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Clearance of flight control laws using optimisation

Final Report Summary - COFCLUO (Clearance of flight control laws using optimisation)

Proving to the certification authorities that an aircraft is safe to fly is a long and complicated process. It is the responsibility of the manufacturer to show that the aircraft complies with the certification specifications, and especially the so-called airworthiness code. This code contains a huge amount of different criteria that has to be met. Before manned flights are performed to show that an aircraft meets all the clearance criteria, simulations and computer computations are performed. The COFCLUO project has focused on the computer computations in the certification process. If the computations can be made faster, time is saved which will reduce time to market for new products and will also allow for rapid prototyping. Moreover, it is also desirable to make the computations more detailed and accurate which will improve the quality of, and thus increase the safety of aircraft.

The project was structured into three work packages, namely modelling, optimisation, evaluation.

Modelling
This work package was dedicated to develop suitable parametric models to serve for aircraft clearance purposes and related software tools to support various modelling activities. The basic aircraft models describe the dynamics of a generic two engines civil aircraft and serves primarily for simulation and structural modes analysis purposes. The provided flight controller covers both the normal as well as peripheral flight envelope. For implementing different clearance criteria for a range of optimisation-based approaches, different types of parametric models were needed to be employed. A non-linear dynamics aircraft model with explicit parametric dependencies has been developed together with appropriate flight control laws to be cleared. Also so-called integral linear models depending on relevant parameters have been provided to model flexible aircraft configurations. A criteria library has been defined and implemented starting from the specifications of the benchmark problem for both the integral linearised as well as non-linear closed-loop aircraft models. The trimming and linearisation tools have been also used to obtain parameter dependent linearised models (so-called LPV models), which can be alternatively described using linear fractional transformation (LFT) based representation of system matrices. LFT-based models for the closed-loop aircraft models (both nonlinear and integral models) have been generated to serve for analysis purposes. While most of the work has been carried out during the first year, the LPV- modelling and LFT-generation activities have been pursued practically during the whole project period by improving successively the quality of approximations, developing new LPV-approximation methods and generating LFT - models of lower complexity.
% Optimisation
Several different techniques were developed to address clearance of flight control laws (CFCL). They can be grouped in two different categories:
1. sufficient techniques based on solving convex optimisation problems and using LFR models of the aircraft;
2. necessary techniques based on solving nonlinear optimisation problems and using standard nonlinear differential equation models of the aircraft.

In the first category LFT models had to be developed and then convex optimisation problems were solved. In case the method delivers a positive answer, it is for sure known that the whole region of the flight envelope and the whole region of uncertain parameters considered are cleared. However, if the method delivers a negative answer, nothing is known, i.e. it could be the case that the region considered is safe, but the method was not able to provide that answer. Therefore the methods in this category are conservative, i.e. they are so- called sufficient techniques for CFCL. Also the methods might provide the wrong answer in case the LFR models do not approximate the nonlinear differential equations of the aircraft accurately enough.

In the second category no LFT models need to be developed. In case a method finds a violation of clearance criteria, it is for sure known that there is a point in the flight envelope which is not cleared. In case the optimisation algorithm is able to find the global optimum at least one unsafe point in a region that has unsafe points will be found. This is the reason why this category of methods is called necessary techniques for CFCL.

The following work was performed:
- translation of a set of representative flight control law clearance problems into simulation-based objective functions for optimisation;
- investigation and enhancement of global search algorithms;
- development of a clearance strategy based on global search that assures detection of worst cases with a prescribed confidence level;
- building up a flexible prototype clearance tool including mechanisms for parallel computation based on a proprietary optimisation tool;
- testing and verification of the tool;
- benchmarking the flexibility of the tool by introducing other simulation models and / or criteria.

Evaluation
In the evaluation work packaged, the link between research techniques and industrial processes has been assessed. The first activity was about formulating a realistic clearance benchmark problem. Two benchmarks were finally submitted. The first benchmark comprises clearance of flight control law considering both rigid aircraft and non-linear modelling of the closed loop. Two major issues have driven this choice: performance assessment in a nonlinear framework, and validation of requirements on the whole flight domain considering a wide class of pilot inputs and wind perturbations. The second submitted benchmark was about flight control law clearance on flexible aircraft. Because of a better overall aircraft design optimisation and widening of aircraft sizes, bandwidth of bending modes slow down and comes very close to the rigid body mode. Then two major issues arise: control laws must not over-shoot loads objectives assigned by structural aircraft design, and control laws can help designers in optimising the a/c structure by reducing the limit loads.

The second activity was the description of the baseline solution in order to be able to evaluate the enhancement after partners had developed their own clearance methodologies. The validation is today performed using a wide set of means from batch simulation to flight tests. The main objective for AIRBUS is to be able to detect bad behaviours as soon as possible in the validation process so as to be able to quickly (and then for a low price) modify the design. Current practices are mainly based on gridding and Monte Carlo-based approaches. The main expectation is thus to get faster worst-case detection methods or a continuously cleared region (rather than a finite set of points).

The project has resulted in new modelling techniques as well as new optimisation-based clearance techniques. It has been demonstrated on an industrial benchmark that the new techniques are very promising, and it is the intention of AIRBUS to use the new techniques in their development process. Industry has made a huge step forward thanks to the COFCLUO project and a part of the developed methods will be certainly used in a development context within AIRBUS. Later on when confidence has been gained internally, AIRBUS could propose to airworthiness authorities that they include the methods in the official clearance process.

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