Flight control law clearance using worst-case inputs

This study explores the effectiveness of applying optimal control techniques to the flight control law clearance problem, which is the challenge of ensuring the safety of an aircraft's flight control system for all allowable inputs. The main criteria chosen were the angle-of-attack limit exceeding criterion in the longitudinal plane, and the angle-of-sideslip limit exceeding criterion in the lateral plane. Other criteria, such as load factor and side-force were also considered. Using general double-engine airplane aero data to obtain realistic aerodynamic coefficients, longitudinal and lateral linear models were developed. The flight control system developed for this aircraft by the Institute of Flight System Dynamics (FSD) of Technische Universität München was used for the clearance task. A linear system of this type has a bang-bang worst case input (i.e. using only maximum or minimum values) when the states are unbounded; but a possible bang-singular-bang or bang-bang-singular worst-case input when one or more states are bounded (i.e. intermediate values are also used). These results were validated with collocation-based optimization using Fal-con.m (FSD Optimal Control Tool for MATLAB). In the physical domain these results translate into actuator rate limiting issues; thus limited elevator/rudder/aileron deflection and rate of elevator/rudder/aileron can lead to even more extreme worst case performance. The input signals in this study were pilot commands (stick and pedal) and/or wind disturbances in the form of gusts. The main findings in the longitudinal plane were that the pilot stick commands typically involve maximal/minimal and sometimes intermediate values (whenever the elevator gets saturated). Wind disturbances in this plane (normal gusts) are typically maximal/minimal (bang-bang) and their effect on the aerodynamic angle-of-attack highly depends on the gust shape (equivalent time constant). The main findings in the lateral plane were that the pilot stick commands have very little effect on the sideslip, thus demonstrating a very good decoupling. The pilot pedals, on the other hand, were very effective in building up sideslips and the worst-case structure was obtained by using them periodically (in a trapezoidal wave shape) at the Dutch-roll frequency. The worstcase wind disturbances are non-periodic maximal/minimal (bang-bang) and their effect on the aerodynamic angle-of-sideslip highly depends on the gust shape.