EP3305710B1 - Method for controlling an anti-oscillatory crane with a third-order filter - Google Patents

Description

The present invention relates to the general field of lifting gear, of the crane type, and more particularly of the type tower cranes, which comprise a mobile attachment point, of the trolley type, which can be suspended a load to move, called " suspended load ", and which are equipped with a control system for carrying out the movement and control of the displacement of said suspended load.

The present invention relates more particularly to control methods for managing the steering system of such lifting gear.

Generally, such control methods, which are intended to provide assistance in the control of the machine, comprise a step of acquiring a control instruction, during which the speed instruction is collected which is expressed by the driver of the lifting machine and which corresponds to the speed that said driver wishes to give to the suspended load, then a processing step during which is developed from said driving instruction, a performance instruction which is applied to the drive motor (s) that move said suspended load.

In addition, in order to ensure the precision and safety of the suspended load transport operations, the known control methods generally seek to control, and more particularly to limit, the amplitude of the oscillatory oscillations, or "swinging", to which the suspended load may be subject to carriage movement.

For this purpose, it is known in particular to combat the ballast by a closed loop servo, in which the actual values of the position and speed of the carriage are measured, as well as the value of the swing angle of the load, for to be able to generate a correction of the setpoint which is applied to the motors which actuate the carriage and which aims at reducing said dangling.

If such a system effectively mitigates the dangling, it may however have some disadvantages.

Indeed, such a closed-loop servocontrol imposes the implementation of numerous sensors, intended for example to measure the actual angle of the ballooning, which increases the complexity, and consequently the cost, as well as the risk of failure, of the control system, and more generally of the hoist equipped with said steering system.

In addition, the complexity of the mathematical model used by such a control system, as well as the quantity of data to be measured and processed, tend to mobilize relatively large and expensive resources in terms of computing power, memory, and memory. energy.

Moreover, the piloting assistance thus offered may tend to excessively dampen the responses (reactions) of the hoist to the instructions of the driver (or "crane operator"), thereby distorting the intuitive perception of the behavior of the machine that can have said driver, and in particular by giving the driver the unpleasant impression that the machine lacks responsiveness and does not faithfully implement his instructions.

A method according to the preamble of claim 1 is known from FR 3 016 872 A1 .

The objects assigned to the invention therefore seek to overcome the aforementioned drawbacks and to propose a new method for controlling the movement of a suspended load which ensures a fast and gentle displacement of the suspended load, with effective control of the dangling, which gives the driver a loyal feeling allowing a very free, responsive and relatively intuitive control, and which is, despite these performances, particularly simple and economical to implement.

The objects assigned to the invention are achieved by means of a method of controlling the movement of a load suspended at a point of attachment of a hoist, said method comprising a step (a) of acquisition of instructions in the course of which is acquired a setpoint called "steering set" which is representative of a speed of movement that the driver of the hoist wishes to give to the suspended load, and then a step (b) of treatment during which a so-called "execution instruction" instruction, which is intended to be applied to at least one drive motor, is developed from said driving instruction in order to move the suspended load, the method being characterized in that the processing step (b) comprises a regulation sub-step (b4) C ³ during which the driving instruction is processed in such a way as to confer on said steering instruction drifting properties third unit with respect to time and continuity with respect to time, in order to generate, from said control setpoint, a so-called "filtered control setpoint" which is of class C ³ , then the execution instruction is defined from said filtered control setpoint.

More preferably, the regulation sub-step (b4) C ³ may consist of a sub-step (a4) of third-order filtering during which a third-order filter is applied to the control setpoint in order to generate a setpoint filtered pilot which is class C ³ .

By "being of class C ³ ", it is indicated, in the mathematical sense of the term, that the parameter considered, here the filtered control setpoint, or more precisely the function which represents the evolution of said parameter considered as a function of time, c ' that is to say here the function representing the evolution of the filtered control set as a function of time, is three times differentiable (with respect to time), and that said function, as well as its temporal derivatives first, second and third are continuous.

Advantageously, the regulation C ³ of the control setpoint (speed setpoint for the suspended load), and more particularly the use for this purpose of a third-order filter applied to said control setpoint, makes it possible to ensure that the filtered control setpoint, which will then be effectively used to define the execution setpoint applied to the drive motors, is class C ³ .

Advantageously, a filtered control setpoint, thus regularized C ³ , has exceptional regularity conditions (in that it is here three times differentiable, and that its first, second and third time derivatives are continuous), and consequently mathematical properties of continuity and boundary that does not generally have the raw control setpoint, as defined and modified in real time by the driver of the machine.

Indeed, it will be recalled that the driver of the machine is likely to vary the steering set at any time, unpredictably.

Depending on the different situations to which the driver of the machine must react, the control setpoint (which here takes the form of a speed reference for the suspended load) can therefore vary from one hand to another when the driver of the machine decides to change the direction of the movement (left / right, distance / approximation), and secondly in amplitude (intensity), when the driver goes from a movement that he wishes fast to a slower movement ( deceleration), or conversely (acceleration).

In addition, the speed of these control setpoint changes can vary considerably, depending on the frequency and speed with which the driver of the machine actuates the commands to make changes or corrections of trajectory.

The gross piloting instruction can therefore present in practice some abrupt variations of ladder type that can be mathematically assimilated to discontinuities.

Likewise, due in particular to these discontinuities, the time derivatives (typically of order one and of order two) of the control setpoint, which will preferably be used in the modeling of the behavior of the suspended load and in the elaboration of the execution instruction, could present punctually, if they were calculated directly, without appropriate regularization (filtering), certain divergences or discontinuities, so that the resulting instruction of execution would be likely to cause jerky or unstable reactions of the suspended charge.

This is why the method according to the invention advantageously smooths the control setpoint before it is actually applied to the (x) drive motor (s), which eliminates the control signal (instruction d). execution) instabilities, discontinuities and other divergences that would be likely to cause jolts and the appearance (or maintenance) of a ballant.

It is thus possible to obtain a movement of the suspended load which is particularly regular and stable, irrespective of the nature of the said movement (that is to say whatever the shape of the trajectory desired by the driver of the machine), and regardless of the speed and amplitude of said movement desired by the driver of the machine.

Advantageously, and as will be detailed hereinafter, the regularity C ³ conferred on the control setpoint furthermore makes it possible to subsequently define the execution instruction, from said control instruction, by means of a simplified mathematical model. which not only is simple and quick to execute, but which, above all, produces an execution instruction which is inherently non-generating dangling, that is to say a performance instruction which, when it is applied to the engines actuation, does not cause (can not cause of itself) the appearance of a ballant.

Furthermore, the method according to the invention notably allows a free and precise adjustment of the coefficients, as well as the pulsation, of the third-order filter which is applied to the control setpoint, which makes it possible to maintain rapid convergence in all circumstances. the speed of the load suspended towards the speed reference expressed by the driver of the machine.

In other words, the method provides a dynamic and responsive control.

Next, the method according to the invention advantageously makes it possible to optimize the use of the drive motor or motors, in that it makes it possible to derive the best possible performance from said motor or said motors, in particular by terms of speed or acceleration conferred to the point of attachment and the load, while respecting at all times the material limits of said engine (s).

