Robust Linear Design for Flight Control Systems with Operational Constraints

Abstract: This paper presents a systematic approach for designing robust linear proportional-integral (PI) servo-controllers that effectively manage control input and output constraints in flight control systems. The control design leverages the Nagumo Theorem and the Comparison Lemma to prove constraint satisfaction, while employing min-norm optimal controllers in a manner akin to Control Barrier Functions. This results in a continuous piecewise-linear state feedback policy that maintains the analyzability of the closed-loop system through the principles of linear systems theory. Additionally, we derive multi-input multi-output (MIMO) robustness margins, demonstrating that our approach enables robust tracking of external commands even in the presence of operational constraints. Moreover, the proposed control design offers a systematic approach for anti-windup protection. Through flight control trade studies, we illustrate the applicability of the proposed framework to real-world safety-critical aircraft control scenarios. Notably, MIMO margin analysis with active constraints reveals that our method preserves gain and phase margins comparable to those of the unconstrained case, in contrast to controllers that rely on hard saturation heuristics, which suffer significant performance degradation under active constraints. Simulation results using a nonlinear six-degree-of-freedom rigid body aircraft model further validate the effectiveness of our method in achieving constraint satisfaction, robustness, and effective anti-windup protection.