Aircraft flight control method and system

Abstract

A system including a set of computation modules configured to be utilized for computation of gains of at least one piloting law relative to at least one piloting axis of the aircraft and a data capture unit for capturing in at least one computation unit associated with a given piloting axis of the aircraft first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of the control chain relative to the given piloting axis, the computation unit being configured to compute the gains of the piloting law utilizing at least a part of the set of computation modules and the computation unit computing inputs intended for at least one actuator of a control surface adapted to control the aircraft relative to the given piloting axis in accordance with a corresponding current control value.

Description

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of the French patent application No. 1659775 filed on Oct. 11, 2016, the entire disclosures of which are incorporated herein by way of reference.

TECHNICAL FIELD

The present invention concerns a flight control method and system for an aircraft, in particular a transport aircraft.

BACKGROUND OF THE INVENTION

It is known that modern civil aircraft are controlled by mathematical piloting laws embedded in dedicated digital computers and the inputs of which come from sensors placed on the aircraft and the outputs of which consist of control surface deflection inputs. These control surface deflection inputs are sent to controllers of actuators of these control surfaces.

The entire control chain linking movements of the aircraft and movements of the control surfaces is therefore subject to a time delay depending on the frequency of refreshing the sensors and sampling asynchronisms between the elements of the control chain and the controller of the control surface.

The piloting law is usually computed using a powerful mathematical tool and then transcribed into the computer in the form of gain tables. This method generates multiple steps before the introduction of the gains into the computer and does not enable modification of the objectives of the law in that computer.

Moreover, on a flexible aircraft, the first structural modes of which are situated at frequencies close to those of the piloting modes, it is necessary to apply frequency-domain filtering to the information from the sensors in order to limit aeroservoelastic coupling between the structure of the aircraft and the piloting law.

The mathematical model representing an entire control chain of this kind can be very complex and make the explicit writing of a corresponding piloting law in a computer impossible.

SUMMARY OF THE INVENTION

An object of the present invention is to eliminate this disadvantage. The invention concerns a method for controlling the flight of an aircraft relative to at least one piloting axis of the aircraft utilizing one or more piloting laws that can be generated and written more easily, the aircraft being provided with an electrical flight control system and either at least one control member (control column, rudder pedals, etc.) that can be actuated manually by a pilot of the aircraft at least for control relative to a piloting axis of the aircraft or at least one virtual control member adapted to be controlled by an automatic pilot type device.

According to the invention, the method includes the following steps:

• • an integration step comprising integrating into at least one processing unit of the flight control system of the aircraft a generic set of parameter computation modules, at least some of the computation modules being intended to be used for computation of gains of at least one piloting law relative to at least one given piloting axis, the generic set of computation modules utilizing first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of a control chain relative to the given piloting axis;
  • at least one data capture step comprising capturing, by means of a data capture unit, in at least one computation unit associated with the given piloting axis of the aircraft, first values illustrating the aerodynamic coefficients of the aircraft and second values defining the delay and filter characteristics of the control chain relative to the piloting axis, the computation unit being configured to compute the gains of the piloting law utilizing at least a part of the generic set of computation modules, the control chain being linearized so as to make it possible to generate the inputs intended for at least one actuator of a control surface adapted to control the aircraft relative to the piloting axis in accordance with at least one current control value of the aircraft, by means of a controlled variable supplied in a raw state (i.e., a non-filtered and non-delayed variable); and
  • at least one control step comprising, during a flight of the aircraft, entering into the computation unit the current control value generated by means of a data generation unit and computing, by means of the computation unit, utilizing this current control value, the inputs for controlling the aircraft relative to the given piloting axis, the inputs computed in this way being transmitted to the actuator of the control surface.

Therefore, due to the invention, the equations of the piloting law are established from a linear representation of the (linearized) control chain, which makes it possible to generate inputs with a non-filtered and non-delayed controlled variable. Moreover, account is taken of a so-called generic set of computation modules, meaning that at least some of those computation modules (that enable computation of particular parameters) can be used to compute inputs relative to different piloting axes (pitch, yaw, roll), using for this purpose appropriate second values (entered by an operator), these second values defining delay and filter characteristics of the control chain relative to the corresponding piloting axis. The piloting law or laws utilized can be generated and written more easily than in the usual situation mentioned above.

Although not exclusively, the present invention is particularly well suited to a so-called flexible aircraft, in which the first structural modes are situated at frequencies close to those of the piloting modes, notably making it possible to implement appropriate frequency-domain filtering.

The linearized control chain advantageously satisfies the following equation:

${\delta }_u=F_{\mathrm{equi}}·\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}s·u+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)$

in which:

• • δ_u is the movement of a control surface, generated by this control chain;
  • F_equi is a global filter illustrating the modelling of a filter and all of the delays and asynchronisms of the control chain;
  • u_c is the control value;
  • u is the non-filtered and non-delayed controlled variable;
  • s is the Laplace variable; and
  • K_uc, K_u, K_udot and K_ui are gains.

At least some of the gains K_uc, K_u, K_udot and K_ui are advantageously determined from equations present in the generic set of computation modules.

Moreover, the global filter F_equi advantageously satisfies the following equation:F_equi=pade(T,2)*B(s)

in which:

• • pade(T,2) is a second order Pade filter; and
  • B(s) is a second order Butterworth filter.

In a preferred embodiment, the generic set of parameter computation modules is utilized by a plurality of control steps to control the flight of the aircraft relative to at least two (and preferably three) of the three piloting axes of the aircraft:

• • the pitch axis;
  • the roll axis; and
  • the yaw axis.

The present invention can therefore be applied to one of the three piloting axes of the aircraft or simultaneously to more than one of them.

In a first application, to control the flight of the aircraft at least relative to a piloting axis corresponding to the pitch axis of the aircraft, the control step advantageously comprises computing an input in the form of a deflection input δq of an elevator of the aircraft from a current control value Nz_c corresponding to a load factor Nz that represents a position of a control column that can be actuated by a pilot of the aircraft, using the following equation:

$\delta q=F_{\mathrm{equi}}·\left(K_D{\mathrm{Nz}}_c+K_{\mathrm{Nz}}\mathrm{Nz}+K_q·q+\frac{K_i}{s}\left({\mathrm{Nz}}_c-\mathrm{Nz}\right)\right)$

in which:

• • F_equi is a global filter;
  • s is the Laplace variable;
  • K_Nz, K_q and K_i are gains; and
  • K_D is a precontrol term.

