Coordinated Roll Control of Conformal Finless Flying Wing Aircraft

Attitude control of tailless aircraft is typically achieved through a system of trailing-edge flaps that produce coupled control effects in pitch, roll and yaw due to changes in lift and drag distributions. This paper presents a novel control allocation method which allows conformal trailing-edge controls to generate yawing moments with no coupling, thereby simplifying the required control suite. The method is demonstrated through modelling of a coordinated roll manoeuvre of a tailless aircraft in which yaw control is provided by trailing-edge flaps only. For a typical tailless aircraft configuration, it is shown that a coordinated rolling manoeuvre can be achieved with a reduction of at least 30% of the required control deflection compared to solutions using non-conformal controls such as split drag rudders.


I. INTRODUCTION
A representative form of a low observable aircraft can be idealised as a blended wing with projected area in a single plane (finless) and with aerodynamic controls that do not affect surface topology when deflected (conformal). The present work is concerned with developing a method for three axis attitude control of such an aircraft that enables fully coordinated roll manoeuvres in which roll rate, angle of attack and angle of sideslip are controlled independently by use of conventional trailing-edge controls only. This is in contrast to existing techniques that require use of non-conformal controls such as split drag rudders or spoilers in addition to conformal trailing-edge flap controls.
In recent years, there has been an increased interest in the development and testing of tailless aircraft demonstrators for both civil [1], [2], [3] and military [4], [5], [6] concepts. Due to the relatively short tail arm on these configurations, a relatively large vertical fin area is typically needed to meet The associate editor coordinating the review of this manuscript and approving it for publication was Rosario Pecora . lateral stability and control requirements. For both civil and military aircraft there is a pressure to reduce the size of these fins to reduce drag and, for military concepts, to also reduce observability [7], [8]. Without fins, the configurations tend to have only marginal directional stability and require stability augmentation to prevent departure in sideslip.
A roll manoeuvre is typically affected by deflection of wing trailing-edge controls to introduce a lateral asymmetry in the spanwise lift distribution and hence rolling moment about the aircraft centre-line. However, the control inputs will also cause a change in spanwise drag distribution and this will introduce a secondary yawing moment, leading to some degree of roll-yaw coupling [9], [10], [11], [12], [13], [14]. For roll manoeuvres used to turn an aircraft, the roll-yaw coupling due to control surface deflection is adverse in the sense that it leads to an out of turn (uncoordinated) moment and hence sideslip.
The magnitude of adverse yaw generated during a rolling manoeuvre can be minimised by appropriate design of the wing trailing-edge control surfaces and control allocation strategy. This can be achieved by tailoring the symmetric spanwise lift distribution such that deflecting the control surfaces generates a proverse yawing moment. This has been shown to be successful through analytical [9], [14], [15], [16], [17], [18], numerical [18], [19], [20] and experimental [21], [22] work. These methods work by using a bell shaped distribution, developed by Prandtl [23], [24] and later Nickel [9] using different assumptions, along with strategic aileron placement such that the upgoing control surface generates a greater induced drag than the downgoing control surface. Although this method is successful in alleviating the impact of adverse yaw, it does not present a solution to the problem of directional control.
To provide yaw control, some studies have investigated continuous control of the spanwise load distribution by means of morphing [15], [21]. These solutions appear to provide control authority which is sufficient for full 3-axis control of an aircraft. However, the actuation systems are typically complex and require high torques compared to conventional control surfaces [21]. A more typical solution would be to use Split Drag Rudders (SDRs), which, when deployed, produce laterally asymmetric drag on the airframe and therefore a yawing moment [10], [25]. Efforts have been made to reduce the observability impact of these control surfaces using improved control allocation [26], however there is still a performance and observability penalty for use of this actuation method.
An alternative method of yaw control uses laterally asymmetric induced drag created by actuating control surfaces on the same wing in opposing directions [13], [27], [28]. This method has the advantage of not requiring any additional control surfaces and hence eliminates the weight and complexity of additional actuators. However, in the method proposed in these studies the inboard and outboard actuators are actuated by an equal magnitude in the opposing sense. Whilst this will produce a yawing moment, there will also be a secondary effect in both pitch and roll. Previous work has also shown the possibility of using trailing-edge control surfaces to generate asymmetric profile drag, known as crowmixing [29]. Similar to the previously discussed methods, the inner and outer control surfaces are deflected in opposing directions but with a much greater magnitude. This has been flight tested on experimental tailless aircraft but has not yet been utilized on operational aircraft [29]. While this does mitigate some of the disadvantages of spoilers and SDRs (i.e., the penalty of integration into the structure and additional actuators), the requirement to deploy large surfaces into the flow to provide a yawing moment remains.
In this paper we propose an alternative yaw control approach which uses only the trailing-edge controls. The control surfaces are deflected in such a way to induce laterally asymmetric induced drag, whilst maintaining the required lift, pitching moment and rolling moment. As these controls are already necessarily present on the aircraft there is no increased complexity of adding extra actuation systems, and the observability impact will also be minimized. Previous works by the authors [30], [31] have demonstrated the applicability of this control method to trim an aircraft in steady sideslip where trailing-edge controls can reduce both the drag (indicator for aerodynamic efficiency) and required control surface deflection (indicator for observability) when compared to wing-tip drag devices. This paper will outline the development of the method to provide yaw control during a rolling manoeuvre and demonstrate the application of this novel control method to an industrially representative aircraft. Calculation of the dynamics of the aircraft through the rolling manoeuvre is performed using low-order methods to allow assessment of handling performance during initial design stages. However, the control method can equally be applied using a higher-order simulation or practical test environment as needed.
Note that, this paper extends our previous (non peerreviewed) conference paper [32]. Specifically, there are three primary developments from this previous work. Firstly, the method presented in the control allocation section has been refined and presented here in much greater detail, allowing improved reproducibility of the model. Secondly, the proposed method has been applied to a more generic flying wing planform (as detailed in section III-A). The previous paper was applied to a demonstrator aircraft which, due to its low wing-loading, has inertia values much smaller than equivalent sized operational aircraft and therefore artificially increases the control effectiveness. Hence, by applying this model to a more representative planform, we demonstrate the generic applicability of this method. Finally, a greater range of flight conditions are evaluated in this work to give confidence that the control method is effective across a wider operational envelope.
The current paper is structured as follows: Section II reviews some necessary theoretical foundational knowledge on how tailoring the lift and induced drag distributions over the span of a wing can be used to control the generated aerodynamic forces and moments. Section III then provides a detailed description of the method proposed, including details of the geometric and inertial configuration of the case study aircraft, modelling of the rolling manoeuvre, the main aspects of the aerodynamic model employed, and the control allocation method conceived and its implementation to the trailing-edge control approach. Section IV provides results demonstrating the applicability of the proposed control allocation method within a rolling manoeuvre for different flight operation conditions, and holistically compares the performance of the proposed trailing-edge control methodology against the classical split drag rudder approach. Finally, Section V highlights the main concluding remarks from the current study.

