Method for monitoring an electromechanical actuator system

Abstract

The invention relates to a method of monitoring an electromechanical actuator system, the method comprising the steps of estimating the voltage drop in the power supply to the motor associated with defects of the inverter by means of a Kalman filter, estimating (300) at least the electromagnetic torque coefficient of the motor by taking account of the estimated voltage drop, and calculating (400) the electromagnetic torque of the motor from the electromagnetic torque coefficient of the motor.

Claims

1. A method of monitoring an electromechanical actuator system including at least one inverter, a motor powered by the inverter, and an actuator driven by the motor, the method comprising the steps of: estimating the drop of voltage in the power supply to the motor associated with defects of the inverter by means of a Kalman filter taking account of operational data including at least one electric current delivered by the inverter to the motor, at least one control voltage of the inverter, and at least one speed of rotation of the outlet shaft of the motor; estimating at least the electromagnetic torque coefficient of the motor by taking account of the estimated voltage drop and the operational data including the current delivered by the inverter to the motor, the control voltage of the inverter, the derivative of the current delivered by the inverter to the motor, and the speed of rotation of the outlet shaft of the motor; and calculating the electromagnetic torque of the motor from the electromagnetic torque coefficient of the motor and the operational data constituted by the electric current delivered by the inverter to the motor.

2. The method according to claim 1, wherein at the same time as estimating the electromagnetic torque coefficient of the motor, other electrical parameters of the electromechanical actuator system are also estimated.

3. The method according to claim 2, wherein the other electrical parameters that are estimated are the resistance of the motor and the inductance of the motor.

4. The method according to claim 1, including an additional step of estimating at least one mechanical parameter of the electromechanical actuator system from the electromagnetic torque, from operational data including at least the speed of rotation of the outlet shaft of the motor, and from the aerodynamic force to which the actuator is subjected.

5. The method according to claim 4, wherein the mechanical parameter is the viscous friction coefficient and/or the dynamic drive friction torque and/or the efficiency of the assembly comprising the motor and the actuator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention can be better understood in the light of the following description of a particular, nonlimiting implementation of the invention. Reference is made to the accompanying figures, in which:

(2) FIG. 1 is a diagrammatic view of an electromechanical actuator system implementing the method in a particular implementation of the invention;

(3) FIG. 2 is a diagram showing the various steps of the method implemented by the system shown diagrammatically in FIG. 1; and

(4) FIGS. 3a and 3b are circuit diagrams modeling an electrical portion of the system shown in FIG. 1 in a frame, respectively relative to the D axis and to the Q axis.

DETAILED DESCRIPTION OF THE INVENTION

(5) With reference to FIGS. 1 and 2, the monitoring method in a particular implementation of the invention is applied in this example to an electromechanical actuator system 1 for actuating an aileron A of an aircraft.

(6) Naturally, this application is not limiting and the method of the invention can be implemented in some other electromechanical actuator system, such as an electromechanical actuator system associated with a cover of a thrust reverser of an aircraft, a flap, or a flight control surface . . . .

(7) In this example, the electromechanical actuator system 1 includes an electrical portion 10 comprising an inverter 11 and a motor 12 powered by the inverter 11. In this example, the motor 12 is a permanent magnet synchronous motor. The electromechanical actuator system also includes a mechanical portion 20 comprising the motor 12 together with an actuator 21 that is connected firstly to the outlet shaft of the motor 12 and secondly to the aileron A, in order to be capable of moving the aileron A. In this example, the actuator 21 is of the linear type, and by way of example it comprises a jack of the ball screw type or of the roller screw type. In a variant, the actuator could be of the rotary type. Under such circumstances, when the motor 12 is powered, it drives the actuator 21, which in turn moves the associated aileron A.

(8) The method of the invention thus serves to monitor the electromechanical actuator system 1 in the manner described below in detail.