Moreover, the gains K_Nz, K_q and K_i and the precontrol term K_D are advantageously computed from the following equations:

$K_{\mathrm{Nz}}=\frac{K_u+p_{\alpha }{K}_{\mathrm{udot}}}{A}$ $K_q=\frac{K_{\mathrm{udot}}}{m_{\delta q}}$ $K_i=\frac{K_{\mathrm{ui}}}{A}$ $K_D=\tau K_i$

in which:

• • τ is a time constant value;
  • m_δq and p_α are parameters obtained from flight mechanics equations;
  • A is a value dependent on m_δq and p_A; and
  • K_udot, K_u and K_ui are parameters that are computed from equations implemented in the generic set of computation modules.

Moreover, in a second application, in addition to or instead of the first application to control the flight of the aircraft at least relative to a piloting axis corresponding to the yaw axis of the aircraft, the control step advantageously comprises computing an input in the form of a deflection input δr of a virtual yaw control surface from a current control value β₃ corresponding to a sideslip angle β of the aircraft that represents the position of pedals that can be actuated by a pilot of the aircraft, using the following equation:

$\delta r=F_{\mathrm{equi}}·\left(K_{{\beta }_c}{\beta }_c+K_{\beta }\beta +K_{\beta \mathrm{dot}}\stackrel{.}{\beta }+\frac{K_{\beta \mathrm{int}}}{s}\left({\beta }_c-\beta \right)\right)$

in which:

• • F_equi is a global filter;
  • s is the Laplace variable;
  • K_β, K_βdot and K_βint are gains; and
  • K_βc is a precontrol term.

Moreover, the gains K_β, K_βdot and K_βint and the precontrol term K_βc are advantageously computed from equations implemented in the generic set of computation modules.

Moreover, in a third application in addition to or instead of the first and second applications to control the flight of the aircraft at least relative to a piloting axis corresponding to the roll axis of the aircraft the control step advantageously comprises computing an input in the form of a deflection input δp of a virtual roll control surface from a current control value p_c corresponding to a roll rate p of the aircraft that represents a position of a control column that can be actuated by a pilot of the aircraft, using the following equation:

$\delta p=F_{\mathrm{equi}}·\left(K_{p_c}{p}_c+K_{p}p+\frac{K_{\mathrm{pint}}}{s}\left(p_c-p\right)\right)$

in which:

• • F_equi is a global filter;
  • s is the Laplace variable;
  • K_p and K_pint are gains; and
  • K_pc is a precontrol term.

Moreover, the gains K_p and K_pint and the precontrol term K_pc are advantageously computed from a set of equations implemented in the generic set of computation modules.

The present invention also concerns an aircraft flight control system intended to control the flight of the aircraft relative to at least one piloting axis.

According to the invention, the system includes:

• • a processing unit comprising a generic set of parameter computation modules, at least some of the computation modules being intended to be used for computation of gains of at least one piloting law relative to at least one given piloting axis of the aircraft, the generic set of computation modules utilizing first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of a control chain relative to the given piloting axis;
  • at least one data capture unit configured to capture in at least one computation unit associated with a given piloting axis of the aircraft first values illustrating the aerodynamic coefficients of the aircraft and second values defining the delay and filter characteristics of the control chain relative to the piloting axis;
  • at least one data entry link configured to enter at least one current control value into the computation unit during a flight of the aircraft; and
  • the at least one computation unit that is configured to compute the gains of the piloting law utilizing at least a part of the generic set of computation modules, the computation unit being configured to compute inputs intended for at least one actuator of a control surface adapted to control the aircraft relative to the piloting axis in accordance with the current control value of the aircraft using a controlled variable supplied in a raw state, the inputs computed in this way being transmitted to the actuator of the control surface.

In one particular embodiment, the system includes:

• • a computation unit associated with the pitch axis;
  • a computation unit associated with the roll axis; and
  • a computation unit associated with the yaw axis.

The system advantageously further includes:

• • at least one control member that can be actuated configured to generate a control value; and
  • at least one actuator of a control surface configured to actuate the control surface as a function of inputs received.

The present invention further concerns an aircraft, in particular a transport aircraft, that is provided with a system like that specified hereinabove.

BRIEF DESCRIPTION OF THE DRAWINGS

The appended figures clearly explain how the invention can be reduced to practice. In these figures, identical references designate similar elements. More specifically:

FIG. 1 is the block diagram of a flight control system and illustrates one embodiment of the invention;

FIGS. 2 to 4 are diagrammatic representations of a control chain; and

FIG. 5 shows the steps of a method implemented by a flight control system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The system 1 represented diagrammatically in FIG. 1 to illustrate the invention is an electrical flight control system of an aircraft, in particular a transport aircraft. This flight control system 1 is intended to control (pilot) the aircraft relative to at least one of its three piloting axes:

• • the pitch axis;
  • the yaw axis;
  • the roll axis.

According to the invention, the system 1 includes:

• • a central unit 2 including a processing unit 3 comprising a generic set of parameter computation modules Mi. At least some of the computation modules Mi are intended to be used for computation of gains of at least one piloting law relative to at least one given piloting axis of the aircraft. The generic set of computation modules Mi utilizes first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of a control chain relative to the given piloting axis;
  • at least one data capture unit 4 (INPUT (keyboard, touch screen, etc.)) connected by way of a link 5 to the central unit 2 and configured to enable an operator, notably a pilot of the aircraft, to capture in at least one computation unit 6, 7, 8 associated with a given piloting axis of the aircraft first values (illustrating the aerodynamic coefficients of the aircraft) and second values (defining the delay and filter characteristics of the control chain relative to the piloting axis);
  • at least one data entry link 9 connected to the central unit 2 and configured to enter into the computation unit 6, 7, 8 at least one current control value received from a data generation unit (see below) during a flight of the aircraft; and
  • one or more computation units 6, 7, 8 (COMP1, COMP2, COMP3, respectively, in FIG. 1).