It is understood that if an engine can not reach the setpoint which is fixed to it because said setpoint is too high with respect to the capabilities of said engine, then the actual training of the hooking point will suffer from an insufficiency with respect to the desired training, so that the movement of said point of attachment (and thus the movement of the suspended load) that will be obtained will not correspond to the desired movement.

However, the execution instruction being by definition calculated precisely to obtain (theoretically) a movement (desired movement) regular and without dangling, it will be understood that if, in practice, the drive motor does not execute correctly said instruction d ' execution, then the control system will not behave as desired, and that may result in the appearance of a ballant and some loss of control of the movements of the point of attachment and load.

Here, thanks to the invention, it is possible to parameterize the regularization C ³ , and more particularly it is possible to parameterize the filtering of the third order, and if necessary to modify this parameterization of the regularization C ³ (or filtering, respectively) over time , so that the execution instruction, while promoting rapid response of the control system, does not exceed the actual capacity of the drive motors in terms of maximum speed and maximum acceleration.

In this respect, it will be noted in particular that on the one hand the maximum acceleration that can be imparted to the point of attachment (carriage) is directly dependent on the maximum acceleration capacity of the drive motors used to move said point of attachment, and that on the other hand there exists mathematically, because of the physical laws of dynamics, a relationship between the acceleration of the point of attachment (acceleration of the carriage) and the third derivative of the speed of the load suspended.

Therefore, when one corrects C ³ the gross control setpoint (suspended load speed setpoint) expressed by the driver of the machine, according to the invention, is advantageously carried out a planning of the profile of the speed reference that we will apply to the drive motors, that is to say that we plan the evolution over time (and more particularly the rate of change per unit of time) of the value of the instruction of execution (trolley speed reference value), according to an evolution profile which best reflects the desired control setpoint but which is also and above all compatible with the ability of the motors to provide a response that is at each moment up to said performance instruction.

In this way, the execution instruction is in practice always "realizable", that is to say that said execution instruction is intrinsically such that said real control system is still capable of "realizing" (to achieve ) actually said performance instruction that is applied to him, and therefore to provide a real response that is consistent with the behavior expected of said steering system, and more particularly consistent with the behavior expected of the truck (such as said expected behavior is defined by the execution instruction).

Thus, the execution instruction never takes the actual control system into default.

More particularly, the proposed third-order filter simplifies the implementation of appropriate saturations, during the processing of the control setpoint, and thus the implementation of "intelligent" dynamic limits of the execution instruction, which make it possible to draw the best of the drive motors while ensuring a permanent, precise and reliable control of the movements of the point of attachment and the suspended load.

Finally, it will be noted that the control method according to the invention advantageously makes it possible to control the hoist by an open-loop servocontrol, simply by applying the execution instruction (speed reference) to the drive motor concerned, without Require no measurement of the effective dangling (that is, without the need for feedback on the actual angle of the balloon), which limits the number of sensors and the computing power necessary to control, and therefore reduces the complexity, congestion, and energy consumption of the steering system.

• La figure 1 illustre, selon une vue schématique en perspective, l'agencement général d'un exemple d'engin de levage piloté par un procédé selon l'invention.
• La figure 2 illustre, selon une vue schématique de côté, le principe général d'un modèle mécanique de pendule qui sous-tend le procédé selon l'invention.
• La figure 3 illustre, sous forme d'un schéma-bloc, le calcul de la pulsation applicable au filtre du troisième ordre ainsi que la saturation préliminaire de la consigne de pilotage, qui précède le filtrage du troisième ordre.
• La figure 4 illustre, sous forme d'un schéma-bloc, le principe de mise en oeuvre d'une étape (b) de traitement selon l'invention, et plus particulièrement le détail d'un filtre du troisième ordre selon l'invention.
• La figure 5 illustre, selon une vue schématique de dessus, la correspondance entre les systèmes de coordonnées cartésiennes et de coordonnées cylindriques permettant d'exprimer les consignes de pilotage, puis les consignes d'exécution, dans des repères appropriés.
• La figure 6 illustre, sous forme d'un schéma-bloc, la mise en oeuvre du procédé selon l'invention pour commander d'une part un moteur d'orientation (l'« orientation » désignant la composante de giration en lacet, autour d'un axe (ZZ') dit « axe d'orientation ») et d'autre part un moteur de distribution (la « distribution » désignant la composante radiale d'éloignement ou de rapprochement par rapport à l'axe (ZZ') d'orientation), à partir d'une consigne de pilotage exprimée en coordonnées cylindriques, comprenant une composante radiale et une composante angulaire.
• La figure 7 illustre, de façon schématique, une consigne de pilotage filtrée obtenue en réponse à une consigne de pilotage brute de type échelon, ainsi qu'une consigne d'exécution qui est déterminée à partir de ladite consigne de pilotage filtrée, tel que cela est illustré sur la figure 6, au moyen d'une formule de conversion issue du modèle mécanique de la figure 2.

Other objects, features and advantages of the invention will appear in more detail on reading the description which follows, and with the aid of the accompanying drawings, provided for purely illustrative and non-limiting purposes, among which:

• The figure 1 illustrates, in a schematic perspective view, the general arrangement of an example of lifting gear driven by a method according to the invention.
• The figure 2 illustrates, in a schematic side view, the general principle of a mechanical pendulum model which underlies the method according to the invention.
• The figure 3 illustrates, in the form of a block diagram, the computation of the pulsation applicable to the third order filter as well as the preliminary saturation of the control setpoint, which precedes the filtering of the third order.
• The figure 4 illustrates, in the form of a block diagram, the principle of implementing a processing step (b) according to the invention, and more particularly the detail of a third-order filter according to the invention.
• The figure 5 illustrates, in a schematic top view, the correspondence between the Cartesian coordinate systems and cylindrical coordinates for expressing the control instructions, and the instructions for execution, in appropriate marks.
• The figure 6 illustrates, in the form of a block diagram, the implementation of the method according to the invention for controlling on the one hand an orientation motor (the "orientation" designating the gyration component in yaw, around a axis (ZZ ') called "axis of orientation") and secondly a distribution motor (the "distribution" designating the radial component of distance or approximation relative to the axis (ZZ') of orientation ), from a control set expressed in cylindrical coordinates, comprising a radial component and an angular component.
• The figure 7 illustrates, schematically, a filtered control setpoint obtained in response to a step-type raw control setpoint, and an execution setpoint which is determined from said filtered control setpoint, as illustrated on FIG. the figure 6 , using a conversion formula derived from the mechanical model of the figure 2 .

The present invention relates to a method for controlling the movement of a load 1 suspended at a point of attachment H of a hoist 2.

The hoist 2 is designed so as to be able to move the point of attachment H, and consequently the suspended load 1, according to a component of yaw rotation Θ about a first vertical axis (ZZ '), called " axis of orientation ", and / or according to a radial component R, corresponding to a movement called" distribution ", here in translation along a second axis (DD ') said" distribution axis "intersecting said axis of orientation (ZZ '), as illustrated in the Figures 1 and 2 .

The hoist 2 may in particular form a tower crane, whose mast 3 materializes the axis of orientation (ZZ '), and whose arrow 4 materializes the axis of distribution (DD'), as it is illustrated on the figure 1 .

