# Integrated optimization of control surface layout for gust load alleviation

## Abstract

Considering active gust load alleviation (GLA) during aircraft design offers great potential for structural weight savings. The effectiveness of a GLA control system strongly depends on the layout of available control surfaces, which is investigated in this article. For the purpose of wing load reduction, a concurrent optimization of controller gains and aileron geometry parameters is carried out. To that end, an efficient update routine for the nonlinear model of a large-scale flexible aircraft with unsteady aerodynamics is presented. Compared to a GLA system using the original aileron configuration, a 9% performance improvement is achieved. Furthermore, a trade-off study is carried out which enables a target-oriented balancing between individual load channels. The significant influence of aileron size and position on overall GLA performance is demonstrated and hence a consideration during the preliminary aircraft design process is recommended.

## Keywords

Multidisciplinary design optimization Control surface design Gust load alleviation Aeroservoelasticity## 1 Introduction

To allow for a more economic and environmentally friendly operation of aircraft, fuel savings are imperative. Besides the efficiency of engines and aerodynamics, the aircraft weight has a major impact on fuel consumption [1]. For instance, a reduction of aircraft weight is achieved using new materials like carbon composites, as it can be seen at the example of the Airbus A350 or the Boeing 787. Another approach is to decrease the design loads of the structure [2, 3] applying active control technologies. For example, the fuel consumption of the Lockheed L-1011 TriStar aircraft could be reduced by 3 % by means of active load alleviation [4]. Considering new aircraft configurations with improved lift-to-drag ratios, a special focus has to be put on gust load alleviation (GLA), as these configurations are prone to have an increased sensitivity to atmospheric disturbances. In [5], an assessment of state of the art GLA applications is made and its potential for weight reductions is pointed out. In industry though, advanced load alleviation functions are still often introduced after the preliminary design phase [5, 6, 7], where only a limited adaption of the structure is possible. Hence, it is advantageous to include the load alleviation system as early as possible in the aircraft design cycle [8]. Promising results are achieved by multidisciplinary design optimization, where aircraft structure and load controller are designed simultaneously (see e.g. [9, 10]). However, less priority is put on optimization of the layout of multifunctional control surfaces and its concrete impact on load alleviation capability.

The aim of this paper is to investigate the potential of simultaneously optimizing the GLA controller gains and the respective control surface layout. To gain realistic results, a flexible aircraft model of industrial complexity is considered in Sect. 2. The nonlinear model includes unsteady aerodynamics and allows to compute cut loads for maneuvers as well as gust encounters. In avoidance of time-consuming model re-building, an efficient update procedure for control surface layout changes is proposed. In the derived optimization setup (Sect. 3), the focus lies on simultaneously optimizing controller and aileron geometry parameters to minimize the wing root bending moment. Additionally, constraints like actuator saturation, passenger comfort and stability requirements are considered. The resulting improvement in load alleviation capability is discussed in Sect. 4, where the optimized aileron layout is compared with a reference configuration. Finally, a trade-off study is carried out to allow a globally balanced load reduction by prioritizing single load channels.

## 2 Modeling and loads computation

### 2.1 Structural and aerodynamic model

*j*located at the three quarter chord respectively (see Fig. 1).

*k*[13]. To enable time domain simulations, a rational function approximation (RFA) of \({\mathbf {Q}}_{ gj }^{\text {}}(k)\) is derived using Roger’s method [14]. According to Eq. (3), the aerodynamic loads depend linearly on the downwash \({\mathbf {w}}_{ j }^{\text {}}\), which consists of a gust-, modal- and control surface (CS)-component. For the gust downwash, the continuous wind field is evaluated at each aerodynamic box and the respective orthogonal components are normalized by the free stream velocity. And the other two downwash components result from the movements of aerodynamic boxes caused by modal displacements and CS deflections, respectively. Note that the translations and rotations of aerodynamic boxes are generally described with respect to the midpoint

*k*of each box (see also Fig. 1) and hence, a transformation to the control point

*j*is necessary. A more detailed explanation on downwash computation is given in [11] and in the next subsection, where the model updating procedure for changing the CS layout is described. Furthermore, it has to be mentioned that the aerodynamic model depends on the current Mach number, air density and free stream velocity, see also [11, 13] for details.