Each computation unit 6, 7, 8 is configured to compute the gains of the associated piloting law utilizing at least a part of the generic set of computation modules Mi.

Moreover, each computation unit 6, 7, 8 is configured to compute inputs intended for at least one actuator of a control surface adapted to control the aircraft relative to the piloting axis in accordance with the current control value of the aircraft, using a controlled variable supplied in a raw state. By raw state is meant the state in which the variable is generated (or measured by an appropriate sensor), i.e., non-filtered and non-delayed.

The system 1 further includes:

• • the data generation unit 10 which includes at least one control member 11, 12 adapted to be actuated manually by a pilot of the aircraft and that is configured to generate a control value representing that action. The data generation unit 10 can include, as the control member, a control column 11 of the usual kind, notably a joystick (STICK), for generating a control value intended for piloting relative to the pitch or roll axis and/or pedals 12 (PED) intended for piloting relative to the yaw axis; and
  • at least one actuator 16, 17, and 18 of a control surface configured to actuate an appropriate control surface as a function of inputs received. The actuators 16, 17, and 18 (ACT1, ACT2 and ACT3, respectively, in FIG. 1) are represented diagrammatically in FIG. 1 in the form of a system 15 connected by a link 14 to the central unit 2 and are associated with the pitch, yaw and roll axes, respectively.

In the particular embodiment shown in FIG. 1, the system 1 includes simultaneously:

• • the computation unit 6 that is associated with the pitch axis;
  • the computation unit 7 that is associated with the yaw axis; and
  • the computation unit 8 that is associated with the roll axis.

These computation units 6, 7 and 8 can be part of one and the same computation element.

The inputs computed by each of the computation units 6, 7 and 8 are transmitted to one or more actuators of a respective appropriate (real or virtual) control surface via the link 14.

The set of computation modules Mi is termed generic because computation modules Mi of this set can be utilized by each of the three computation units 6, 7 and 8.

Moreover, the system 1 is generic. It is, in fact, suited to any aircraft (see below). The code determined as described above (which is installed in the central unit 2) is directly usable for any aircraft without modification (provided the system architecture of the aircraft allows embedding of this code).

The system 1 therefore applies to piloting relative to the pitch, roll and/or yaw axes of an aircraft that is equipped with control surfaces enabling movement of this aircraft relative to these three axes.

The definition of the various computation elements utilized in the central unit 2 can be explained on the basis of two successive phases, respectively comprising:

• • establishing a particular representation, of optimized complexity, of the (closed loop) control chain; and
  • on the basis of that modelling, defining a piloting law the objectives of which are then explicitly apparent and the equations of which compute the inputs of the law in real time. These equations can then be directly coded in the central unit 2 of the flight control system 1.

To implement these two phases the following aircraft model is utilized.

The aircraft, without considering the flexible modes or the digital control system, can be represented by the usual flight mechanics differential equations for the pitch axis or for the coupled roll and yaw axes.

In the case of the pitch axis, these equations are written:

$\left[\begin{array}{c}\stackrel{.}{\alpha }\\ \stackrel{.}{q}\end{array}\right]=\left[\begin{array}{cc}{p}_{\alpha }& 1\\ m_{\alpha }& m_q\end{array}\right]·\left[\begin{array}{c}\alpha \\ q\end{array}\right]+\left[\begin{array}{c}0\\ m_{\delta q}\end{array}\right]·{\delta }_q$

where α is the angle of attack, q is the pitch rate and δ_q is the deflection of the elevator.

The vertical load factor N_z is computed as follows:

$\mathrm{Nz}=\frac{V}{g}\frac{\pi }{180}\left(q-\stackrel{.}{\alpha }\right)=-\frac{V}{g}\frac{\pi }{180}{p}_{\alpha }\alpha =-\frac{V}{g}\frac{\pi }{180}\frac{p_{\alpha }}{s-p_{\alpha }}q$

Using the Laplace variable, we obtain:

$\begin{array}{cc}\left(s^2-\left(p_{\alpha }+m_q\right)s+m_q{p}_{\alpha }-m_{\alpha }\right)\mathrm{Nz}=-\frac{V}{g}\frac{\pi }{180}{p}_{\alpha }{p}_{\delta q}\delta q& \left(i\right)\end{array}$

In the case of the roll and yaw axes, these equations are written in the usual way:

$\left[\begin{array}{c}\stackrel{.}{\beta }\\ \stackrel{.}{r}\\ \stackrel{.}{p}\\ \stackrel{.}{\phi }\end{array}\right]=\left[\begin{array}{cccc}\frac{Y_{\beta }}{V}& -\cos \alpha & \sin \alpha & 0\\ n_{\beta }& n_r& n_p& 0\\ l_{\beta }& l_r& l_p& 0\\ 0& \tan \theta & 1& 0\end{array}\right]\left[\begin{array}{c}\beta \\ r\\ p\\ \phi \end{array}\right]+\left[\begin{array}{cc}0& 0\\ n_{\delta l}& n_{\delta n}\\ l_{\delta l}& l_{\delta n}\\ 0& 0\end{array}\right]\left[\begin{array}{c}\delta l\\ \delta n\end{array}\right]$

where β is the sideslip angle, r is the yaw rate, p is the roll rate, φ is the roll angle, δl is the deflection of the main roll control surface, δn is the deflection of the main yaw control surface, α is the angle of attack, and θ is the longitudinal pitch angle.