For the sake of simplicity of description, such a tower crane configuration will be considered in the following, and more particularly a configuration of a tower crane with horizontal boom 4, it being understood that it is perfectly possible to apply the principle of invention to other lifting gear, and in particular to mobile cranes or luffing jib cranes.

Note the intersection O of the dispensing axis (DD ') and the orientation axis (ZZ').

The point of attachment H is preferably formed by a carriage 5, which can advantageously be guided in translation along the distribution axis (DD '), along the arrow 4.

For convenience, we can assimilate the carriage 5 and the point of attachment H in what follows.

The orientation movement Θ, and, respectively, the dispensing movement R , and more particularly the drive movement of the carriage 5 in translation R along the arrow 4, can be provided by any drive motor 7, 8 suitable, preferably electric, and more particularly by at least one (electric) motor 8 and, respectively, a motor (electric) distribution 7.

The load 1 is suspended at the point of attachment H by a suspension device 6, such as a suspension cable. In the following, said suspension device will be assimilated to such a suspension cable 6, for convenience.

The suspended load 1 may also preferably be moved in a vertical component, called "lifting", so as to vary the height at which the suspended load 1 relative to the ground.

Preferably, it will be possible for this purpose to vary the length L of the suspension cable 6, typically by means of a winch driven by a motor (preferably electric) lifting, so as to change the distance of the suspended load 1 at the point of attachment H, and thus either raise the load 1 by shortening the length L (by winding the suspension cable 6), or on the contrary lower said load 1 by an elongation of said length L ( by unwinding the cable 6).

For convenience, the term "steering system" may be used to designate the movement and the control of the displacement of the suspended load 1, said assembly typically comprising the module or modules (calculators) 10, 12, 13 , 14, 15, 16, 17 for carrying out the method according to the invention, as well as the driving motor or motors 7, 8 (Actuators), and if necessary the moving parts (effectors) of the machine driven by said drive motors 7, 8; said movable members here correspond on the one hand to the mast 3 and to the arrow 4, yawable according to the orientation movement Θ, and on the other hand to the carriage 5 providing the dispensing movement R along the arrow 4.

According to the invention, the method comprises a control instruction acquisition step (a) during which a setpoint known as a "control setpoint" V _u is acquired that is representative of a traveling speed V _load that the driver of the hoist 2 wishes to confer on the suspended load 1.

The method according to the invention then comprises a step (b) of processing during which is developed, from said control setpoint V _u , here by means of a processing module 10, an instruction called "instruction d ' V _trol , which is intended to be applied to at least one drive motor 7, 8 to move the suspended load 1, and, more particularly, to move the carriage 5 to which said load 1 is suspended.

It will be noted that, advantageously, the method makes it possible to control the speed, rather than the trajectory, and more particularly to control the speed of the carriage 5, from a speed reference V _u which corresponds to the desired speed. for suspended load 1.

As such, the execution instruction V _trol will preferably express the speed setpoint that must reach the point of attachment H (that is to say, the speed setpoint that must reach the carriage 5).

In other words, the method preferably comprises a step (a) during which the driver defines (freely) and expresses (voluntarily) a driving instruction in the form of a speed instruction he wishes or even followed by the suspended load 1, then a processing step (b) during which said control setpoint (setpoint in suspended load speed) is processed, here more particularly filtered by a third order filter, to be converted into a corresponding instruction the speed of the carriage 5, forming the instruction of execution (in speed) V _trol which is applied to the drive motor 7, 8 adequate.

It will be noted moreover that the method offers the operator of the machine a great freedom of maneuver, since said driver can fix freely, at any moment, and according to the amplitude that he chooses, the control setpoint (speed setpoint) V _u it wants to be executed by the load 1, and this without being forced, for example, to respect a predetermined fixed trajectory.

It will be noted moreover that the method according to the invention is valid both for controlling the orientation movement Θ and for controlling the dispensing movement R, or for controlling any combination of these two movements simultaneously.

From the formal point of view, it will be noted that the position of the movable members, namely the point of attachment H / carriage 5 on the one hand, the load 1 suspended on the other, and the movements said movable members, either in a Cartesian coordinate system (O, X, Y, Z) associated with the base (considered fixed) of the lifting vehicle 2, or in a "polar" type reference (O, r, θ) using cylindrical or even spherical coordinates.

• P_trol ^x et P_trol ^y les positions en X (premier axe horizontal), respectivement en Y (second axe horizontal, perpendiculaire au premier axe horizontal X), du chariot 5 (l'indice « trol » désignant le chariot ou « trolley ») ;
• V_trol ^x et V_trol ^y les composantes de vitesse en X, respectivement en Y, dudit chariot 5 ;
• P_load ^x et P_load ^y les positions en X, respectivement en Y, de la charge 1 suspendue (l'indice « load » désignant la charge suspendue 1) ;
• V_load ^x et V_load ^y les composantes de vitesse en X, respectivement en Y, de ladite charge suspendue 1, qui correspondent aux composantes de la vitesse (voulue) de la charge suspendue 1, et donc, en pratique, aux composantes de la consigne de pilotage V_u.

By convention, it will thus be possible to note, in said Cartesian frame:

• P _trol ^x and P _trol ^y the positions in X (first horizontal axis), respectively in Y (second horizontal axis, perpendicular to the first horizontal axis X), of the carriage 5 (the index "trol" denoting the trolley or "trolley");
• V _trol ^x and V _trol ^y speed components in X, respectively Y, said carriage 5;
• P _load ^x and P _load ^y the positions in X, respectively in Y, of the suspended load 1 (the "load" index denoting the suspended load 1);
• V _load ^x and V _load ^y the speed components in X, respectively in Y, of said suspended load 1, which correspond to the components of the (wanted) speed of the suspended load 1, and therefore, in practice, to the components of the pilot setpoint V _u .

When the cylindrical coordinates (r, θ) are used, it will be possible more particularly to attach to each mobile member considered a Frenet coordinate system making it possible to express the radial component V ^r (according to the distribution movement R ) and the orthoradial component V ^θ (according to the tangent to the orientation movement Θ) of the speed of the movable member in question, as shown in particular in FIG. figure 5 .

Thus, on said figure 5 , as well as on the figure 6 , V _load ^r and V _load ^θ represent the radial and respectively orthoradial components of the velocity vector V _load of the load 1 suspended (that is to say in practice the radial and orthoradial components of the speed control setpoint V _u ) , while V _trol ^r and V _trol θ represent the radial and respectively orthoradial components of the velocity vector V _trol of the carriage 5 (that is to say the radial and orthoradial components of the speed execution instruction V _trol , which are respectively applied to the distribution motor 7 and the orientation motor 8).

As illustrated on the Figures 3, 4 and 6 , the driving setpoint V _u can be provided by the driver of the machine by means of any appropriate control member 11.

Said control member 11 may in particular take the form of a joystick, or a set of joysticks, which will allow the driver to express the orientation speed reference (yaw rate, orthoradial) V _load ^θ and the delivery speed setpoint (radial speed) V _load ^r it wishes to print to the suspended load 1.

By simple convenience of notation, the driving instruction V _u brute, as expressed by the driver of the machine at the control member 11, that is to say the signal provided by the joystick at the input of the control system, will preferably refer to V _JOY in the aforementioned figures.