II. THEORY
Adverse yaw can be well understood using low order tools such as Prandtl's lifting line theory. Prandtl hypothesised that the induced drag on a wing section is a function of the lift on that section and the angle of attack induced at that section due to downwash. Both of these quantities are functions of the spanwise lift distribution: the lift on a section can be found directly from the lift distribution and the downwash (and therefore induced angle of attack) is a function of the derivative of the distribution. Therefore, we can think of induced drag at a section as proportional to the product of the magnitude and derivative of the spanwise lift distribution at that section (i.e., C di (η) ∝ C l (η) ∂C l (η) ∂η ; where C l (η) is the local lift coefficient and η is the non-dimensional spanwise location). Note that, for clarity, the main symbols used in this paper are defined in the appendix in section V.
Consider an unswept, untwisted rectangular wing of aspect ratio 5 with control surfaces extrema at 90% and 60% span. If these control surfaces are deflected to induce an anticlockwise rolling moment (port wing down, starboard wing up) the lift distribution is modified as shown in Fig. 1. This leads to a large increase in drag on the starboard wing and a large decrease in drag on the port wing, generating the adverse yawing moment.

A. CASE STUDY AIRCRAFT
The aircraft selected to demonstrate the efficacy of our proposed method is taken to be representative of a generic future, low observable UAV. It is therefore of low aspect ratio and moderately swept. The geometry and assumed inertia are described in Table 1, and the control surface layout is presented in Fig. 2. The sweep angle is selected so that the leading-edge sweep is greater than 45 degrees but less than 60 degrees to avoid the formation of strong leading-edge vortices [33]. The inertia of the aircraft is estimated by assuming a uniform mass distribution over the planform and concentrated to the x-y plane. Under these assumptions, the off-diagonal terms in the inertia tensor become zero.
The layout in Fig. 3 shows the two control surface arrangements considered in this work. The configuration shown in Fig. 3a uses the two inboard control surfaces for pitch and roll control in a conventional manner and the outer control surface is implemented as a Split Drag Rudder (SDR) and primarily used for yaw control.
The configuration shown in Fig. 3b employs a mode shaping approach in which the control surfaces are deflected to effect a change in induced drag but zero change in lift and pitching moment. The pitch and roll of the aircraft are controlled in the conventional way, i.e., by using a combination of symmetric and antisymmetric components (Fig. 4). This will have some secondary control effect in yaw, due to the adverse yaw effect discussed in section II. However, by introducing the third asymmetric component it is possible to independently control the yawing moment such that full three axis control can be achieved using only the trailing-edge controls. The crux of this control method is designing the asymmetric component such that it does not produce any change in pitching moment, rolling moment or lift and is discussed further in section III-D4.

B. MANOEUVRE MODELLING
In order to assess the effectiveness of each control surface arrangement specified in the previous section, the state of the aircraft will be modelled through a rolling manoeuvre. A summary of the process used to perform this is shown in Fig. 5. The section enclosed within the broken lines indicates the models used within this work to assess the efficacy. However, if this method was to be implemented in flight this would be replaced with the aircraft actuation systems and sensors to ascertain the aircraft state.
To begin the manoeuvre, the aircraft is initially trimmed wings level at a specified angle of attack. There is then a step antisymmetric control input to begin the roll, the magnitude of this input will be discussed in section III-D1. The aircraft state and control input are then passed to the aerodynamic model to calculate the forces and moments. Depending on the implementation, this block can be replaced with any model which takes the aircraft and control states and outputs forces and moments. In this work we use a modified lifting surface method described in section III-C. These forces and moments are then passed to a flight dynamics model. Again, when implementing this method any flight dynamics model could be used. In this implementation, we assume that at all points during the rolling manoeuvre the turn is coordinated, and the vertical component of lift is maintained, reducing the complexity required.
The aircraft state is then passed to the dynamic inversion block which calculates the required pitching and yawing moment required to maintain the required angle of attack and zero sideslip. This process is detailed in section III-D2. Finally, the controls are updated using the control allocation method described in section III-D3 and III-D4 for the SDR and mode shape configurations, respectively.

C. AERODYNAMIC MODELLING
To allow for efficient computation of aerodynamic forces and moments within the manoeuvre modeling, a low-order aerodynamic model was used to reduce the computational expense. The selection of the most appropriate low-order model for this task, performed previously by the authors, can be found in [30], with the Lifting Surface (LS) model [34] identified as the preferred approach due to its generality and agreement with experimental data for tailless aircraft. The implementation of the lifting surface model, including VOLUME 11, 2023 FIGURE 1. Lift and induced drag distributions for an unswept, untwisted rectangular wing of aspect ratio 5. Green region has control surfaces deflected 3 • downwards and red region has control surfaces deflected 3 • upwards. The lift and induced drag in the green region is greater than the red leading to a roll to the right, but out of turn yaw to the left. ''undisturbed'' lines show the distribution with no control deflection, the ''control'' lines show the incremental distribution induced by control deflection, and ''Undisturbed+controls'' show the overall distribution where controls are deflected.  the treatment of control surfaces, is fully discussed in [30], so details will not be repeated here, and only key considerations will be discussed in what follows. The aerodynamic modelling process is, also, summarized in Fig. 6. The lifting surface model calculates the spanwise (γ ) and chordwise (µ) load distributions for a given geometry through the solution of a linear system of Aerodynamic Influence Coefficients (AIC). The assembly and inversion of the AIC matrix is the most computationally expensive part of the model. As the AIC must be reconstructed and therefore inverted every time the sideslip angle changes, we use a process of linear superposition to remove this reformation from the process (see Fig. 6). To achieve this, the spanwise and chordwise load distributions are calculated for a range of sideslip angles at zero angle of attack (i.e., γ (β)| α=0 • and µ(β)| α=0 • ); these distributions are then superimposed with the load distribution calculated at each time step from the state given by the flight dynamics model (i.e., γ (α)| β=0 • and µ(α)| β=0 • ). In this way, LS evaluations are dramatically reduced allowing efficient execution.
To calculate the load distribution at zero angle of sideslip, the angular rates of the aircraft must be taken into account as these will modify the local angle of attack as a function of the spanwise location. An intermediate angle of attack is found as the sum of the geometric angle of attack and the change due to roll and pitch rates: Roll rate is accounted for by changing the local angle of attack at each section by: Similarly, for the pitch rate: 61404 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.   Finally, the angle of attack is updated in response to yaw rate to represent the increased lift due to asymmetries in the oncoming flow. This leads to the final local angle of attack below, which is used by the lifting surface model to calculate the load: Now we must find the magnitude of aileron input required for the manoeuvre. As a first step, we define the variable τ as the time taken to roll to 45 degrees. We then consider the rolling aircraft as a one dimensional system in which the only moments acting on the aircraft are due to control input and roll damping from the wing: By solving (5) for φ(t) with a constant ξ , we find: Finally, to find the required control deflection we substitute φ(τ ) = 45 • ( π 4 rad) into (6):