The values of α and θ are considered sufficiently small to simplify the sine, cosine and tangent terms. The model commonly used is then:

$\left[\begin{array}{c}\stackrel{.}{\beta }\\ \stackrel{.}{r}\\ \stackrel{.}{p}\\ \stackrel{.}{\phi }\end{array}\right]=\left[\begin{array}{cccc}\frac{Y_{\beta }}{V}& -1& 0& 0\\ n_{\beta }& n_r& n_p& 0\\ l_{\beta }& l_r& l_p& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}\beta \\ r\\ p\\ \phi \end{array}\right]+\left[\begin{array}{cc}0& 0\\ n_{\delta l}& n_{\delta n}\\ l_{\delta l}& l_{\delta n}\\ 0& 0\end{array}\right]\left[\begin{array}{c}\delta l\\ \delta n\end{array}\right]$

If the terms in n_p, l_β and l_r can be ignored, or if a first piloting law enables compensation thereof, the model then becomes:

$\left[\begin{array}{c}\stackrel{.}{\beta }\\ \stackrel{.}{r}\\ \stackrel{.}{p}\\ \stackrel{.}{\phi }\end{array}\right]=\left[\begin{array}{cccc}\frac{Y_{\beta }}{V}& -1& 0& 0\\ n_{\beta }& n_r& 0& 0\\ 0& 0& l_p& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}\beta \\ r\\ p\\ \phi \end{array}\right]+\left[\begin{array}{cc}0& 0\\ n_{\delta l}& n_{\delta n}\\ l_{\delta l}& l_{\delta n}\\ 0& 0\end{array}\right]\left[\begin{array}{c}\delta l\\ \delta n\end{array}\right]$

Adopting the notation:

$\begin{array}{cc}B=\left[\begin{array}{cc}{n}_{\delta l}& n_{{\delta }_n}\\ l_{\delta l}& l_{\delta n}\end{array}\right]\mathrm{and}\left[\begin{array}{c}\delta l\\ {\delta }_n\end{array}\right]=B^{-1}\left[\begin{array}{c}\delta r\\ \delta p\end{array}\right]& \left(\mathrm{ii}\right)\end{array}$

we obtain:

$\begin{array}{cc}\left(s^2-\left(n_r+\frac{Y_{\beta }}{V}\right)s+\left(n_{\beta }+n_r\frac{Y_{\beta }}{V}\right)\right)\beta =-{\delta }_r& \left(\mathrm{iii}\right)\end{array}$

and:(s−l_p)p=δ_p  (iv)

As indicated above, a linearized global control chain is considered, i.e., a system without saturation or parameter thresholds. In mathematical terms this linearized control chain comprises mutually commutative elements. The delays linked to the various steps of this control chain can therefore be grouped into one and the same term.

Consequently, if all the delays and asynchronisms of the control chain are related by an identity function, an equivalent single delay corresponding to the sum of all the delays can be assumed to apply in the final position of the control chain. Likewise, the structural filtering applied to the inputs of the piloting law can in an equivalent manner be placed downstream of the law, on the final inputs.

The usual representation of the control chain is shown in more detail in FIG. 2.

In FIG. 2:

• • C represents the set of sensors;
  • F1 represents a first structural filter;
  • D1 represents a first delay;
  • L represents the piloting law;
  • D2 represents a second delay; and
  • TR represents the transfer function of the actuator.

The control chain can be represented in an equivalent manner, as in FIG. 3, in which DT represents a total delay corresponding to the accumulated delays D1 and D2 of the FIG. 2 control chain.

Moreover, the representation shown in FIG. 4 is obtained by combining the structural filter F1 and the transfer function TR of the actuator as a filter FT illustrating total filtering.

The entire control chain can therefore be considered as a law L applied to non-filtered and non-delayed sensors C the inputs from which pass through a delay unit DT and a single filter FT.

A generalized form of a PID (proportional-integral-derivative) type piloting law is written:

$L=\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}s·u+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)$

where u_c is the setpoint of the law (or control value) and u is the controlled variable, considered non-filtered and non-delayed, i.e., in its raw state.

The control chain corresponding to the FIG. 4 representation is then written:

$\begin{array}{cc}{\delta }_u={\mathrm{delay}}_{\mathrm{global}}\left(s\right)*\mathrm{Filter}\left(s\right)\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}\mathrm{su}+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)& \left(v\right)\end{array}$

δ_u is the control surface movement (deflection) generated by this control chain.

The definition of the various computation elements for obtaining the final piloting law can therefore be explained on the basis of two successive phases. The first phase, based on the equation (v) of the control chain, comprises establishing an equivalent representation of that chain and the second phase utilizes that new representation to establish the equations of the piloting law.

Where the first phase is concerned, FILT(s)=delay_global(s)*Filter(s) is modelled in the form of a single global filter of order N (N≥1) denoted F_equi (s) and enables FILT(s) to be represented with great fidelity in a pass-band corresponding to that of the piloting law.

A preferred formulation enabling the filter and delay characteristics of the control chain to be represented with great fidelity and simplicity is as follows:F_equi(s)=pade(T,2)*B(s)

where pade(T,2) is a second order Pade filter, with time constant T:

$\mathrm{pade}\left(T,2\right)=\frac{\frac{T^2}{12}{s}^2-\frac{T}{2}s+1}{\frac{T^2}{12}{s}^2+\frac{T}{2}s+1}$

and B(s) is a second order Butterworth filter of angular frequency ω0 and and damping ξ:

$B\left(s\right)=\frac{1}{\frac{s^2}{{\omega }_0^2}+2\xi \frac{s}{{\omega }_0}+1}$

The pade(T,2) filter is well known to represent mathematically the effect on a control chain of a delay T.

Moreover, with a second order filter, the structure of the filter B(s) enables a good representation of the low-pass characteristic of a filter whilst also representing very well its Q (overvoltage factor).

A fourth order global filter F_equi(s) is therefore chosen (the fourth order corresponding to the sum of the second order of the pade(T,2) filter and the second order of the B(s) filter) to represent faithfully, at the piloting frequencies of the aircraft, the low-pass filter and overvoltage factor characteristics given by B(s) and the chain delay characteristics given by T.

We obtain

$\begin{array}{cc}{\delta }_u=\frac{\frac{T^2}{12}{s}^2-\frac{T}{2}s+1}{\frac{T^2}{12}{s}^2+\frac{T}{2}s+1}\frac{1}{\frac{s^2}{{\omega }_0^2}+2\xi \frac{s}{{\omega }_0}+1}\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}\mathrm{su}+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)& \left(\mathrm{vi}\right)\end{array}$

Moreover, concerning the aforementioned second phase, if the pitch or yaw axes are considered, the system representing the aircraft is a second order system (equations (i) and (iii)). On the other hand, if the roll axis is considered, the system representing the aircraft is a first order system (equation (iv)), which is a special case of a second order system, the second order coefficient of which is zero.