(9) Because the motor 12 is powered by the inverter 11 with three-phase AC, the electrical portion 10 is modeled in a frame (direct axis and quadrature axis), as shown in FIGS. 3a and 3b. The various electrical magnitudes calculated or measured in the present method are thus projected onto the two primary axes of the two-phase model, namely the D (direct) axis and the Q (quadrature) axis. In the description below, the index I refers to the projection of a magnitude onto the U axis, and the index Q refers to the projection of a magnitude onto the q axis.

(10) In order to estimate the voltage drops in the power supply of the motor 12 that are associated with faults of the inverter 11, the first step 100 of the method consists in constructing linear, stationary, and stochastic Kalman filters of the type:
{dot over (x)}(t)=Ax(t)+Bu(t)+Mw(t)(1)
y(i)=Cx(i)+Du(t)+(t)(2)
continuous; or
{dot over (x)}(k+1)=A.sub.disx(k)+B.sub.disu(k)+M.sub.disw(k)
y(k)=C.sub.disx(k)+D.sub.disu(k)(k)
discrete.

(11) Such a Kalman model is well known to the person skilled in the art and is therefore not described in detail herein. For more information, reference may be made by way of example to the book Stochastic Models, Estimation and Control, Volume 141-1, Mathematics in Science and Engineering, by P. S. Maybeck.

(12) In order to apply the Kalman estimator, the following equations are written for the synchronous motor 12 in the frame:

(13) $\begin{array}{cc}\sqrt{\frac{2}{3}}\left(V_D+V_{D_{\mathrm{Inverter}}}\right)={\mathrm{Ri}}_D+L_D\frac{d}{\mathrm{dt}}{i}_D-L_{Q}p.Math..Math.i_Q-\sqrt{\frac{2}{3}}{V}_D& \left(3\right)\\ \sqrt{\frac{2}{3}}\left(V_Q+V_{Q_{\mathrm{Inverter}}}\right)={\mathrm{Ri}}_Q+L_Q\frac{d}{\mathrm{dt}}{i}_Q-L_{D}p.Math..Math.i_D-\sqrt{\frac{2}{3}}{V}_Q& \end{array}$
where; V.sub.D and V.sub.Q are the power supply voltages that the inverter 11 is controlled to deliver, referred to as the control voltages (which are measured in this example in the current regulator loop of the inverter 11); V.sub.D.sub.Inverter and V.sub.Q.sub.Inverter are the inverter voltage drops due to defects of the inverter; V.sub.D and V.sub.Q are the uncertainties about the inverter voltage drops due to the uncertainties concerning various electrical parameters of the electrical portion 10; i.sub.D and i.sub.Q are the currents transmitted by the inverter 11 to the motor 12 (which in this example are measured in the motor 12); R is the resistance of the motor 12; L.sub.D and L.sub.Q are the inductances of the stator phases of the motor 12; p is the number of pairs of poles of the motor 12; is the speed of rotation of the outlet shaft of the motor 12; and Ke is the electromagnetic torque coefficient of the motor 12.

(14) The data i.sub.D, i.sub.Q, V.sub.D and V.sub.Q, and comprises operational data as measured by the sensors or as recovered from the commands transmitted by the computer to the inverter 11 while the aircraft is in flight, either in real time, or else by being measured/recovered and then stored in a memory (e.g. of the computer) for subsequent use by the method of the invention.

(15) Before establishing the Kalman model for estimating the voltage drops V.sub.D.sub.Inverter and V.sub.Q.sub.Inverter due to inverter defects consideration is given to the following three assumptions.