2) REQUIRED CONTROL MOMENTS -DYNAMIC INVERSION
To compute the required control moments in pitch and yaw, we first define a state vector (x) which describes the full state of the aircraft at some point in time. We define this as x T = ψ θ φ p q r γ C l .
At any timestep we can find the rate of change of the state variable using the state space equation: In this approach we use the non-linear, functional representation, of the state space rather than the more conventional approach of a linear system. The utility of this will become clear later in this section.
The angular velocities of each of the Euler angles (ψ,θ anḋ φ ) are updated using the angular rates (p, q and r) which are defined in the stability axes. Therefore, by appropriate transformation the angular velocity of each of the Euler angles is readily obtained.
The angular rates are updated by calculating the moments on the aircraft, these are calculated in stability axis using the matrix of aerodynamic derivatives below: Using an appropriate transformation matrix these moments are transformed to the body axis. The vector of moments is then divided by the aircraft inertia tensor to calculate the rate of change of the angular rates p, q and r. The change in flight path angle (γ ) is readily obtained using the assumption that at all points during the manoeuvre the aircraft is in a coordinated turn. If this is the case, then the rate of change of the flight path angle must be:γ Finally, the rate of change of the rolling moment is zero as we have defined this in a previous step. We can then define the desired properties of the aircraft in the form: In this case y is a 2 element vector which maintains a constant vertical component of lift: And also maintains zero side slip. To calculate the required moment, we then differentiate (11) to obtain: Substituting in (8): Which we simplify as: However, in this case G(x) (i.e., ∇hg(x)) is zero. This is to be expected as the control inputs will change the angular rates but do not directly change the flight path or orientation of the aircraft. This means that equation (15) is non-invertible and therefore cannot be solved in this form for u. To overcome this, we differentiate again giving: Again, substituting (8): To linearise the output, we define an auxiliary input (v): Which we differentiate in time and substitute into (15) to yield:ÿ =v +d We then define an error vector (e) which describes the difference between our current and desired state: Substituting this into (19) gives an expression for the error dynamics as:ë If we choose a simple PI controller to select an appropriate value for v, the error dynamics become a second order ODE: For this work, the proportional and integral gains were set at 20 and 800, respectively, for the angle of attack objective (12) and 40 and 400, respectively, for sideslip (β = 0). This was found to provide a satisfactory performance in the cases analysed. Finally, we substitute (22) into (21) and the result into (19). The required moments are then calculated from:

3) SPLIT DRAG RUDDER
With the required moments calculated from the previous section, the required control surface deflections can be easily calculated for the SDR configuration. First, the inboard two control surfaces are deflected antisymmetrically by the angle ξ calculated in section III-D1. Similarly, the symmetric part of the deflection is calculated using the pitch derivative and the required pitching moment: The resultant deflection angle of the two most inboard control surfaces on each semi-span are therefore the sum of the antisymmetric (ξ ) and symmetric (ι) parts.
The SDR's operate in a bias mode as defined in [13], with a bias angle of 20 degrees. This achieves two things, firstly the roll-yaw and pitch-yaw coupling of the SDR is reduced and secondly it linearises the yaw response with respect to SDR angle. Therefore, the deflection required by the split drag rudders is:

4) TRAILING-EDGE CONTROLS
The yaw response of the aircraft to trailing-edge control deflection is a somewhat more complex problem. However, as we have defined the mode shapes in such a way that the pitching moment and rolling moment are held constant we can define the trailing-edge control deflection as three unique components: A symmetric part, which controls pitch; An antisymmetric part, which controls roll; and, an asymmetric part, which controls yaw. The pitch and roll deflections are easily defined using the linear control derivatives and required control moments. Note, however, that the control derivatives will be different to the SDR configuration as we actuate all three trailing-edge surfaces. To define the asymmetric control surface deflection, we use the representation of yawing moment coefficient as a function of control surface deflection from [30]: where δ i is the deflection of the ith control surface; this is made up of the symmetric and antisymmetric components for pitch and roll control (δ s and δ a ) and the gains for each mode shape (k), which represent the asymmetric component: where n i * represents the ith row of the null space matrix n. The principle by which the asymmetric mode shapes induce a yawing moment is based upon introducing an asymmetry in the spanwise loading which introduces an imbalance in the induced drag. However, during a rolling manoeuvre there is an additional antisymmetric loading induced, the strength of which is proportional to the non-dimensional rollrate ( pb V ∞ ). This affects the value of C n0 and the matrix D. The matrices E and F are unaffected by this as they represent the interaction between control surfaces and profile drag of the control surface, respectively. We can therefore write equation (26) as: For this configuration with six control surfaces in total, there are three mode shapes and therefore equation (28) is under defined (one equation and three unknown gains). Therefore, to find a control deflection we use a Sequential Quadratic Programming optimizer which finds the mode shape gains which satisfy the yawing moment demand for the minimum total deflection and ensure all control surface deflections are less than ten degrees so that the assumption of linear aerodynamics remains valid. Additionally, the speed of the control surfaces is restricted to 30 • /s to represent a typical actuator. We can write this as the optimisation problem: This optimisation may fail as it is not guaranteed a feasible region will exist (for example the yawing moment demand could exceed maximum authority of the trailing-edge controls). If this is the case the optimisation reruns to minimise the error in yawing moment whilst keeping the maximum deflection less than ten degrees and deflection rate less than 30 • /s: With the optimal mode shape gains obtained through the optimization, the control surface positions can be updated using equation (27). It should be noted that depending on the design intent for implementing this control allocation method, designers may select any cost function for equations (29) & (30) which best suits their application. The total deflected area is used in this case as a surrogate for observability.

IV. RESULTS
To assess the efficacy of the proposed control allocation method, a rolling manoeuvre was simulated for each of the control configurations. The case study aircraft was initially at a trimmed, wings level flight condition at a specified angle of attack between 1 and 6 degrees. At t=0 there was a step asymmetric input sufficient to roll the aircraft to a bank angle of 45 degrees in τ seconds. τ was varied between 1.2 seconds and 8 seconds to show the efficacy of the control allocation methods for both aggressive and gentle manoeuvres. We compare the performance of the aircraft to the requirements in MIL-F-8785C [35], which require the angle of sideslip remains within the limits of 2 degrees proverse and 5 degrees adverse. We also introduce a metric of angle of attack excursion, which compares the angle of attack through the manoeuvre to the target in (12): The manoeuvre is deemed to fail if the difference between the instantaneous angle of attack (α(t)) and target angle of VOLUME 11, 2023 attack as a function of the bank angle (α(φ)) is greater than 10% of the target.