### 2.2 Control surfaces

*k*to a downwash at the control point

*j*(see also [11]). Besides, the Laplace variable is denoted by

*s*and the reference chord length of the aircraft is \(c_{\text {ref}}\).

When changing the geometry of a CS, it is necessary to rebuild the underlying aerodynamic lattice to align it with the new boundaries of the modified CS. This, in turn, requires the AIC matrix to be recomputed and approximated again by a rational function. To avoid this rather time-consuming process during optimization, an alternative approach is proposed here. The AIC matrix is computed only once and the aerodynamic lattice is not further modified. Instead, the present aerodynamic boxes are assigned to the current CSs in a proportional manner.

In summary, each box is weighted according to the percentage of its area overlapping with the respective CS. Thus, only the entries of \({\mathbf {\Phi }}_{ kx }^{\text {}}\) related to the modified CSs need to be updated, whereas the rest of the aircraft model remains unchanged. As the mass distribution and stiffness are assumed not to be influenced, the emerging approximation error is negligible for sufficiently small aerodynamic boxes.

### 2.3 Actuators and sensors

### 2.4 Limit loads computation

To size the structure of an aircraft, it is necessary to determine the limit loads. According to the certification requirements [2, 3], the limit loads are the lower and upper boundary of all loads occurring during aircraft operation at any time. Denoted as \({\mathbf {P}}_{ \text {c,lower} }^{\text {}}\) and \({\mathbf {P}}_{ \text {c,upper} }^{\text {}}\), the limit loads are determined in this paper by simulating extreme flight maneuvers and severe atmospheric turbulence as described in the following subsections.

#### 2.4.1 Maneuver limit loads

*q*and zero roll rate

*p*is trimmed through the horizontal stabilizer. Additionally, the push-over maneuver M1a and the pull-up maneuver M1b are performed. Both maneuvers are trimmed by means of elevator deflections \(\eta\) and differ from each other only by the load factor \(n_z\). The load factors \(n_{z,\text {min}}\) and \(n_{z,\text {max}}\) are specified in the flight maneuvering envelope (

*V–n*diagram) [2, 3] and depend on the design airspeed. Similarly, the bidirectional rolling maneuvers M3a and M3b are trimmed by means of the aileron deflections \(\xi\). Moreover, sudden pilot commands are approximated by the accelerated roll maneuvers M4a and M4b, and the accelerated pitching maneuvers M2a and M2b. The extreme pilot inputs are determined by the CS deflections resulting from the previous maneuvers and are assumed to be established instantly.

Trim table of maneuvers to compute limit loads

ID | Maneuver name | \(n_z\) | | \(\dot{p}\) | | \(\dot{q}\) | \(\eta\) | \(\xi\) |
---|---|---|---|---|---|---|---|---|

M0 | Horizontal flight | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

M1a | Push-over | \(n_{z,\text {min}}\) | 0 | 0 | ? | 0 | ? | 0 |

M1b | Pull-up | \(n_{z,\text {max}}\) | 0 | 0 | ? | 0 | ? | 0 |

M2a | Pilot pull | ? | 0 | 0 | ? | ? | \(\eta (\text {M1a})\) | 0 |

M2b | Pilot push | ? | 0 | 0 | ? | ? | \(\eta (\text {M1b})\) | 0 |

M3a | Roll and pull | 0 | \(\pm\, p_{\text {max}}\) | 0 | ? | 0 | ? | ? |

M3b | Roll and push | \(\frac{2}{3}n_{z,\text {max}}\) | \(\pm\, p_{\text {max}}\) | 0 | ? | 0 | ? | ? |

M4a | Pilot roll and pull | 0 | 0 | ? | ? | 0 | ? | \(\pm \,\xi (\text {M3a})\) |

M4b | Pilot roll and push | \(\frac{2}{3}n_{z,\text {max}}\) | 0 | ? | ? | 0 | ? | \(\pm \,\xi (\text {M3b})\) |

By definition, the maximum roll rate \(p_{\text {max}}\) is set to \(15^{\circ } {\mathrm{s}}^{-1}\) for all operation points, which is a common value for civil aircraft. Furthermore, for all maneuvers, inner and outer ailerons are deflected equally but with opposite sign on the left and right wing. In contrast, elevators are always deflected symmetrically.