(16) In a first assumption, the voltage drops V.sub.D.sub.Inverter and V.sub.Q.sub.Inverter due to inverter defects are integral type variables associated with random variables w.sub.D(t) and w.sub.Q(t) white noise type without bias and with known spectral power density, i.e.:

(17) $\frac{{\mathrm{dV}}_{D_{\mathrm{Inverter}}}}{\mathrm{dt}}=w_D\left(t\right)$$\frac{{\mathrm{dV}}_{Q_{\mathrm{Inverter}}}}{\mathrm{dt}}=w_Q\left(t\right)$

(18) In a second assumption, it is considered that the following changes of variable make decoupling possible:

(19) $U_D=\sqrt{\frac{2}{3}}{V}_D+L_{Q}p.Math..Math.i_Q$$U_Q=\sqrt{\frac{2}{3}}{V}_Q-L_{D}p.Math..Math.i_D-.Math.\mathrm{Ke}$

(20) In a first assumption, all of the Kalman convergence conditions are satisfied. For more information, reference may be made by way of example to the book Stochastic Models, Estimation and Control, Volume 141-1, Mathematics in Science and Engineering, by P. S. Maybeck.

(21) Thus, the final model for estimating the voltage drops V.sub.D.sub.Inverter and V.sub.Q.sub.Inverter due to defects of the inverter 11 is given by the following state representations:

(22) $\left[\begin{array}{c}\frac{d}{\mathrm{dt}}{i}_D\\ \frac{{\mathrm{dV}}_{D_{\mathrm{Inverter}}}}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{cc}-\frac{R}{L_D}& \frac{1}{L_D}\sqrt{\frac{2}{3}}\\ 0& 0\end{array}\right][\begin{array}{c}{i}_D\\ V_{D_{\mathrm{Inverter}}}\end{array}]+\left[\begin{array}{c}\frac{1}{L_D}\\ 0\end{array}\right]U_D+\left[\begin{array}{cc}\frac{1}{L_D}\sqrt{\frac{2}{3}}& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{V}_D\\ w_D\left(t\right)\end{array}\right]\left[\begin{array}{c}\frac{d}{\mathrm{dt}}{i}_Q\\ \frac{{\mathrm{dV}}_{Q_{\mathrm{Inverter}}}}{\mathrm{dt}}\end{array}\right]=\left[\begin{array}{cc}-\frac{R}{L_Q}& \frac{1}{L_Q}\sqrt{\frac{2}{3}}\\ 0& 0\end{array}\right]\left[\begin{array}{c}{i}_Q\\ V_{Q_{\mathrm{Inverter}}}\end{array}\right]+\left[\begin{array}{c}\frac{1}{L_Q}\\ 0\end{array}\right]U_Q+\left[\begin{array}{cc}\frac{1}{L_Q}\sqrt{\frac{2}{3}}& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}{V}_Q\\ w_Q\left(t\right)\end{array}\right]$

(23) There can thus be found the state representations in the general form (1) and (2) for the two axes d and with:

(24) $x\left(t\right)=\left[\begin{array}{c}{i}_I\\ V_{D_{\mathrm{Inverter}}}\end{array}\right],A=\left[\begin{array}{cc}-\frac{R}{L_D}& \frac{1}{L_D}\sqrt{\frac{2}{3}}\\ 0& 0\end{array}\right],B=\left[\begin{array}{c}\frac{1}{L_D}\\ 0\end{array}\right],M=\left[\begin{array}{cc}\frac{1}{L_D}\sqrt{\frac{2}{3}}& 0\\ 0& 1\end{array}\right],w\left(t\right)=\left[\begin{array}{c}{V}_D\\ w_D\left(t\right)\end{array}\right]x\left(t\right)=\left[\begin{array}{c}{i}_Q\\ V_{Q_{\mathrm{Inverter}}}\end{array}\right],A=\left[\begin{array}{cc}-\frac{R}{L_Q}& \frac{1}{L_Q}\sqrt{\frac{2}{3}}\\ 0& 0\end{array}\right],B=\left[\begin{array}{c}\frac{1}{L_Q}\\ 0\end{array}\right],M=\left[\begin{array}{cc}\frac{1}{L_Q}\sqrt{\frac{2}{3}}& 0\\ 0& 1\end{array}\right],w\left(t\right)=\left[\begin{array}{c}{V}_Q\\ w_Q\left(t\right)\end{array}\right]$
and for the output matrices:
C=[R0],D=[0].

