Robustness Analysis of Flight Controllers for Fixed-Wing Unmanned Aircraft Systems Using Integral Quadratic Constraints

A robust analysis framework for mathematical validation of flight control systems is presented. The framework is specifically developed for the complete uncertainty characterization, quantification, and analysis of small fixed-wing unmanned aircraft systems (UAS). The analytical approach presented within is based on integral quadratic constraint (IQC) analysis and uses linear fractional transformations on uncertainties to represent system models. While IQC analysis has a sound theoretical foundation, there remains a lack of literature on applying IQCs to complex engineering systems and evaluating their effectiveness with physical data. One difficulty lies in appropriately characterizing and quantifying the uncertainties such that the resulting uncertain model is representative of the physical system while forming a computationally tractable problem that is not overly conservative. This paper addresses these challenges by applying IQC analysis tools to analyze the robustness of a UAS flight control system. Uncertainties are characterized and quantified based on mathematical models and flight test data obtained in-house for a small commercial off-the-shelf platform with a custom autopilot. Furthermore, an established gradient-based minimization routine is implemented with IQC analysis to demonstrate how IQC analysis can guide the control design process. This approach also reveals the controlled system's sensitivities to uncertainties, thereby assisting the designer in determining how much uncertainty allowance ought to exist in certain aspects of the UAS. Finally, these methods are tested in physical flight to showcase the effectiveness of IQC analysis and assess the conservativeness of the approach. The proposed framework is also transferable to other fixed-wing UAS platforms, effectively taking IQC analysis beyond academic examples to practical application in UAS system design, control design, and airworthiness certification.