#### 2.4.2 Gust limit loads

To compute the structural loads in atmospheric turbulence, the “1-cos” gust model according to the certification requirements [2, 3] is used. For wing loads, gusts in up- and downwards direction are considered as the most critical. Thus, time domain simulations are carried out for vertical gusts with different gust gradient distances *H* varying from 9 m (30 ft) to 107 m (350 ft).

## 3 Optimization setup

### 3.1 Controller structure

### 3.2 Parameterization of ailerons

### 3.3 Objective function

*F*and

*H*denote the considered discrete flight points and gust gradient distances, respectively. Hereinafter, the objective function

*V*is also referred to as performance index for GLA controller evaluation.

### 3.4 Constraints

#### 3.4.1 Limit loads

*c*-set includes all relevant cut loads for aircraft sizing.

#### 3.4.2 Passenger comfort

#### 3.4.3 Stability

#### 3.4.4 Actuators

#### 3.4.5 Handling qualities

As ailerons are also used for lateral control of the aircraft, lateral maneuverability must be maintained. According to the certification requirements [2, 3] as well as the handling qualities requirements [20], roll performance is defined by the time a certain bank angle change can be accomplished. By defining an achievable roll rate of at least \(15^{\circ } \hbox {s}^{-1}\) (see also Sect. 2.4), these requirements are generally fulfilled, not considering any changes in the acceleration behavior. However, roll acceleration basically depends on actuator dynamics and mass moment of inertia [17], which are both assumed not to be affected when changing the control surface layout. Thus, no further handling quality constraints are introduced here.

#### 3.4.6 Rigid body motions

### 3.5 Optimization problem formulation

*V*from Sect. 3.3 and the constraints \(C_1 \cdots C_{6}\) defined in Sect. 3.4. The design variables are the controller tuners \({\mathbf {D}}_{ K }^{\text {}}\) from Sect. 3.1 and the aileron parameters \({\mathbf {D}}_{ \text {ail} }^{\text {}}\) defined in Sect. 3.2. The optimization is performed with MOPS [21] using a gradient based sequential quadratic programming (SQP) algorithm. In each optimization step, the limit loads (Sect. 2.4) of the current aircraft configuration without GLA are computed. Subsequently, the GLA controller is derived, and the objectives and constraints are evaluated with respect to the actual limit loads.

## 4 Results and discussion

*F*at an altitude \(h=8297 \hbox {m}\) and a Mach number \(Ma=0.85\) is considered. The aircraft is assumed to be fully loaded with a minimum amount of fuel in the wings, which is the mass case yielding the largest wing loads during gust encounters. Furthermore, up- and downwards gusts with four different gust gradient distances

*H*= 30 ft, 150 ft, 300 ft and 350 ft are evaluated in each optimization step. Additional flight points and gusts can be taken into account easily, but have been neglected to simplify result interpretation and to save computation time. Besides, the unsteady AIC matrix is computed at 8 frequency points, where the lifting surfaces are discretized by 3526 aerodynamic boxes, see also Fig. 6. Subsequently, the RFA is performed with a number of 6 predefined poles. Taking into account the first 40 flexible modes, this leads to a total number of 888 states for the nonlinear aircraft model.

To obtain satisfying optimization results, it has been found sufficient to consider the shear force, bending- and torsional-moment at three cross sections of the wing (including the wing root) and the root of the horizontal tail plane (HTP). Note that due to the symmetric excitation, the resulting loads and accelerations at the left- and right-hand side of the aircraft are identical and thus are only considered once. In summary, the optimization problem consists of 154 constraints and 10 tuning parameters.