The second order general differential equation (enabling representation of the aircraft on each of the axes) of a state variable system u is then considered, where the deflection of the control surface is δ_u:(K₂s²+K₁s+K₀)u=δ_u  (vii)

The piloting law is defined by rewriting (vi) with more general notation:

$\begin{array}{cc}{\delta }_u=\frac{{\theta }_2{s}^2-{\theta }_{1}s+{\theta }_0}{{\theta }_2{s}^2+{\theta }_{1}s+{\theta }_0}\frac{1}{{\mathrm{as}}^2+\mathrm{bs}+d}\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}\mathrm{su}+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)& \left(\mathrm{viii}\right)\end{array}$

The differential equation (vii) then becomes:

$\left({\theta }_2{s}^2+{\theta }_{1}s+{\theta }_0\right)\left({\mathrm{as}}^2+\mathrm{bs}+d\right)\left(K_2{s}^2+K_{1}s+K_0\right)u=\left({\theta }_2{s}^2-{\theta }_{1}s+{\theta }_0\right)\left(K_{\mathrm{uc}}{u}_c+K_{u}u+K_{\mathrm{udot}}\mathrm{su}+\frac{K_{\mathrm{ui}}}{s}\left(u_c-u\right)\right)$

The piloting law therefore includes:

• • a precontrol gain K_uc applied to the control value u_c;
  • a direct feedback on u, denoted K_u;
  • a feedback on the derivative of u, denoted K_udot; and
  • an integral feedback denoted K_ui, applied to (u_c-u).

The closed loop system is then:(T₇s⁷+T₆s⁶+T₅s⁵+(T₄−θ₂K_udot)s⁴+(T₃−θ₂K_uθ₁K_udot)s³+(T₂+θ₂K_ui+θ₁K_u−θ₀K_udot)s²+(T₁−θ₁K_ui−θ₀K_u)s+θ₀K_ui)u=(θ₂s²−θ₁s+θ₀)(K_ucs+K_ui)u_c  (ix)

the terms of which are computed via a function coefequationBF such that:[T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂]=coefequationBF(a,b,d,T K₀,K₁,K₂)

By way of illustration, the following equations are considered in this case:

${\theta }_2=\frac{T^2}{12}$ ${\theta }_1=\frac{T}{2}$ ${\theta }_0=1.0$ $T_7=a{\theta }_2{K}_2$ $T_6=a{\theta }_2{K}_1+\left(b{\theta }_2+a{\theta }_1\right)K_2$ $T_5=a{\theta }_2{K}_0+\left(b{\theta }_2+a{\theta }_1\right)K_1+\left(d{\theta }_2+b{\theta }_1+a{\theta }_0\right)K_2$ $T_4=\left(b{\theta }_2+a{\theta }_1\right)K_0+\left(d{\theta }_2+b{\theta }_1+a{\theta }_0\right)K_1+\left(d{\theta }_1+b{\theta }_0\right)K_2$ $T_3=\left(d{\theta }_2+b{\theta }_1+a{\theta }_0\right)K_0+\left(d{\theta }_1+b{\theta }_0\right)K_1+d{\theta }_0{K}_2$ $T_2=\left(d{\theta }_1+b{\theta }_0\right)K_0+d{\theta }_0{K}_1$ $T_1=d{\theta }_0{K}_0$

The system described by the equation (ix) has seven poles, which are defined as the roots of the seventh order polynomial corresponding to the left-hand part of the equation (ix).

The PID type law does not have sufficient degrees of freedom to place the seven poles of the system. It enables only three of them to be constrained.

Three poles of the system are therefore placed by the law on the objectives of the law and are therefore the roots of the polynomial:

$\left(s^2+2\varepsilon \omega s+{\omega }^2\right)\left(s+\frac{1}{\tau }\right)={\mu }_3{s}^3+{\mu }_2{s}^2+{\mu }_{1}s+{\mu }_0$

where ω and ξ are the angular frequency and damping objectives of the complex mode, and τ is the time constant objective of the real mode.

In a closed loop the last four poles become values that are not objectives but consequences of the law. These four poles are the roots of a polynomial.

The set of closed loop poles therefore defines the polynomial of the closed loop system:(x₄s⁴+x₃s³+x₂s²+x₁s+x₀)·(μ₃s³+μ₂s²+μ₁s+μ₀)·u   (x)

The left-hand part of the equation (ix) and the equation (x) can therefore be related via an identity function.

This identity function is performed via a cascade of equations, defined in a function equation_law_input, such that:[K_u,K_ui,K_udot]=equation_law_input(μ₀,μ₁,μ₃,T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂)

The three unknowns K_u, K_ui and K_udot are defined by a system of three equations:K₁₁K_u+K₁₂K_udot+K₁₃K_ui=D₁₁ K₂₁K_u+K₂₂K_udot+K₂₃K_ui=D₂₂ K₃₁K_u+K₃₂K_udot+K₃₃K_ui=D₃₃

In this system, the determinants are:

$D=K_{11}\begin{array}{cc}{K}_{22}& K_{23}\\ K_{32}& K_{33}\end{array}-K_{21}\begin{array}{cc}{K}_{12}& K_{13}\\ K_{32}& K_{33}\end{array}+K_{31}\begin{array}{cc}{K}_{12}& K_{13}\\ K_{22}& K_{23}\end{array}$ $\mathrm{Rq}=D_{11}\begin{array}{cc}{K}_{22}& K_{23}\\ K_{32}& K_{33}\end{array}-D_{22}\begin{array}{cc}{K}_{12}& K_{13}\\ K_{32}& K_{33}\end{array}+D_{33}\begin{array}{cc}{K}_{12}& K_{13}\\ K_{22}& K_{23}\end{array}$ $\mathrm{Rz}=K_{11}\begin{array}{cc}{D}_{22}& K_{23}\\ D_{33}& K_{33}\end{array}-K_{21}\begin{array}{cc}{D}_{11}& K_{13}\\ D_{33}& K_{33}\end{array}+K_{31}\begin{array}{cc}{D}_{11}& K_{13}\\ D_{22}& K_{23}\end{array}$ $\mathrm{Ri}=K_{11}\begin{array}{cc}{K}_{22}& D_{22}\\ K_{32}& D_{33}\end{array}-K_{21}\begin{array}{cc}{K}_{12}& D_{11}\\ K_{32}& D_{33}\end{array}+K_{31}\begin{array}{cc}{K}_{12}& D_{11}\\ K_{22}& D_{22}\end{array}$

D is not zero if it is assumed that the system is controllable.

