|M.Sc Student||Hermann Avriel|
|Subject||Flight Control Law Clearance Using Optimal Control Theory|
|Department||Department of Aerospace Engineering||Supervisor||Professor Yoseph Ben-Asher|
|Full Thesis text|
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 specific criterion chosen was the angle-of-attack limit exceedance criterion, and two different cost functions were constructed that accurately describe it. Using Aero Data Model In Research Environment to obtain accurate aerodynamic coefficients, a longitudinal short-period model was developed. It was proven for both cost functions that the general system has a bang-bang worst case input when the states are unbounded, and a possible bang-singular-bang worst case input when one or more states are bounded. Next, these results were validated with simulations using General Pseudospectral Optimal Control Software. Three different cases were tested: an ideal servomechanism base case, one with a first order servomechanism added to the dynamics, and another with a second order servomechanism added. Results indicated that using the second cost function with a set time interval and a Lagrange formulation was faster and more accurate than using the first cost function with a free final time and Mayer formulation. Next, it was shown that the base case has a bang-bang worst case input with the first costate as its switching function. The first and second order servomechanism cases with unbounded states yielded bang-bang worst case inputs as well, with the switching functions dependent on the third and fourth costates respectively. When tested again with bounded states, their worst case inputs changed to bang-singular-bang form. In the physical domain these results translate into actuator rate limiting issues; that limited elevator deflection and rate of elevator deflection can lead to even more extreme worst case performance. Experimenting with approximations of these input signals in the ADMIRE model demonstrated that they achieve high maximum angle-of-attack outputs even in a complex system. Furthermore, it was confirmed that bang-singular-bang inputs in a realistic system, on average, attain a higher maximum angle-of-attack than bang-bang inputs. While GPOPS simulations took too long to be useful in the industrial setting, the optimal control formulation of the clearance problem still appears promising, and further investigation is recommended.