(25) The method thus makes it possible to establish two Kalman models for the electromechanical actuator system 1 along the axis d and alone the axis q, that it is appropriate to process independently.

(26) For these two Kalman models, the constants R, L.sub.Q and L.sub.D, and Ke are theoretical values. The uncertainties concerning these values are considered to be an external disturbance, which disturbance is already taken into account in the two Kalman models. By way of example, it is possible to rely on manufacturer data for imposing these values. Likewise, p is known from manufacturer data, for example.

(27) Once the two Kalman models have been established, the method thus includes a second step 200 of determining the states x(t) of these two models by Kalman filters.

(28) For this purpose, the above specified models are used in this example in discrete form.

(29) Putting the Kalman model into the discrete form and applying the Kalman algorithm to the resulting discrete model are well known to the person skilled in the art and are therefore not described in detail herein. For further details on putting two Kalman models into discrete form and on the recurrence equations of the Kalman algorithm, reference may be made by way of example to the book Stochastic Models, Estimation and Control, Volume 141-1, Mathematics in Science and Engineering by P. S. Maybeck.

(30) The known Kalman algorithm applied to the two discrete Kalman models thus makes it possible to obtain estimates for x(t) and thereby to obtain estimates for the voltage drops V.sub.D.sub.inverter and V.sub.Q.sub.inverter of the inverter 11 on the two axes d and q, and thus from the operational data i.sub.D, i.sub.Q, VD, VQ, and . Once the voltage drops of the inverter 11 have been estimated, the method has a third step 300 of estimating various electrical parameters associated with the electromechanical actuator system 1, including at least the estimated motor torque constant Ke.sub.est. Preferably, the method serves to estimate other electrical parameters, namely R.sub.est the resistance of the motor 12, and L.sub.est the inductance of the motor 12, it being understood that in the first step, the values R, L.sub.D, and L.sub.Q were set at nominal theoretical values selected on the basis of manufacturer data.

(31) To this end, it should be recalled that the electrical equations (3) set out above may be written with the real parameters in the following form:

(32) $\begin{array}{cc}\{\begin{array}{c}\sqrt{\frac{2}{3}}\left(V_D+V_{D_{\mathrm{Inverter}}}\right)=R_{\mathrm{real}}{i}_D+L_{D_{\mathrm{real}}}\frac{{\mathrm{di}}_I}{\mathrm{dt}}-L_{Q_{\mathrm{real}}}p{i}_Q\\ \sqrt{\frac{2}{3}}\left(V_Q+V_{Q_{\mathrm{Inverter}}}\right)=R_{\mathrm{real}}{i}_Q+L_{Q_{\mathrm{real}}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+L_{D_{\mathrm{real}}}p{i}_D+{\mathrm{Ke}}_{\mathrm{real}}\end{array}& \left(4\right)\end{array}$

(33) It is assumed that L.sub.Q.sub.real=L.sub.D.sub.realL=L.sub.real.

(34) On the basis of this assumption and from the system of equations (4), the following system of linear equations (5) is obtained corresponding to the n.sup.th measurements taken and used in the method (current delivered by the inverter 11 to the motor 12, control voltage, and speed of rotation of the outlet shaft of the motor 12):