We finally obtain:

$K_u=\frac{R_q}{D}$ $K_{\mathrm{udot}}=\frac{R_z}{D}$ $K_{\mathrm{ui}}=\frac{R_i}{D}$

In these expressions, the following formulas are used:

$x_4=\frac{T_7}{{\mu }_3}$ $x_3=\frac{T_6-x_4{\mu }_2}{{\mu }_3}$ $x_2=\frac{T_5-\left(x_4{\mu }_1+x_3{\mu }_2\right)}{{\mu }_3}$ $C_1=\frac{T_4-\left(x_4{\mu }_0+x_3{\mu }_1+x_2{\mu }_2\right)}{{\mu }_3}$ $C_2=\frac{T_3-x_3{\mu }_0-x_2{\mu }_1}{{\mu }_3}$ $C_3=C_2-\frac{{\mu }_2{C}_1}{{\mu }_3}$ $K_{11}={\theta }_1+\frac{{\mu }_2{\theta }_2}{{\mu }_3}$ $K_{12}=\frac{{\mu }_1{\theta }_2}{{\mu }_3}-{\theta }_0-\frac{{\mu }_2\left({\theta }_1+\frac{{\mu }_2}{{\mu }_3}{\theta }_2\right)}{{\mu }_3}$ $K_{13}={\theta }_2$ $D_{11}=x_2{\mu }_0+{\mu }_1{C}_1+{\mu }_2{C}_3-T_2$ $K_{21}={\theta }_0-\frac{{\mu }_1{\theta }_2}{{\mu }_3}$ $K_{22}=\frac{{\mu }_1\left({\theta }_1+\frac{{\mu }_2{\theta }_2}{{\mu }_3}\right)-{\mu }_0{\theta }_2}{{\mu }_3}$ $K_{23}={\theta }_1$ $D_{22}=T_1-{\mu }_0{C}_1-{\mu }_1{C}_3$ $K_{31}=\frac{-{\mu }_0{\theta }_2}{{\mu }_3}$ $K_{32}=\frac{{\mu }_0\left({\theta }_1+\frac{{\mu }_2{\theta }_2}{{\mu }_3}\right)}{{\mu }_3}$ $K_{33}=-{\theta }_0$ $D_{33}=-{\mu }_0{C}_3$

This piloting law can then be applied to the pitch, yaw or roll axes of an aircraft, the equation (vii) and the equations (i), (iii) or (iv) being related by an identity function. The control chain (vi) of the aircraft and the equation (viii) are related by an identity function.

In a first application, to control the aircraft relative to its pitch axis, the computation unit 6 (FIG. 1) is configured to compute an input in the form of a deflection input 5q of an elevator of the aircraft on the basis of a current control value Nz_c (corresponding to a load factor Nz) that represents the position of the control column 11 that can be pivoted toward the front or toward the rear by the pilot of the aircraft.

The computation unit 6 computes the deflection input δq using the following equation:

$\delta q=F_{\mathrm{equi}}·\left(K_D{\mathrm{Nz}}_c+K_{\mathrm{Nz}}\mathrm{Nz}+K_q·q+\frac{K_i}{s}\left({\mathrm{Nz}}_c-\mathrm{Nz}\right)\right)$

that is to say:

$\delta q=\frac{\frac{T^2}{12}{s}^2-\frac{T}{2}s+1}{\frac{T^2}{12}{s}^2+\frac{T}{2}s+1}·\frac{1}{{\mathrm{as}}^2+\mathrm{bs}+1}·\left(K_D{\mathrm{Nz}}_c+K_{\mathrm{Nz}}\mathrm{Nz}+K_{q}q+\frac{K_i}{s}\left(\mathrm{Nzc}-\mathrm{Nz}\right)\right)$

This equation is obtained by rewriting the equation (vi) with the names of variables corresponding to the equation (i).

Using the notation:

$=-\frac{V}{g}\frac{\pi }{180}{p}_{\alpha }{m}_{\delta q},K_0=m_q{p}_{\alpha }-m_{\alpha },K_1=-\left(p_{\alpha }+m_q\right),K_2=1.0$

we obtain:[T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂]=coefequationBF(a,b,d,T,K₀,K₁,K₂)

The objectives of the law, which can be selected, are:

• • ω the required value of the angular frequency of the attack oscillation;
  • ξ the required value of the damping of the attack oscillation; and
  • τ the required value of the time constant of the real mode linked to the presence of an integrator.

We then write:

${\mu }_3=1.0$ ${\mu }_2=2\mathrm{\zeta \omega }+\frac{1}{\tau }$ ${\mu }_1={\omega }^2+\frac{2\mathrm{\zeta \omega }}{\tau }$ ${\mu }_0=\frac{{\omega }^2}{\tau }$

We obtain:[K_u,K_ui,K_udot]=equation_law_input(μ₀,μ₁,μ₂,μ₃,T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂)

and

$K_{\mathrm{Nz}}=\frac{K_u+p_{\alpha }{K}_{\mathrm{udot}}}{A}$ $K_q=\frac{K_{\mathrm{udot}}}{m_{\delta q}}$ $K_i=\frac{K_{\mathrm{ui}}}{A}$

The precontrol term K_D enables compensation of the real mode:K_D=τK_i

Moreover, in a second application, to control the aircraft relative to its yaw axis, the computation unit 7 (FIG. 1) is configured to compute an input in the form of a deflection input δr of a virtual yaw control surface, on the basis of a current control value β_c (corresponding to a sideslip angle β of the aircraft), which represents the position of the pedals 12 that can be actuated by the pilot of the aircraft.