### 4.1 Comparison of optimization results

Aileron effectiveness for rolling

Ailerons | Reference layout | Optimized layout |
---|---|---|

Inner only | 0.8 | 1.4 |

Outer only | 0.4 | 0.1 |

Both | 1.2 | 1.5 |

### 4.2 Discussion of the optimized aileron layout

*V*of the respective aircraft configuration. It can be seen that the WRBM is clearly dominated by the first symmetric wing bending mode (mode 1). Hence, the GLA system should primarily damp this mode without exciting any other modes, which is assumed to be crucial when using the reference aileron layout for GLA. Comparing the first two rows of Table 3, it is shown that the contributions of the modes 10, 12 and 21 are increased when using the reference aileron configuration. In contrast, using the optimized ailerons for GLA, modes 10 and 12 are damped instead of excited. The reason for that can be seen in Fig. 12, where the vertical wing displacements for the corresponding mode shapes are shown for the maximum WRBM at \(t\approx 0.6 \hbox {s}\). Again, in the upper part of the plot, the positions of the reference ailerons are marked, and in the lower part, the positions of the optimized ailerons are marked. The mode shapes 10 and 12 appear to be very similar for this mass case and it can be seen that the optimized inner ailerons are placed further inward than the respective oscillation node. Hence, the vertical displacements of modes 1, 10 and 12 point in the same direction at the range of the inner ailerons. For this reason, a coordinated deflection of the optimized inner ailerons allows damping all three modes simultaneously at this instant of time. Furthermore, the undesired excitation of mode 21 indicates that a compromise is made for the optimal placement of the ailerons. Note that this interpretation is not unambiguous as, for instance, the solution of the optimization problem also depends on many different constraints given in Sect. 3.4.

Comparison of modal contributions to maximum WRBM

Aircraft configuration |
| Mode 1 (%) | Mode 10 (%) | Mode 12 (%) | Mode 21 (%) |
---|---|---|---|---|---|

Without GLA | 100 | 93.79 | 2.72 | 1.36 | 0.82 |

With GLA (reference ailerons) | 79 | 69.78 | 3.54 | 1.7 | 2.07 |

With GLA (optimized ailerons) | 70 | 61.79 | 2.53 | 0.42 | 3.53 |

### 4.3 Load balancing

As already mentioned, actively reducing the wing bending moment is at the cost of an increased wing torsional moment. In addition to that, the loads at the HTP are increased as well due to the deflections of the elevators for pitching moment compensation. This can also be seen in Fig. 13a, b, where the correlated gust loads of the wing root and the HTP root are compared, respectively. A trade-off study is carried out to identify the Pareto front between the WRBM and the WRTM. To that end, the allowable WRTM is successively reduced and the respective achievable GLA performance is determined. As depicted in Fig. 14, this results in a monotonic decrease of the GLA performance for both the fixed reference aileron configuration and a variable aileron configuration to be optimized. In case the closed-loop WRTM is limited to the open-loop WRTM (no GLA), an active alleviation of the WRBM is not possible, even if the aileron layout is optimized. Furthermore, not limiting the WRTM at all does not lead to any better performance than already presented above. Interestingly, setting the WRTM limits to the values from the reference GLA system but allowing an optimization of the aileron layout does not lead to an improvement of the GLA performance. This means that the reference aileron configuration is already optimal if no further increase of the WRTM is allowed.

## 5 Conclusion and outlook

The aeroservoelastic optimization framework presented in this paper allows to simultaneously tune the controller and the control surface (CS) layout for the purpose of active (GLA). An efficient update routine for changes of the nonlinear aircraft model with unsteady aerodynamics is introduced. To obtain a reasonable solution, multiple constraints are introduced including limitations of loads at different cross sections, actuator bandwidth and passenger comfort. The resulting GLA system with an optimized aileron geometry allows to reduce the wing root bending moment (WRBM) by 30%, whereas with the reference aileron configuration only 21% can be achieved. An active reduction of the WRBM leads to an increase of the wing root torsional moment (WRTM) and the horizontal tail plane (HTP) loads, and thus, a trade-off has to be made. On the basis of individual mode shapes, the optimal placement of the ailerons is explained, where the dependency on the actual mass case needs to be considered. For future investigations, it is necessary to take into account the whole design envelope, which increases the complexity of the optimization problem. In addition to that, the interaction of the GLA system with the electronic flight control system (EFCS) also has to be considered. Apart from that, further performance improvements are expected if a more advanced controller structure or additional CSs like spoilers are used. Last but not least, the concrete weight savings need to be determined to evaluate the impact on the direct operating costs of the aircraft.

## Notes

### Acknowledgements

Part of the research has been funded in the course of the European Union’s Seventh Framework Program (FP7/2007-2013) in the Clean Sky Joint Technology Initiative under Grant agreement CSJU-GAM-SFWA-2008-001.