To better explain the invention, some elements of theoretical mechanics for modeling a pendulum system will now be exposed, with reference to the figure 2 .

Note that the explanation given here in a plane, with reference to a single dimension of displacement, along the axis X, which is considered parallel to the arrow 4 and to the distribution axis (DD '), remains valid in three dimensions.

où

• M représente la masse de la charge suspendue 1 ;
• a _load représente l'accélération de la charge suspendue 1 (que l'on considère ici portée par la direction horizontale X) ;
• T représente la tension du câble de suspension 6 ;
• g représente la gravité (accélération de pesanteur).

According to the fundamental principle of the dynamics (Newton's law), and neglecting any external forces such as the wind, we have: $$M{\overrightarrow{\mathrm{at}}}_{\mathit{load}}=\overrightarrow{T}+M\overrightarrow{g}$$

or

• M represents the mass of the suspended load 1;
• at _load represents the acceleration of the suspended load 1 (considered here borne by the horizontal direction X);
• T represents the tension of the suspension cable 6;
• g represents gravity (gravitational acceleration).

avec β l'angle (angle de ballant) que forme le câble de suspension 6 avec la verticale Z.The equation above implies that the vector M at _load - M g is collinear (parallel) to the vector T . As a result, we have: $\tan \beta =\frac{{\mathit{My}}_{\mathit{load}}}{\mathit{mg}}=\frac{{\mathrm{at}}_{\mathit{load}}}{g}$

with β the angle (swinging angle) that forms the suspension cable 6 with the vertical Z.

avec

• P_trol la position (ici en X) du chariot 5,
• P_load la position (ici en X) de la charge 1, et
• L la longueur du câble de suspension 6.

Assuming small angles, we can also write: $$\sin \beta \approx \tan \beta =\frac{P_{\mathit{trol}}-P_{\mathit{load}}}{\mathrm{The}}$$

with

• P _trol the position (here in X) of the carriage 5,
• P _load the position (here in X) of the load 1, and
• L the length of the suspension cable 6.

et, en dérivant l'expression ci-dessus par rapport au temps, on obtient une équation différentielle du second degré, dite « formule de conversion », qui exprime la vitesse V_trol du chariot 5 en fonction de la vitesse V_load de la charge suspendue 1 : $$V_{\mathit{trol}}=V_{\mathit{load}}+\frac{L}{g}\frac{d^2}{{\mathit{dt}}^2}{V}_{\mathit{load}}$$

ce qui peut également s'exprimer par la transformée de Laplace : $$V_{\mathit{trol}}\left(p\right)=\left(1+\frac{L}{g}{p}^2\right)V_{\mathit{load}}$$

The following relation is deduced between the position P _trol of the carriage on the one hand, and the position P _load of the suspended load and the speed V _load of the load on the other hand: $$P_{\mathit{trol}}=P_{\mathit{load}}+\frac{\mathrm{The}}{g}{\mathrm{at}}_{\mathit{load}}=P_{\mathit{load}}+\frac{\mathrm{The}}{g}\frac{d}{\mathit{dt}}{V}_{\mathit{load}}$$

and, by deriving the above expression with respect to time, one obtains a differential equation of the second degree, called "conversion formula", which expresses the speed V _trol of the carriage 5 as a function of the speed V _load of the load suspended 1: $$V_{\mathit{trol}}=V_{\mathit{load}}+\frac{\mathrm{The}}{\mathrm{<figure-callout\; id="2"\; label="g\; d"\; filenames="imgf0001.png"\; state="\{\{state\}\}">g\; </figure-callout>}}\frac{d^{}}{}\frac{{}^2}{{\mathit{dt}}^2}{V}_{\mathit{load}}$$

which can also be expressed by the Laplace transform: $$V_{\mathit{trol}}\left(p\right)=\left(1+\frac{\mathrm{The}}{g}{p}^2\right)V_{\mathit{load}}$$

In practice, thanks to the conversion formula above, it is therefore possible to calculate the speed reference of the trolley V _trol , that is to say specifically the execution instruction V _trol , from the value of the speed V _load that one wishes to confer to the suspended load, that is to say from the control setpoint V _u .

doit d'une part exister, et d'autre part être bornée (c'est-à-dire être majorée par une valeur fixe finie).However, it is also necessary to take into account the fact that, in the actual control system, the carriage 5 necessarily has a finite (bounded) acceleration. This material condition requires that, from a mathematical point of view, the acceleration of the carriage, that is to say the time derivative of the speed of the carriage, ${\dot{V}}_{\mathit{trol}}=\frac{d}{\mathit{dt}}{V}_{\mathit{trol}}$

must on the one hand exist, and on the other hand be bounded (that is to say, be increased by a finite fixed value).

de la vitesse de la charge suspendue (vitesse de pilotage) V_load.However, the calculation of the speed of the trolley (execution instruction) V _trol according to the conversion formula above involves the second time derivative. ${\ddot{V}}_{\mathit{load}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png"\; state="\{\{state\}\}">d</figure-callout>}}^2}{{\mathit{dt}}^2}{V}_{\mathit{load}}$

the speed of the suspended load (driving speed) V _load .

peut donc s'exprimer sous forme d'une fonction de la dérivée temporelle troisième ${\stackrel{⃛}{V}}_{\mathit{load}}=\frac{d}{\mathit{dt}}{\ddot{V}}_{\mathit{load}}=\frac{d^3}{{\mathit{dt}}^3}{V}_{\mathit{load}}$

de la vitesse de la charge V_load.With respect to this conversion formula, the acceleration of the trolley ${\dot{V}}_{\mathit{trol}}=\frac{d}{\mathit{dt}}{V}_{\mathit{trol}}$

can therefore be expressed as a function of the third time derivative ${\stackrel{⃛}{V}}_{\mathit{load}}=\frac{d}{\mathit{dt}}{\ddot{V}}_{\mathit{load}}=\frac{{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^3}{{\mathit{dt}}^3}{V}_{\mathit{load}}$

the speed of the load V _load .

de la vitesse de la charge V_load existe et soit bornée, c'est-à-dire que la vitesse de la charge suspendue V_load (et par conséquent la consigne de pilotage V_u qui va servir à fixer ladite vitesse de la charge suspendue) soit trois fois dérivable, et que sa dérivée troisième soit continue (et bornée).It follows that the condition of existence and of bounding of the acceleration of the carriage V̇ _trol requires that the temporal derivative third ${\stackrel{⃛}{V}}_{\mathit{load}}$

the speed of the load V _load exists and is bounded, that is to say that the speed of the suspended load V _load (and consequently the control setpoint V _u which will serve to fix said speed of the suspended load) is three times differentiable, and that its third derivative is continuous (and bounded).

In other words, it must be ensured that the driving instruction V _u actually used to calculate (according to the conversion formula above) the execution instruction V _trol is (at all times and in all circumstances) of class C ³ , even though said driving instruction V _u is initially expressed by the driver of the machine, and acquired substantially in real time, in a raw form V _JOY which is likely to vary unpredictably with the wire. time, at the free choice of the driver, and therefore does not necessarily have these properties of regularity C ³ .