The computation unit 7 computes the deflection input δr using the following equation:

$\delta r=F_{\mathrm{equi}}·\left(K_{{\beta }_c}{\beta }_c+K_{\beta }\beta +K_{\beta \mathrm{dot}}\stackrel{.}{\beta }+\frac{K_{\beta \mathrm{int}}}{s}\left({\beta }_c-\beta \right)\right)$

that is to say:

$\delta r=\frac{\frac{T^2}{12}{s}^2-\frac{T}{2}s+1}{\frac{T^2}{12}{s}^2+\frac{T}{2}s+1}·\frac{1}{{\mathrm{as}}^2+\mathrm{bs}+1}·\left(K_{{\beta }_c}{\beta }_c+K_{\beta }\beta +K_{\beta \mathrm{dot}}\stackrel{.}{\beta }+\frac{K_{\beta \mathrm{int}}}{s}\left({\beta }_c-\beta \right)\right)$

This equation is obtained by rewriting the equation (vi) with the names of variables corresponding to the equation (iii).

Using the notation:

$K_2=1.0,K_1=-\left(\frac{Y_{\beta }}{V}+n_r\right),K_0=n_{\beta }+n_r\frac{Y_{\beta }}{V}$

we obtain:[T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂]=coefequationBF(a,b,d,T,K₀,K₁,K₂)

The objectives of the law, which can be selected, are:

• • ω_β the required value of the angular frequency of the Dutch roll mode;
  • ξ_β the required damping value of the Dutch roll mode;
  • τ_βint the required value of the time constant of the real mode linked to the presence of an integrator.

We then write:

${\mu }_3=1.0,{\mu }_2=2{\xi }_{\beta }{\omega }_{\beta }+\frac{1}{{\tau }_{\beta \mathrm{int}}},{\mu }_1={\omega }_{\beta }^2+\frac{2{\xi }_{\beta }{\omega }_{\beta }}{{\tau }_{\beta \mathrm{int}}},{\mu }_0=\frac{{\omega }_{\beta }^2}{{\tau }_{\beta \mathrm{int}}}$

We obtain:[K_β,K_βi,K_βdot]=equation_law_input(μ₀,μ₁,μ₂,μ₃,T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂)

The precontrol term K_βc enables compensation of the real mode:K_βc=τ_βint·K_βint

Moreover, in a third application, to control the aircraft relative to its roll axis, the computation unit 8 (FIG. 1) is configured to compute an input in the form of a deflection input δp of a virtual roll control surface on the basis of a current control value p_c (corresponding to a rate of roll p of the aircraft) that represents the position of the control column 11 that can be pivoted toward the right and toward the left by the pilot of the aircraft.

The computation unit 8 computes the deflection input δp using the following equation:

$\delta p=F_{\mathrm{equi}}·\left(K_{p_c}{p}_c+K_{p}p+\frac{K_{\mathrm{pint}}}{s}\left(p_c-p\right)\right)$

that is to say:

$\delta p=\frac{\frac{T^2}{12}{s}^2-\frac{T}{2}s+1}{\frac{T^2}{12}{s}^2+\frac{T}{2}s+1}·\frac{1}{{\mathrm{as}}^2+\mathrm{bs}+1}·\left(K_{p_c}{p}_c+K_{p}p+\frac{K_{\mathrm{pint}}}{s}\left(p_c-p\right)\right)$

This equation is obtained by rewriting the equation (vi) with the names of variables corresponding to the equation (iv).

Using the notation: K₂=0.0, K₁ =1.0, K₀=−l_p

we obtain:[T₁,T₂,T₃,T₄,T₅,T₆,T₇,θ₀,θ₁,θ₂]=coefequation_BF(a,b,d,T,K₀,K₁,K₂)

The objectives of the law, which can be selected, are:

• • T_rp the required value of the time constant of the real mode corresponding to the pure roll mode of the aircraft;
  • T_sp the required value of the time constant of the real mode corresponding to the spiral mode of the aircraft.

We then write:

${\mu }_2=1.0,{\mu }_1=\frac{T_{\mathrm{rp}}+T_{\mathrm{sp}}}{T_{\mathrm{rp}}{T}_{\mathrm{sp}}},{\mu }_0=\frac{1}{T_{\mathrm{rp}}{T}_{\mathrm{sp}}}$

Because the law to be defined is of lower order, instead of the subfunction equation_law_input a slightly different subfunction equation_law_input is defined:[K_u,K_ui]=equation_law_input(μ₀,μ₁,μ₂,T₁,T₂,T₃,T₄,T₅,T₆,θ₀,θ₁,θ₂)

Ku and Kui are the solutions of a system of two equations:

$K_u=\frac{D_{11}{K}_{22}-D_{22}{K}_{12}}{\det D}{K}_{\mathrm{ui}}=\frac{K_{11}{D}_{22}-K_{21}{D}_{11}}{\det D}$

The following equations are used for these equations:

$x_4=\frac{T_6}{{\mu }_2}$ $x_3=\frac{T_5-x_4{\mu }_1}{{\mu }_2}$ $C_1=\frac{T_4-\left(x_4{\mu }_0+x_3{\mu }_1\right)}{{\mu }_2}$ $C_2=\frac{T_3-x_3{\mu }_0}{{\mu }_2}$ $C_3=C_2-\frac{{\mu }_1{c}_1}{{\mu }_2}$ $C_4=\frac{T_2-\left({\mu }_0{c}_1+{\mu }_1{c}_3\right)}{{\mu }_2}$ $K_{11}={\theta }_0-\frac{{\mu }_0{\theta }_2}{{\mu }_2}+\frac{{\mu }_1\left({\theta }_1+{\mu }_1{\theta }_2\right)}{{\mu }_2}$ $K_{12}={\theta }_1+\frac{{\mu }_1{\theta }_2}{{\mu }_2}$ $D_{11}=T_1-{\mu }_0{C}_3-{\mu }_1{C}_4$ $K_{21}=\frac{{\theta }_1+{\mu }_1{\theta }_2}{{\mu }_2}$ $K_{22}=-{\theta }_0$ $D_{22}=-{\mu }_0{C}_4$ $\det D=K_{11}{K}_{22}-K_{12}{K}_{21}$

We obtain:K_p=K_u K_pint=K_ui

The precontrol term K_βc enables compensation of the real mode T_sp:K_pc=T_sp·K_pint

The installation and operation of the flight control system 1 as described above can be effected using a sequence of steps E1 to E3 shown in FIG. 5.