(35) $\begin{array}{cc}\{\begin{array}{c}\sqrt{\frac{2}{3}}\left(V_D\left(t_n\right)+V_{D_{\mathrm{Inverter}}}\left(t_n\right)\right)=R_{\mathrm{real}}\left(t_n\right)i_D\left(t_n\right)+L_{\mathrm{real}}\left(t_n\right)\frac{{\mathrm{di}}_D\left(t_n\right)}{{\mathrm{dt}}_n}{L}_{\mathrm{real}}\left(t_n\right)p\left(t_n\right)i_Q\left(t_n\right)\\ \sqrt{\frac{2}{3}}\left(V_Q\left(t_n\right)+V_{Q_{\mathrm{Inverter}}}\left(t_n\right)\right)=R_{\mathrm{real}}\left(t_n\right)i_Q\left(t_n\right)+L_{\mathrm{real}}\left(t_n\right)\frac{{\mathrm{di}}_Q\left(t_n\right)}{{\mathrm{dt}}_n}+L_{\mathrm{real}}\left(t_n\right)p\left(t_n\right)i_I\left(t_n\right)+\left(t_n\right){\mathrm{Ke}}_{\mathrm{real}}\left(t_n\right)\end{array}& \left(5\right)\end{array}$
that can also be written in the form X.sub.n=h.sub.n.sub.n.sub.real with:

(36) $X_n=\left[\begin{array}{c}\sqrt{\frac{2}{3}}\left(V_D\left(t_n\right)+V_{D_{\mathrm{Inverter}}}\left(t_n\right)\right)\\ \sqrt{\frac{2}{3}}\left(V_Q\left(t_n\right)+V_{Q_{\mathrm{Inverter}}}\left(t_n\right)\right)\end{array}\right]$$h_n=\left[\begin{array}{ccc}{i}_D\left(t_n\right)& \left(\frac{{\mathrm{di}}_D\left(t_n\right)}{{\mathrm{dt}}_n}-p\left(t_n\right)i_Q\left(t_n\right)\right)& 0\\ i_Q\left(t_n\right)& \left(\frac{{\mathrm{di}}_Q\left(t_n\right)}{{\mathrm{dt}}_n}+p\left(t_n\right)i_D\left(t_n\right)\right)& \left(t_n\right)\end{array}\right]$${}_{n_{\mathrm{read}}}=\left[\begin{array}{c}{R}_{\mathrm{real}}\left(t_n\right)\\ L_{\mathrm{real}}\left(t_n\right)\\ {\mathrm{Ke}}_{\mathrm{real}}\left(t_n\right)\end{array}\right]$

(37) Nevertheless, as already mentioned, the measurements taken and used by the electromechanical actuator system 1 are usually found to be noisy. To make the system of equations (5) more realistic by causing account to be taken of these uncertainties about the measurements, a vector .sub.n corresponding to nonbiased white noise is introduced into the system of equations, thus giving:
Y.sub.n=h.sub.n.sub.n.sub.est.sub.n
where:

(38) $Y_n=\left[\begin{array}{c}\sqrt{\frac{2}{3}}\left(V_D\left(t_n\right)+V_{D_{\mathrm{Inverter}}}\left(t_n\right)\right)\\ \sqrt{\frac{2}{3}}\left(V_Q\left(t_n\right)+V_{Q_{\mathrm{Inverter}}}\left(t_n\right)\right)\end{array}\right]$$h_n=\left[\begin{array}{ccc}{i}_D\left(t_n\right)& \left(\frac{{\mathrm{di}}_D\left(t_n\right)}{{\mathrm{dt}}_n}-p\left(t_n\right)i_Q\left(t_n\right)\right)& 0\\ i_Q\left(t_n\right)& \left(\frac{{\mathrm{di}}_Q\left(t_n\right)}{{\mathrm{dt}}_n}+p\left(t_n\right)i_D\left(t_n\right)\right)& \left(t_n\right)\end{array}\right]$${}_{n_{\mathrm{est}}}=\left[\begin{array}{c}{R}_{\mathrm{est}}\left(t_n\right)\\ L_{\mathrm{est}}\left(t_n\right)\\ {\mathrm{Ke}}_{\mathrm{est}}\left(t_n\right)\end{array}\right]$

(39) Knowing that the data V.sub.D.sub.Inverter and V.sub.Q.sub.Inverter was estimated in preceding step 200, that the data p is known (from manufacturer data), and that the data in, i.sub.D, i.sub.Q, V.sub.D, V.sub.Q, and is measured data, it only remains to determine the parameter vector .sub.n.sub.est.