This is particularly why, according to the invention, the treatment step (b) advantageously comprises a regulation sub-step (b4) C ³ during which the driving instruction V _u is processed so as to confer on said control setpoint V _u of the properties of differentiability third with respect to time and of continuity with respect to time, in order to generate, from said control setpoint V _u , a filtered control setpoint V _f which is of class C ³ , then the execution setpoint V _{trol is set} from said filtered control setpoint V _f .

According to one possible variant of implementation, the regularization C ³ can be carried out using interpolation polynomials.

According to this variant, the control setpoint V _u is interpolated, and more particularly several or all of the values considered among the succession of different values taken by the control setpoint V _u during a given time interval, by means of a polynomial.

Said polynomial intrinsically possesses a class of regularity (at least) C ³ , and thus provides an accurate and class-specific approximation C ³ of the control setpoint, in the form of a filtered control setpoint V _f of polynomial type.

Such a polynomial thus provides a class C ³ planning of the control set.

However, according to another particularly preferred variant which is simpler to implement than the variant by polynomial interpolation, during the regulation sub-step (b4) C ³ , the control setpoint V _u is applied to regulate C ³ said control setpoint, a third order filter F3 in order to generate the filtered control setpoint V _f which is of class C ³ .

In other words, the sub-step (b4) preferably constitutes a third-order filter sub-step in the course of which a third-order filter F3 is applied to the control setpoint V _u in order to generate an instruction of filtered control V _f which is three times differentiable (and more exactly regularity class C ³ ).

Preferably, the regularization C3, and more particularly the third-order filtering, is performed by means of a third-order filtering module 12, formed by a computer or electronic computer.

avec :

• ω la pulsation du filtre du troisième ordre F3 ;
• C₁, C₂ les coefficients, respectivement du premier ordre et du second ordre, utilisés par ledit filtre du troisième ordre F3.

Third-order filtering F3 can be written as a transfer function: $$V_f\left(p\right)=\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">F</figure-callout>}3\cdot V_u\left(p\right)=\frac{1}{\frac{{\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}}^3}{{\mathrm{<figure-callout\; id="3"\; label="\omega "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\omega </figure-callout>}}^3}+c_2\frac{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0001.png"\; state="\{\{state\}\}">p</figure-callout>}}^2}{{\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\omega </figure-callout>}}^2}+c_1\frac{p}{\omega }+1}{V}_u\left(p\right)$$

with:

• ω the pulsation of the third order filter F3;
• C ₁ , C ₂ the coefficients, respectively of the first order and the second order, used by said third order filter F3.

In the time domain, the third order filter F3 results in the following differential equation: $$V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{\omega }{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }^2}{\ddot{V}}_f+\frac{1}{{\omega }^3}{\stackrel{⃛}{V}}_f=V_u$$

In order to optimize the filter of the third order F3, we will preferably choose: c ₁ = 2.15 and c ₂ = 1.75, as it appears on the figure 4 .

These values make it possible to optimize the reactivity of the filter F3, by minimizing its response time to 5% (ie the time required to converge the response to a step-type setpoint with an error of less than 5%). % of the value of said step), while limiting the overshoot.

It will be noted that, according to one possible variant of implementation of the invention, the filtered control setpoint V _f could be used directly as the execution setpoint V _trol applied to the drive motors 7, 8, that is to say that one could ask: V _trol = V _f .

Indeed, thanks to the regularization C ³ , obtained here by the filtering of the third order, the filtered control setpoint V _f is intrinsically defined, and more generally "planned", so as to gradually converge towards the control setpoint V _u , without ever being too stiff.

In this way, said filtered control setpoint V _f , regularized C ³ , is actually achievable, the drive motors 7, 8 being able to follow said filtered control setpoint V _f .

So, in the example shown on the figure 7 , where the driver of the machine applies a control setpoint V _u of the step type, it is found that the filtered control setpoint V _f actually evolves in a more gradual slope than that of said step, and without discontinuity.

avec :

• V_f la consigne de pilotage filtrée (régularisée C³), ici plus préférentiellement issue du filtre du troisième ordre F3,
• L la longueur du câble de suspension 6 qui relie la charge suspendue au point d'accroche,
• g la gravité.

However, according to another particularly preferred variant embodiment of the invention, after having determined the filtered control setpoint V _f , the execution instruction can then be defined (and calculated) as follows, by applying the conversion formula mentioned above: $$V_{\mathit{trol}}=V_f+\frac{\mathrm{The}}{g}{\ddot{V}}_f$$

with:

• V _f filtered control setpoint (regularized C ³ ), here more preferably from the third order filter F3,
• L the length of the suspension cable 6 which connects the suspended load to the point of attachment,
• g gravity.

This conversion formula, simple and fast to execute, has the advantage of being intrinsically an anti-dangling function.

Thus, using the above conversion formula is advantageously equivalent to applying to the filtered piloting set V _f an (additional) anti-dangling function, which makes it possible to produce a non- _ballistic V _trol execution instruction.

Indeed, the above conversion formula comes from a simplified model of pendulum, in which it is considered that the swing angle β is almost zero, that is to say that the suspended load 1 is not balanced not (or almost no) with respect to the carriage 5.

Advantageously, this means, reciprocally, that a V _trol execution _instruction developed from this model is such that, if said execution instruction is actually faithfully executed by the drive motors 7, 8, and therefore by the carriage 5, said V _trol performance instruction can not, in itself, cause dangling.

The figure 7 shows a V _trol execution _instruction thus obtained by applying the conversion formula to a filtered control setpoint V _f resulting from a control setpoint V _u of the step type.

The conversion of the filtered setpoint V _f to the execution setpoint V _trol can be performed by any appropriate conversion module (computer) 13 of the electronic circuit type or computer programmed module.

It will also be noted that the determination of the V _trol execution _instruction according to the invention can advantageously be carried out without it being necessary to know, and even more so without it being necessary to measure, the mass M of the load. suspended 1, insofar as this parameter (the mass M of the load 1) does not intervene in the formulas used during step (b) of treatment, and in particular does not intervene in the definition of the third order filter F3 or in the aforementioned conversion formula.

It is therefore possible to economize on a measurement of the mass M of the suspended load 1 or of a treatment of this mass parameter M, which again makes it possible to simplify the structure of the lifting machine 2 , and to simplify and speed up the execution of the process.

Advantageously, the anti-dangling effects intrinsically provided on the one hand by the C ³ regularization itself, and on the other hand by the use of a non-dangling conversion formula, will combine to offer optimized servocontrol of the movement of the suspended load 1, totally devoid of dangling.

Given the ability of the method to generate a performance instruction that does not cause a ballad, we can, particularly preferably, implement the servo according to the invention in open loop.

Thus, it will be possible in particular to control the hoist 2, and more particularly the movements of the carriage 5 (here typically in orientation Θ and in distribution R ), by applying "blindly" the instruction of execution (here preferably a set speed) V _trol the (x) drive motor (s) 7, 8, without providing slaving that would aim to reduce then the actual dangling that might result from the application of this performance instruction or even who result from external disturbances.

In particular, it will thus be possible to drive the hoist 2 without having to use a measured or calculated feedback ("feedback") of the actual (real) swing angle of the suspended load 1, or of measured or calculated return of the angular velocity of the effective ballad of said suspended load 1 and, preferably, without having to use a measured return of the effective (real) speed of the displacement of the point of attachment H.