This sequence of steps comprises:

• • an integration step E1 comprising integrating (i.e., coding) the generic set of computation modules Mi in the processing unit 3 of the flight control system 1. This generic set of computation modules Mi has been determined in a previous step E0, notably employing the above two phases;
  • at least one data capture step E2 comprising capturing by means of the data capture unit 4 in at least one of the computation units 6, 7, 8 and preferably in the three computation units 6, 7, 8 first values illustrating the aerodynamic coefficients of the aircraft and second values defining the delay and filter characteristics of the control chain relative to the corresponding piloting axis; and
  • a control (or piloting) step E3 comprising, during a flight of the aircraft, entering into the computation unit or units 6, 7 and 8 the current control value or values generated by means of the data generation unit 10 and computing the inputs for controlling the aircraft relative to the piloting axis or axes concerned by means of the computation unit or units 6, 7 and 8 using this/these current control value or values.

Consequently, the invention comprises coding equations which, utilized in cascade, enable real time computation of the gains of a piloting law embedded in a computer (central unit 2) of an aircraft. The system 1 is applied to piloting relative to the pitch, roll and/or yaw axes of any aircraft provided with control surfaces enabling maneuvering of the aircraft about those axes.

For reducing the invention to practice:

• • the aerodynamic coefficients of the aircraft being known, the delay characteristics of the control chain being known, and the various filters of the control chain being known (sensor acquisition filters, structural filters, actuator transfer functions), the parameters T, ω₀ and ξ and T, ω₀ and ξ of the equation (vi) can be assigned values;
  • the objectives of placement of the piloting law are then freely defined; and
  • the solution can then be applied to piloting the aircraft.

While at least one exemplary embodiment of the present invention(s) is disclosed herein, it should be understood that modifications, substitutions and alternatives may be apparent to one of ordinary skill in the art and can be made without departing from the scope of this disclosure. This disclosure is intended to cover any adaptations or variations of the exemplary embodiment(s). In addition, in this disclosure, the terms “comprise” or “comprising” do not exclude other elements or steps, the terms “a” or “one” do not exclude a plural number, and the term “or” means either or both. Furthermore, characteristics or steps which have been described may also be used in combination with other characteristics or steps and in any order unless the disclosure or context suggests otherwise. This disclosure hereby incorporates by reference the complete disclosure of any patent or application from which it claims benefit or priority.

Claims

1. A method for controlling the flight of an aircraft with respect to at least one piloting axis of the aircraft, said aircraft being provided with an electrical flight control system, comprising the following steps: integrating into at least one processing unit of the flight control system of the aircraft a generic set of parameter computation modules in an integration step, at least some of said computation modules being intended to be used for computation of gains of at least one piloting law relative to at least one given piloting axis, said generic set of computation modules utilizing first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of a control chain relative to the given piloting axis;capturing by means of a data capture unit in at least one computation unit associated with the given piloting axis of the aircraft, in at least one data capture step, first values illustrating the aerodynamic coefficients of the aircraft and second values defining the delay and filter characteristics of the control chain relative to said piloting axis, said computation unit being configured to compute the gains of the piloting law utilizing at least a part of said generic set of computation modules, the control chain being linearized so as to make it possible to generate inputs intended for at least one actuator of a control surface adapted to control the aircraft relative to said piloting axis in accordance with at least one current control value of the aircraft by means of a controlled variable supplied in a raw state, the control chain being linearized and verifying the following equation:

2. The method according to claim 1, wherein at least some of said gains Kuc, Ku, Kudot and Kui are determined from equations present in said generic set of computation modules.

3. The method according to claim 1, wherein said generic set of parameter computation modules is utilized by a plurality of control steps to control the flight of the aircraft relative to at least two of the following three piloting axes of the aircraft: the pitch axis;the roll axis; andthe yaw axis.

4. The method according to claim 1, wherein the control step comprises computing an input in the form of a deflection input δq of an elevator of the aircraft from a current control value Nzc corresponding to a load factor Nz that represents a position of a control column that can be actuated by a pilot of the aircraft using the following equation:

5. The method according to claim 4, wherein said gains KNz, Kq and Ki and the precontrol term are computed from the following equations:

6. The method according to claim 1, wherein the control step comprises computing an input in the form of a deflection input δr of a virtual yaw control surface from a current control value βc corresponding to a sideslip angle β of the aircraft that represents the position of pedals that can be actuated by a pilot of the aircraft, using the following equation:

7. The method according to claim 6, wherein said gains Kβ, Kβdot and Kβint and the precontrol term Kβr are computed from equations implemented in said generic set of computation modules.

8. The method according to claim 1, wherein the control step comprises computing an input in the form of a deflection input δp of a virtual roll control surface from a current control value pc corresponding to a roll rate p of the aircraft that represents a position of a control column that can be actuated by a pilot of the aircraft, using the following equation:

9. The method according to claim 8, wherein said gains Kp and Kpint and the precontrol term Kpr are computed from a set of equations implemented in said generic set of computation modules.

10. An aircraft electrical flight control system configured to control the flight of the aircraft relative to at least one piloting axis, said system comprising: a processing unit comprising a generic set of parameter computation modules, at least some of said computation modules being intended to be used for computation of gains of at least one piloting law relative to at least one given piloting axis of the aircraft, said generic set of computation modules utilizing first values illustrating aerodynamic coefficients of the aircraft and second values defining delay and filter characteristics of a control chain relative to the given piloting axis;at least one data capture unit configured to capture in at least one computation unit associated with a given piloting axis of the aircraft first values illustrating the aerodynamic coefficients of the aircraft and second values defining the delay and filter characteristics of the control chain relative to said piloting axis, the control chain being linearized and satisfying the following equation:

11. The system according to claim 10, further comprising: a computation unit associated with the pitch axis;a computation unit associated with the roll axis; anda computation unit associated with the yaw axis.

12. The system according to claim 10, further comprising: at least one control member that can be actuated configured to generate a control value; andat least one actuator of a control surface configured to actuate the control surface as a function of inputs received.

13. An aircraft comprising a flight control system according to claim 10.