(40) In this example, this determination is performed by stochastic calculation. More precisely, this determination is performed by a recursive least-squares algorithm that makes it possible to search for .sub.n.sub.est while minimizing the criterion .sub.n=(Y.sub.nX.sub.n).sup.T(Y.sub.nX.sub.n).

(41) Such an algorithm is well known to the person skilled in the art, and is therefore not described in detail herein. For more details, reference may be made by way of example to the book Stochastic Models, Estimation and Control, Volume 141-1, Mathematics in Science and Engineering, by P. S. Maybeck.

(42) This thus makes it possible to estimate the electromagnetic torque coefficient of the motor Ke.sub.est, the resistance of the motor R.sub.est, and the inductance of the motor L.sub.est. This makes it possible to monitor the state of health of the electromechanical actuator system 1 on the basis of known ageing relationships of said system and on the basis of these estimated parameters, and/or to put into place optionally preventative maintenance operations next time the aircraft remains on the ground.

(43) Once the electromagnetic torque coefficient of the motor Ke.sub.est has been estimated, the method includes a fourth step 400 of calculating the electromagnetic torque of the motor C.sub.elec from the following formula:

(44) 0$C_{\mathrm{elec}}=\frac{3}{2}{\mathrm{Ke}}_{\mathrm{phase}}{i}_Q+\frac{3}{2}{\mathrm{Ke}}_{\mathrm{phase}}{i}_Q$
where i.sub.Q is the error on electric current measurement, which is bounded.

(45) Preferably, the method includes a fifth step 500 of estimating a plurality of mechanical parameters associated with the electromechanical actuator system 1, namely the viscous friction coefficient Coef.sub.f-visc of the mechanical portion 20, the dynamic dry friction torque C.sub.f-dry of the mechanical portion 20, and the direct efficiency .sub.direct of mechanical portion 20 (i.e. the efficiency when the load connected to the motor opposes the movement of the outlet shaft of the motor, as contrasted to the indirect efficiency .sub.indirect, which corresponds to the efficiency when the load connected to the motor accompanies the movement of the outlet shaft of the motor, with the relationship between direct efficiency and indirect efficiency being given by:

(46) $\left(\frac{1}{{}_{\mathrm{direct}}}-1\right)=\left(1-{}_{\mathrm{indirect}}\right)).$

(47) To this end, the fundamental principle of dynamics is applied to the outlet shaft of the motor 12 gives:

(48) $C_{\mathrm{elec}}+C_{\mathrm{load}}-{\mathrm{Coef}}_{\mathrm{f\_visc}}-\mathrm{sign}\left(\right)\left(C_{\mathrm{f\_dry}}+.Math.C_{\mathrm{load}}.Math.\left(\frac{1}{{}_{\mathrm{direct}}}-1\right)\right)=J_{\mathrm{mom}}\frac{d}{\mathrm{dt}}$
with

(49) $C_{\mathrm{load}}=F\frac{{\mathrm{pitch}}_{\mathrm{screw}}}{2},$
where F is the aerodynamic force to which the actuator 21 is subjected as measured using a sensor carried by the actuator 21, and J.sub.mom is the moment of inertia of the system as seen by the shaft of the motor 12.

(50) $K_{\mathrm{eff}}=\frac{1}{{}_{\mathrm{direct}}}-1$

(51) The following can be written:

(52) $J_{\mathrm{mom}}\frac{d}{\mathrm{dt}}-C_{\mathrm{elec}}-C_{\mathrm{load}}=\left[\begin{array}{ccc}-& -\mathrm{sign}\left(\right)& -\mathrm{sign}\left(\right).Math.C_{\mathrm{load}}.Math.\end{array}\right]\left[\begin{array}{c}{\mathrm{Coef}}_{\mathrm{f\_visc}}\\ C_{\mathrm{f\_dry}}\\ K_{\mathrm{eff}}\end{array}\right]$