By using the method according to the invention in an open loop, it is therefore advantageously possible to obtain excellent control of the displacement of the suspended load 1, and more particularly to offer the operator of the machine excellent possibilities of manual control of the displacement of the load. suspended, by means of a process that combines simplicity and speed of execution, while simplifying the structure of the hoist 2, and in particular by the economy of sensors for measuring the ballant.

This being the case, the method according to the invention remains perfectly compatible, as an alternative embodiment, with a closed-loop servocontrol, according to which the execution instruction V _{trol is first} determined in accordance with the invention, in particular by making intervening third-order filtering, then said V _trol execution instruction is then applied to the drive motors 7, 8 while providing a closed-loop servocontrol (as described above) for actively reducing a possible dangling, to a case where such a ballant would appear despite being caused by disturbances external to the control system, such as gusts of wind, for example.

Advantageously, according to such an alternative embodiment, the determination of the execution instruction V _trol according to the invention, with regularization C ³ on the one hand and use of the anti-dangling conversion formula mentioned above on the other hand, however, it will be possible to generate an execution instruction (trolley speed reference) V _trol already optimized, not generating a dangling (intrinsically), so that the dancer compensation task assigned to the closed loop of the servo will be greatly simplified. (since this will only reduce possible dangling caused by the only disturbances external to the control system).

It will also be recalled that the drive motors 7, 8 have, by their nature, limited (finite) speed, acceleration, and torque capabilities.

Therefore, it is necessary that the V _trol execution _instruction is compatible with these capabilities, so that the motors 7, 8 can actually execute said V _trol execution _instruction , and thus generate, as a result of the application of said V _trol performance instruction to said motors 7, 8, movements of the carriage 5 and the suspended load 1 without dangling, which are consistent with the movements that are expected with respect to said performance instruction.

In other words, it is necessary to take care to generate a V _trol execution _instruction which is feasible, that is to say coherent and compatible with the actual hardware capacities of the drive motors 7, 8, so not to seek to solicit the control system beyond its capabilities, and so as to avoid any situation in which a failure of a motor 7, 8 would lead the actual motion to differ from the expected ideal motion, and would cause, for example, the appearance or accentuation of a dangling.

• Contrainte n°1 : la consigne de vitesse filtrée V_f(t) doit être trois fois dérivable, et plus particulièrement de classe C³ ;
• Contrainte n°2 : la consigne de vitesse filtrée V_f doit converger le plus rapidement possible vers la consigne de pilotage V_u (en réponse typiquement à une consigne de pilotage V_u formant un échelon constant) ;
• Contrainte n°3 : l'accélération du chariot 5 ne doit jamais dépasser la capacité d'accélération intrinsèque maximale du moteur d'entraînement 7, 8 correspondant, c'est-à-dire que l'on a en permanence : |V̇_trol | ≤ a_MAX, soit $\left|{\dot{V}}_f+\frac{L}{g}{\stackrel{⃛}{V}}_f\right|\le a_{\mathit{MAX}}$
  
  où a_MAX est une valeur représentative de l'accélération maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1 (c'est-à-dire ici au chariot 5) ;
• Contrainte n°4 : la consigne de vitesse du chariot (consigne d'exécution) V_trol ne doit jamais dépasser la vitesse maximale que le moteur d'entraînement 7, 8 peut conférer au chariot 5, c'est-à-dire que l'on a en permanence: |V_trol |≤ V_MAX soit: $\left|V_f+\frac{L}{g}{\ddot{V}}_f\right|\le$
  
  V_MAX où V_MAX est une valeur représentative de la vitesse maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1 (c'est-à-dire ici au chariot 5).

Finally, with regard to the criteria of stability, speed of convergence, and compliance with the hardware capabilities of the drive motors 7, 8, it can be considered that, overall, the filtered control setpoint (filtered speed setpoint) V _f must meet (simultaneously) four cumulative constraints:

• Constraint n ° 1: the filtered speed setpoint V _f (t) must be three times differentiable, and more particularly of class C ³ ;
• Constraint No. 2: the filtered speed setpoint V _f must converge as quickly as possible towards the control setpoint V _u (in response typically to a control setpoint V _u forming a constant step);
• Constraint No. 3: the acceleration of the carriage 5 must never exceed the maximum intrinsic acceleration capacity of the corresponding drive motor 7, 8, that is to say that there is always: V̇ _trol | ≤ a _MAX , either $\left|{\dot{V}}_f+\frac{\mathrm{The}}{g}{\stackrel{⃛}{V}}_f\right|\le {\mathrm{at}}_{\mathit{MAX}}$
  
  where _MAX is a value representative of the maximum acceleration that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended (that is to say here to the carriage 5);
• Constraint n ° 4: the trolley speed reference (execution instruction) V _trol must never exceed the maximum speed that the drive motor 7, 8 can give to the trolley 5, that is to say that the trolley we always have: | V _trol | ≤ V _MAX is: $\left|V_f+\frac{\mathrm{The}}{g}{\ddot{V}}_f\right|\le$
  
  V _MAX where V _MAX is a value representative of the maximum speed that the drive motor 7, 8 can give to the point of attachment H to which the load 1 is suspended (that is to say here to the carriage 5).

The regularization C ³ , and more particularly the application of the third-order filter F3, makes it possible to satisfy the constraint n ° 1 (three-fold differentiable setpoint, and more particularly of class C ³ ).

Stress No. 2 (fast convergence) can be satisfied by appropriately selecting the coefficients c1, c2 of said third order filter F3, as indicated above, and secondly by adapting the pulsation ω of said third order filter F3. depending on the circumstances, as will be detailed below.

We can finally satisfy the constraints No. 3 (acceleration limit) and No. 4 (speed limit), that is to say, make sure that the execution instruction (instruction of trolley speed) V _trol is achievable, by applying saturation functions SAT1, SAT2, SAT3 appropriate, which will be detailed in the following.

Thus, according to a preferred characteristic which can constitute an entirely separate invention, during the regulation sub-step (b4) C ³ , it is possible to use, to generate the filtered control setpoint V _f , a parameter which is representative of the maximum acceleration _MAX that the drive motor 7, 8 can give the point of attachment H to which the load 1 is suspended, so that the execution instruction V _trol which derives from said filtered control set point V _f depends of said maximum acceleration so as to be achievable by said drive motor 7,8.

More particularly, said parameter chosen as representative of the maximum acceleration _MAX admissible by the drive motor 7, 8 may be the pulsation ω of the third order filter F3, in the form of a so-called "calculated pulsation" pulse ω ₀ which will be determined in particular according to said maximum acceleration value permissible at _MAX .

The inventors have indeed established that there is a link between pulsation and maximum acceleration.

Indeed, we have seen that the acceleration of the trolley is worth ${\dot{V}}_{\mathit{trol}}={\dot{V}}_f+\frac{\mathrm{The}}{g}{\stackrel{⃛}{V}}_f.$

Suppose that we apply at time t = 0 (initial moment), to a load suspended 1 at rest, that is to say to a system initially at equilibrium, a setpoint V _u of step type.