First, we examine the performance of the SDR configuration throughout the manoeuvre, Fig. 7. It can be seen here that for even the most aggressive manoeuvres, the SDR comfortably maintains the desired angle of attack and keeps the sideslip less than half a degree in all cases. Examining the case where τ = 1.4s, the performance prescribed by [35], we see that the manoeuvre can be completed for all angles of attack examined within a sidelslip angle of less than one degree.
Next, we examine the performance of the aircraft through the manoeuvre in the trailing-edge control configuration, Fig. 8. Cases where the manoeuvre fails, either because the error in angle of attack is greater than 10% or the sideslip exceeds the limits defined in [35], are represented with a broken line. The agility of the aircraft is clearly reduced compared to the SDR configuration and is only able to complete the manoeuvre in 1.4s as specified by MIL-F-8785C at an angle of attack of one degree.
However, examining the aerodynamic angles in Fig. 8 we see that in all cases the manoeuvre fails due to an error in the angle of attack rather than sideslip. Due to the non-zero roll rate of the aircraft, the magnitude of yawing moment has some influence on the angle of attack. However, as the yaw control is saturated (i.e., the yaw demand is greater than the control authority) the correct combined moment of pitching and yawing moment, as requested by the dynamic inversion controller, is not imparted to the aircraft. This results in this error in angle of attack. It is thought that with a different method of calculating the desired moment, this error could  Relative control deflection during rolling manoeuvre. A value of less than unity indicates the total deflection of the mode shaping configuration is less than that of the SDR configuration. be reduced. Although it is likely that the agility of the aircraft would still be reduced compared to the SDR configuration.
However, the goal of the method using only trailing-edge controls was not to achieve an improved agility but rather to reduce the control system complexity and aggregate deflection required to manoeuvre. We compare the mean and maximum control deflection throughout the manoeuvre, defined as the area presented in the normal plane of the aircraft, in Fig. 9. Examining the mean deflection we can see that in all cases examined in this work, the total deflection is at least 40% using the trailing-edge controls only compared to the SDR configuration. Furthermore, we can see that for gentle manoeuvres at angles of attack of 4 degrees and below the reduction in deflection is greater than 70%.
Examining the maximum deflection of each configuration the pattern is less clear, although it can be seen that again in all cases the maximum deflection is reduced by at least 30%. The reason for the behaviour shown in Fig. 9 is due to the fact that there is not one unique solution which satisfies the requirement on yawing moment. There is one solution in which the outermost control surface on the starboard wing is deflected upwards and one in which it is deflected downwards, this is shown in Fig. 10 where the roll at τ = 3s is shown for angles of attack of 1-3 degrees. In Fig. 10a, the outer control surface is deflected upwards and in Figure 10c it is deflected downwards. Deflecting the trailing-edge downwards gives a greater maximum yawing moment, however the total deflection is increased. Once an initial direction is selected however, this solution becomes the only viable solution in the optimiser due to the constraint on the actuation speed of 30 • /s.
Examining Fig. 10d we can see that using either control configuration has very little effect on the roll angle with time and Fig. 10e shows that both control methods also keep the angle of attack error less than 0.5%. In Fig. 10f, we see that for the one and two degree angle of attack cases there is very little difference between the mode shape and SDR configurations in terms of the sideslip angle. However, for the three degree case we see that the sideslip on the mode shape configuration overshoots that of the SDR before returning to the same level. This is because, as we can see in Fig. 10c, the control is briefly saturated at its maximum deflection of ten degrees as the required yawing moment exceeds the control authority. This is the reason why the actuation strategy at three degrees looks so different. Rather than meeting the control requirement for the minimum total deflection the optimiser instead seeks to minimise the difference between the required and delivered control moment. To do this, it must deflect the outer control surface down to maximise the yawing moment.

