identified prediction matrices with the changes of the analytical model due to damage [11]. The fourth step is to integrate the output response error due to the identified damage and the response error due to the identified dominant uncertainty coordinates into the cost function for predictive control design. The design for the system with damage is done by tuning the weights of the error term corresponding to the identified damage and the quantified uncertainty.