As the system is initially at equilibrium, it can then be considered that the acceleration of the suspended load 1 is initially zero, that is to say that, at time t = 0: V̇ _f ( 0) ≈ 0, because of the inertia, while the V̇ _trol acceleration of the carriage 5 is maximum at the same time t = 0, and is then $\frac{\mathrm{The}}{g}{\stackrel{⃛}{V}}_f\left(0\right)=\frac{\mathrm{The}}{g}{\omega }^3{V}_u.$

c'est-à-dire : $\omega \le {\left(\frac{a_{\mathit{MAX}}\times g}{V_u\times L}\right)}^{\frac{1}{3}}$

Stress No. 3 (acceleration limit) therefore imposes: $\frac{\mathrm{The}}{g}{\omega }^3{V}_u\le {\mathrm{at}}_{\mathit{MAX}}$

that is to say : $\omega \le {\left(\frac{{\mathrm{at}}_{\mathit{MAX}}\times g}{V_u\times \mathrm{The}}\right)}^{\frac{1}{3}}$

Therefore, the processing step (b) may therefore preferably comprise a sub-step (b1) for adjusting the pulsation of the third-order filter F3, during which the pulsation ω, ω _{0 of} said filter of the filter is calculated. third order F3 from a value a _MAX which is representative of the maximum acceleration that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended.

Moreover, and to the extent that the equation above also shows, as a consequence of the constraint No. 3 (acceleration limit), a link between the pulsation ω and the speed reference V _u , the step (b) processing will preferably comprise a sub-step (b1) for adjusting the pulsation ω of the third order filter F3, during which the third order filter's pulsation ω is adjusted, and more particularly the calculated pulsation ω ₀ , depending on the value of the control setpoint V _u , V _JOY applied by the driver of the hoist at time t considered.

More preferably, the value of the pulsation ω of the third order filter F3 is modified according to whether the control set point V _u , V _JOY is lower or on the contrary higher than a reference speed V _thresh which is defined from the value of maximum speed V _MAX that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended.

In practice, the pulsation ω will be varied so as to increase said pulsation ω and thus use a pulsation considered as high, called "high value" ω _high , and therefore a more reactive filter F3, when the absolute value of the pilot setpoint (that is to say the amplitude of the speed reference) V _u , V _JOY is low compared to the maximum permissible speed V _MAX , and decreasing on the contrary said pulsation ω in favor of a lower pulsation so-called "low value" ω _low , when the absolute value of the driving setpoint V _u , V _{JOY will} increase to approach the maximum permissible speed V _MAX .

In particular, when the speed reference corresponds to the maximum permissible speed: V _u = V _MAX , the constraint n ° 3 (acceleration limit) will impose: $\omega \le {\left(\frac{{\mathrm{at}}_{\mathit{MAX}}\times g}{V_{\mathit{MAX}}\times \mathrm{The}}\right)}^{\frac{1}{3}}$

• on choisit V_thresh = k*V_MAX, avec 0 < k <1, par exemple k = 0,5 ;
• si V_u ≤ V_thresh, alors on définit la pulsation calculée ω₀ comme ${\omega }_0={\omega }_{\mathit{high}}={\left(\frac{a_{\mathit{MAX}}\times g}{V_{\mathit{thresh}}\times \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}\right)}^{\frac{1}{3}},$
  
  formant ici une valeur haute ;
• si V_u > V_thresh, alors on définit la pulsation calculée ω₀ comme ${\omega }_0={\omega }_{\mathit{low}}={\left(\frac{a_{\mathit{MAX}}\times g}{V_{\mathit{MAX}}\times \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">L</figure-callout>}}\right)}^{\frac{1}{3}},$
  
  formant ici une valeur basse, car V_MAX > V_thresh, si bien que ω_low < ω_high ; avec :
  • V_u la consigne de pilotage (ici égale à la consigne de pilotage brute V_JOY), k un facteur de réglage choisi, compris entre 0 et 1,
  • L la longueur du câble de suspension 6 qui relie la charge suspendue 1 au point d'accroche H,
  • g la gravité (accélération de pesanteur),
  • V_MAX une valeur arbitraire (de réglage) que l'on considère comme représentative de la vitesse maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1 ; en pratique V_MAX sera arbitrairement choisie en fonction des caractéristiques de l'engin de levage 2, de la charge 1 prévue, et du moteur d'entraînement 7, 8 concerné, et pourra par exemple être égale à la valeur de vitesse maximale effective que le moteur d'entraînement 7, 8 est effectivement capable, d'après des essais, de conférer au chariot 5, ou bien, de préférence, être égale à une fraction (strictement inférieure à 100%, mais non nulle) de cette valeur de vitesse maximale effective ;
  • a_MAX une valeur arbitraire (de réglage) que l'on considère comme représentative de l'accélération maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1 ; a_MAX pourra par exemple être égale à la valeur maximale effective d'accélération du moteur, déterminée par des essais, ou bien, de préférence, être égale à une fraction (strictement inférieure à 100%, mais non nulle) de cette valeur maximale effective d'accélération.

In practice, in the light of the foregoing, and as illustrated in the figure 3 it is therefore possible, for example, to calculate the pulsation ω of the third order filter F3, during the sub-step (b1) of adjusting the pulsation of the third order filter, from a calculated pulse ω ₀ determined as follows:

• V _thresh = k * V _MAX is chosen, with 0 <k <1, for example k = 0.5;
• if V _u ≤ V _thresh , then we define the calculated pulsation ω ₀ as ${\omega }_0={\omega }_{\mathit{high}}={\left(\frac{{\mathrm{at}}_{\mathit{MAX}}\times g}{V_{\mathit{thresh}}\times \mathrm{The}}\right)}^{\frac{1}{3}},$
  
  forming here a high value;
• if V _u > V _thresh , then we define the calculated pulsation ω ₀ as ${\omega }_0={\omega }_{\mathit{low}}={\left(\frac{{\mathrm{at}}_{\mathit{MAX}}\times g}{V_{\mathit{MAX}}\times \mathrm{The}}\right)}^{\frac{1}{3}},$
  
  forming here a low value, because V _MAX > V _thresh , so that ω _low <ω _high ; with:
  • V _u the control setpoint (here equal to the raw control setpoint V _JOY ), k a selected adjustment factor, between 0 and 1,
  • L the length of the suspension cable 6 which connects the suspended load 1 to the point of attachment H ,
  • g gravity (gravitational acceleration),
  • V _MAX an arbitrary value (of adjustment) which is considered as representative of the maximum speed that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended; in practice V _MAX will be arbitrarily chosen according to the characteristics of the hoist 2, the load 1 provided, and the drive motor 7, 8 concerned, and may for example be equal to the maximum effective speed value that the drive motor 7, 8 is actually capable, according to tests, of conferring on the carriage 5, or, preferably, being equal to a fraction (strictly less than 100%, but not zero) of this value of maximum effective speed;
  • a _MAX an arbitrary value (of adjustment) which is considered as representative of the maximum acceleration that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended; a _MAX could for example be equal to the maximum effective value of acceleration of the motor, determined by tests, or, preferably, be equal to a fraction (strictly less than 100%, but not zero) of this maximum effective value acceleration.