## References

- 1.International Energy Agency: Transport, Energy and CO\(_2\). IEA Publication, Paris, France (2009)Google Scholar
- 2.Federal Aviation Administration: Federal Aviation Regulations Part 25. Transport Category, Airworthiness Standards (2015)Google Scholar
- 3.Agency, European Aviation Safety: Certification Specifications and Acceptable Means of Compliance for Large Aeroplanes, CS-25. Amendment 16 (2015)Google Scholar
- 4.Johnston, J.: Accelerated development and flight evaluation of active controls concepts for subsonic transport aircraft. Volume 1: load alleviation/extended span development and flight tests. NASA (1979)Google Scholar
- 5.Regan, C.D., Jutte, C.V.: Survey of applications of active control technology for gust alleviation and new challenges for lighter-weight aircraft. NASA (2012)Google Scholar
- 6.Flaig, A.: Airbus A380: solutions to the aerodynamic challenges of designing the worlds largest passenger aircraft. Royal Aeronautical Society Hamburg Branch Lecture Series (2008)Google Scholar
- 7.Kaminski-Morrow, D.: Airbus exploits A320 load-alleviation to offer higher MTOW. Flight Global (2008). http://www.flightglobal.com/news/articles/airbus-exploits-a320-load-alleviation-tooffer-higher-mtow-319049/
- 8.Livne, E.: Integrated aeroservoelastic optimization: status and direction. J. Aircr.
**36**(1), 122–145 (1999). https://doi.org/10.2514/2.2419 CrossRefGoogle Scholar - 9.Haghighat, S., Martins, J.R.R.A., Liu, H.H.T.: Aeroservoelastic design optimization of a flexible wing. J. Aircr.
**49**(2), 432–443 (2012)CrossRefGoogle Scholar - 10.Xu, J., Kroo, I.: Aircraft design with active load alleviation and natural laminar flow. J. Aircr.
**51**(5), 1532–1545 (2014)CrossRefGoogle Scholar - 11.Kier, T., Looye, G.: Unifying manoeuvre and gust loads analysis models. In: International Forum on Aeroelasticity and Dynamics. Seattle (2009)Google Scholar
- 12.Waszak, M.R., Schmidt, D.K.: Flight dynamics of aeroelastic vehicles. J. Aircr.
**25**(6), 563–571 (1988)CrossRefGoogle Scholar - 13.Rodden, W., Johnson, E.: MSC.Nastran Version 68, Aeroelastic Analysis and User’s Guide (2004)Google Scholar
- 14.Roger, K.L.: Airplane math modelling methods for active control design. Structures and Materials Panel (1977)Google Scholar
- 15.Bisplinghoff, R., Ashley, H., Halfman, R.: Aeroelasticity. Dover Publications, Mineola, NY, USA (1955)zbMATHGoogle Scholar
- 16.Fezans, N., Joos, H.D.: Combined feedback and lidar-based feedforward active load alleviation. In: AIAA Atmospheric Flight Mechanics Conference, p. 3548 (2017)Google Scholar
- 17.Sadraey, M.H.: Aircraft Design: A Systems Engineering Approach. Wiley, Chichester, UK (2012)CrossRefGoogle Scholar
- 18.Kubica, F., Madelaine, B.: Passenger comfort improvement by integrated control law design. Tech. rep, DTIC Document (2000)Google Scholar
- 19.Hoblit, F.M.: Gust loads on aircraft: concepts and applications. AIAA (1988)Google Scholar
- 20.Moorhouse, D., Woodcock, R.: US Military Specification MIL-F-8785C (1980)Google Scholar
- 21.Joos, H.D.: A multiobjective optimisation-based software environment for control systems design. In: Computer Aided Control System Design, 2002. Proceedings. 2002 IEEE International Symposium, pp. 7–14. IEEE (2002)Google Scholar
- 22.Pusch, M., Knoblach, A., Kier, T.: Integrated optimization of ailerons for active gust load alleviation. In: International Forum on Aeroelasticity and Structural Dynamics, Saint Petersburg, Russia, paper, p. 199 (2015)Google Scholar
- 23.Pratt, K.G., Walker, W.G.: A revised gust-load formula and a re-evaluation of v-g data taken on civil transport airplanes from 1933 to 1950. Tech. rep., NACA Report No. 1206 (1954)Google Scholar
- 24.Schmidt, D.K.: Modern flight dynamics. McGraw-Hill, New York (2012)Google Scholar

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