(53) This leaves the following linear equation corresponding to the n.sup.th measurements taken and used in the method:

(54) $J_{\mathrm{mom}}\frac{d\left(t_n\right)}{{\mathrm{dt}}_n}-C_{\mathrm{elec}}\left(t_n\right)-C_{\mathrm{load}}\left(t_n\right)=\left[\begin{array}{ccc}-\left(t_n\right)& -\mathrm{sign}\left(\right)& -\mathrm{sign}\left(\right).Math.C_{\mathrm{load}}.Math.\end{array}\right]\left[\begin{array}{c}{\mathrm{Coef}}_{\mathrm{f\_visc}}\\ C_{\mathrm{f\_dry}}\\ K_{\mathrm{eff}}\end{array}\right]$
(6) that can also be written in the form X.sub.n=h.sub.n.sub.n, with:

(55) $X_n=\left[J_{\mathrm{mom}}\frac{d\left(t_n\right)}{{\mathrm{dt}}_n}-C_{\mathrm{elec}}\left(t_n\right)-C_{\mathrm{load}}\left(t_n\right)\right]$$h_n=\left[\begin{array}{ccc}-\left(t_n\right)& -\mathrm{sign}\left(\left(t_n\right)\right)& -\mathrm{sign}\left(\left(t_n\right)\right).Math.C_{\mathrm{load}}\left(t_n\right).Math.\end{array}\right]$${}_n=\left[\begin{array}{c}{\mathrm{Coef}}_{\mathrm{f\_visc}}\\ C_{\mathrm{f\_dry}}\\ K_{\mathrm{eff}}\end{array}\right]$

(56) Nevertheless, as already mentioned, the measurements taken and used by the electromechanical actuator system 1 are usually found to be noisy. Because of the electric current measurement error i.sub.Q, there remains uncertainty concerning the electromagnetic torque of the motor C.sub.elec. In order to make equation (6) more realistic, equation (6) is modified so as to make it take this uncertainty into account. In this example, the uncertainty concerning the electromagnetic torque of the motor C.sub.elec is expressed by centered white noise .sub.n of known spectral power density:

(57) $\{\begin{array}{c}{C}_{\mathrm{elec}}\left(t_n\right)={}_n=\frac{3}{2}{\mathrm{Ke}}_{\mathrm{phase}}{i}_Q\left(t_n\right)\\ C_{\mathrm{elec\_nom}}\left(t_n\right)=\frac{3}{2}{\mathrm{Ke}}_{\mathrm{phase}}{i}_Q\left(t_n\right)\\ C_{\mathrm{elec}}\left(t_n\right)=C_{\mathrm{elec\_nom}}\left(t_n\right)+C_{\mathrm{elec}}\left(t_n\right)\end{array}$

(58) The following equation is thus obtained:
Y.sub.n=h.sub.n.sub.n.sub.est+.sub.n where:

(59) $Y_n=\left[J_{\mathrm{mom}}\frac{d\left(t_n\right)}{{\mathrm{dt}}_n}-C_{\mathrm{elec\_nom}}\left(t_n\right)-C_{\mathrm{load}}\left(t_n\right)\right]$$h_n=\left[\begin{array}{ccc}-\left(t_n\right)& -\mathrm{sign}\left(\left(t_n\right)\right)& -\mathrm{sign}\left(\left(t_n\right)\right).Math.C_{\mathrm{load}}\left(t_n\right).Math.\end{array}\right]$${}_{n_{\mathrm{est}}}=\left[\begin{array}{c}{\mathrm{Coef}}_{{\mathrm{f\_visc}}_{\mathrm{est}}}\\ C_{{\mathrm{f\_dry}}_{\mathrm{est}}}\\ K_{{\mathrm{eff}}_{\mathrm{est}}}\end{array}\right]$

(60) The angular acceleration

(61) 0$\frac{d}{\mathrm{dt}}$
in this example is calculated from the angular speed , but in a variant it could be measured at the motor 12. Also, knowing that the data Ke was estimated in the first step 300, that the data J.sub.mom and pitch.sub.screw is known, and that the data , i.sub.Q, F is measured operational data, it only remains to determine the parameter vector .sub.n.sub.est.