V. CONCLUSION
The method presented in this paper demonstrates an opportunity to provide a full three axis control solution using only the trailing-edge controls. By utilising combinations of mode shapes, an asymmetric control component can be defined. This has no effect in pitch or roll but has sufficient control authority to overcome adverse yaw effects from the trailing-edge controls operating in a conventional sense, and to provide sufficient yaw control during a rolling manoeuvre.
In this work, an example geometry, taken to be representative of an industry standard design, was analysed and the control authority from the mode shaping approach was shown to be sufficient to perform a rolling manoeuvre within the limits specified by relevant standards for angles of attack up to one degree. For higher angles of attack, there was a reduction in the agility of the aircraft which means it no longer meets the requirements of the standard. However, when comparing the total deflection of the mode shaping configuration to the typically used split drag rudder there was at least a 30% reduction. This reduction could impact on the observability of such an aircraft, improving its survivability in complex threat environments. Additionally, removing a SDR in favour of a standard trailing-edge control would lead to a reduction in the weight of the actuation system.
Finally, in implementing the method proposed in this work, designers may also find opportunities to configure an aircraft depending on its mission profile. It is conceivable there is a configuration in which the outer control surface is operated as a conventional surface which can also split to act as a SDR. In this configuration, the control allocation on the aircraft could choose to implement a mode shaping or more conventional approach depending on whether observability or agility is the greatest concern at the time. WILLIAM J. CROWTHER received the B.Eng. and Ph.D. degrees from the University of Bath in 1990 and 1994, respectively. He is currently a Professor of Aerospace Engineering at the University of Manchester, U.K. His research interests are broadly focused on the design and application of Unmanned Aerial Vehicles (UAVs). He has contributed to work on insect-scale flapping wings, multi-rotor vehicles and larger fixed wing technology demonstrators including MAGMA for which he was academic lead.

APPENDIX 1-NOMENCLATURE
CLYDE WARSOP received the B.Sc. and Ph.D. degrees from the University of Bath in 1981 and 1987, respectively. He is currently an independent Engineering Consultant having recently retired from his role as an Engineering Fellow at BAE Systems where he had a long career that included leading the company's research and flight demonstration of active control technologies.