(62) In this example, this determination is performed by stochastic calculation. More precisely, this determination is performed by a recursive least-squares algorithm that makes it possible to search for .sub.n while minimizing the criterion .sub.n=(Y.sub.nX.sub.n).sup.T(X.sub.nY.sub.n).

(63) Furthermore, it should be recalled that the algorithm needs to take account of the fact that the preceding equation is applicable only if the speed of rotation of the motor 12 is not zero. Under such circumstances when the speed of rotation of the motor 12 in absolute value was above a certain threshold value that is defined as being arbitrarily close to zero, the parameters estimated in the algorithm are frozen on the most recent value. Preferably, the pressure is adjusted so as to be as close as possible to zero as the accuracy of the Kalman filter becomes greater.

(64) Considering P to be the self correlation matrix of the estimation error .sub.n and R.sub. to be the covariance matrix of the noise .sub.n, the algorithm is written as follows:
if (n)<threshold or if threshold<(n) then K.sub.n=K.sub.n-1
{tilde over ()}.sub.n.sub.est={tilde over ()}.sub.n-1.sub.est
P.sub.n=P.sub.n-1
else

(65) if n=1 (initial conditions), then
K.sub.n=P.sub.00h.sub.n[R.sub.+h.sub.n.sup.TP.sub.00h.sub.n].sup.1
{circumflex over ()}.sub.n.sub.est={circumflex over ()}.sub.00.sub.est+K.sub.n(Y.sub.nh.sub.n.sup.T{circumflex over ()}.sub.00 .sub.est)
P.sub.n=(IK.sub.nh.sub.n.sup.T)P.sub.00

(66) else
K.sub.n=P.sub.n-1h.sub.n[R.sub.+h.sub.n.sup.TP.sub.n-1h.sub.n].sup.1
{circumflex over ()}.sub.n.sub.est={circumflex over ()}.sub.n-1.sub.est+K.sub.n(Y.sub.nh.sub.n.sup.T{circumflex over ()}.sub.n1.sub.est)
P.sub.n=(IK.sub.nh.sub.n.sup.T)P.sub.n1

(67) This thus enables the viscous friction coefficient Coef.sub.f-visc, the dynamic dry friction torque C.sub.f.sub._.sub.dry, and the direct efficiency .sub.direct to be estimated. This makes it possible to monitor the state of health of the electromechanical actuator system 1 from known ageing relationships for said system and for the estimated parameters. By way of example, it is thus possible to estimate the ageing of the electromechanical actuator system 1 and/or to undertake optionally preventative maintenance operations next time the aircraft remains on the ground.

(68) The above-described method thus makes it possible to estimate various electrical and mechanical parameters suitable for monitoring the state of health of the electromechanical actuator system 1. As mentioned above, the method is implemented during a real flight of the aircraft and not during a maneuver dedicated to estimating these parameters or while the aircraft is out of service.

(69) The method can thus be performed directly during a maneuver of the aircraft that requires the electromechanical actuator system 1 to be operated, or indeed after the maneuver has been undertaken, with the various measurements needed for performing the method previously being recorded during the maneuver so that they can be used retrospectively by the method.

(70) The data obtained by the method of the invention thus makes it possible to implement various strategies for monitoring and taking action on the electromechanical actuator system 1. For example, the method may include an additional step of forming a database made up of the various values for the electrical and mechanical parameters as estimated over time and on different flights of the aircraft. This database thus makes it possible to determine how the various electrical or mechanical parameters of the system vary over time. The database may also serve to facilitate monitoring other electromechanical actuator systems.

(71) Naturally, the invention is not limited to the implementation described, and variant implementations may be provided without going beyond the ambit of the invention as defined by the claims.