The dual purpose of this adaptation (in real time) of the pulsation ω is to optimize the reactivity of the third order filter 3 (constraint No. 2) by increasing said pulsation ω when possible, because the response time of the filter F3 is inversely proportional to said pulsation ω (with the coefficients c ₁ , c ₂ chosen as indicated above, the response time at 5% is of the order of 4 / ω), while respecting the constraint No. 3 related not exceeding the maximum acceleration capacity of the drive motor 7, 8, which sets an allowable upper limit for said pulsation ω.

It will be noted moreover that whatever the law adopted to determine the pulsation ω, the use of an adjustable pulsation makes it possible to dynamically adjust the filter of the third order F3, and to integrate directly and intrinsically within said filter F3, particularly simple way, some of the constraints in particular the material capacities of speed and acceleration of the drive motors 7, 8.

The adjustment of the pulsation ω of the third order filter F3 can be achieved by any appropriate pulsation adjustment module 14, forming a computer comprising for example an electronic circuit or a suitable computer program.

Furthermore, the inventors have empirically found that, in order to avoid destabilizing the third order filter F3, especially during transitions between the high value ω _high and the low value ω _low , the (calculated) pulse ω, ω ₀ should be two once differentiable (in relation to time).

As such, the inventors have found that it was desirable to smooth the (calculated) pulsation ω, ω ₀ , in particular to ensure that its evolutions over time, and in particular the high value transitions ω _{high /} low value ω _low mentioned above, be continuous and twice differentiable.

Therefore, according to a preferred characteristic which may constitute an entire invention, during the sub-step (b1) of adjusting the pulsation ω of the third order filter F3, it is applied during the determination of the pulsation ω , and more particularly one applies to the calculated pulsation ω ₀ , a second order filter F2, so that the filter of the third order F3 uses as pulsation ω a filtered calculated pulse ω _F.

avec :

• ω₀ la pulsation calculée (dite aussi « pulsation-cible »), obtenue comme indiqué plus haut, avant filtrage du second ordre F2,
• ω_x la pulsation propre du filtre du second ordre F2, par exemple égale à 4 rad/s,
• m le coefficient d'amortissement du filtre du second ordre F2, de préférence égal à 0,7 (ce choix de valeur permettant d'obtenir un bon compromis entre temps de réponse faible et dépassement limité du filtre du second ordre).

Said filtered calculated pulsation ω _F is thus preferentially defined as: $${\omega }_F\left(p\right)=\frac{1}{1+2m\frac{p}{{\omega }_X}+\frac{{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="imgf0001.png"\; state="\{\{state\}\}">p</figure-callout>}}^2}{{\mathrm{<figure-callout\; id="2"\; label="\omega \; X"\; filenames="imgf0001.png"\; state="\{\{state\}\}">\omega \; </figure-callout>}}_X{}^2}}{\omega }_0\left(p\right)$$

with:

• ω ₀ the calculated pulsation (also called "target pulsation"), obtained as indicated above, before filtering the second order F2,
• ω _x the proper pulsation of the second-order filter F2, for example equal to 4 rad / s,
• m the damping coefficient of the second order filter F2, preferably equal to 0.7 (this choice of value makes it possible to obtain a good compromise between low response time and limited second order filter overflow).

c'est-à-dire $\omega \le {\left(\frac{a_{\mathit{MAX}}\times g}{V_u\times L}\right)}^{\frac{1}{3}}$

qui résulte de la contrainte n°3 (capacité limitée d'accélération) pourrait temporairement être violée.On the other hand, it will be noted that if the pulsation ω of the third order filter F3, and more particularly the filtered pulsation ω = ω _{F of} said third order filter F3, calculated as described above, varies continuously (i.e. say regularly, without discontinuity in the mathematical sense of the term) to converge to the calculated target-pulse ω ₀ , and more particularly to change continuously from the high value ω _high to the low value ω _low or vice versa, then, in absolute terms, There may be situations in which inequality $\frac{\mathrm{The}}{g}{\omega }^3{V}_u\le {\mathrm{at}}_{\mathit{MAX}},$

that is to say $\omega \le {\left(\frac{{\mathrm{at}}_{\mathit{MAX}}\times g}{V_u\times \mathrm{The}}\right)}^{\frac{1}{3}}$

resulting from constraint # 3 (limited acceleration capability) could be temporarily violated.

Indeed, suppose, for example, that we are initially in a situation in which the driver of the machine does not request little or no movement of the suspended load 1, so that the steering setpoint (in speed) V _u is low, or even zero, so that it is less than the reference speed: V _u <V _thresh , for example with V _u = 0 m / s.

The pulse ω, ω _F of the third order filter F3 is then close to, or equal to, its high value ω _high .

Suppose now that the driver of the machine suddenly applies a speed reference V _u of high amplitude, higher than the reference speed V _thresh , and for example close to the maximum permissible speed: V _u = V _MAX . In practice, this amounts to applying to the control system a step according to which the driver passes almost instantaneously the driving instruction V _u from its initial low value, or even zero (typically 0 m / s) to a high value, typically V _MAX .

Since the setpoint V _u = V _MAX now exceeds the V _thresh reference _speed , the automatic adjustment of the third order filter's pulsation, according to the substep (b1), redefines the target pulsation value w ₀ , and in that 'instance lowers it to the low value: ω ₀ = ω _low .

However, because of the second order filtering F2 which is applied to obtain the filtered pulsation ω _F , as actually used by the third order filter F3, the transition of said filtered pulsation ω _F from its high value ω _high initial to its (new) low target value ω ₀ = ω _low is not instantaneous, but on the contrary relatively progressive, in that said transition (in this case, the decrease) of the pulsation is that is, the convergence of the filtered pulsation ω _F towards the low value ω _low can take place more slowly than the change (here the increase) of the control setpoint V _u , that is to say more slowly that the convergence of the control setpoint V _u to its high value V _MAX .

It will therefore be understood that during the short time that is necessary to adapt the pulse ω, ω _F of the third order filter F3 to the new setpoint V _u pilot can therefore temporarily be in a situation where coexist a steering setpoint close to its high value (V _u being substantially equal to V _MAX ) and a pulse ω, ω _F also close to its high value ω _high because said pulsation "delays" to decrease to reach its low value ω _low .

et pourrait ainsi temporairement excéder la capacité maximale d'accélération ${\mathrm{a}}_{\mathrm{MAX}}=\frac{L}{g}{\omega }_{\mathit{low}}{}^3{V}_{\mathit{MAX}}$

du moteur 7, 8, puisque ω_high > ω_low.In such a case, the acceleration requested from the carriage 5 would then be provisionally substantially equal to $\frac{\mathrm{The}}{g}{\omega }_{\mathit{high}}{}^3{V}_{\mathit{MAX}},$

and could thus temporarily exceed the maximum acceleration capacity ${\mathrm{at}}_{\mathrm{MAX}}=\frac{\mathrm{The}}{g}{\omega }_{\mathit{low}}{}^3{V}_{\mathit{MAX}}$

of the motor 7, 8, since ω _high > ω _low .

l'étape (b) de traitement comprend de préférence, selon une caractéristique qui peut constituer une invention à part entière, une sous-étape (b2) de saturation préliminaire, au cours de laquelle on applique à la consigne de pilotage V_u, V_JOY une première loi de saturation SAT1 qui est calculée en fonction de la pulsation ω, ω_F du filtre du troisième ordre F3 (c'est-à-dire en fonction de la valeur instantanée prise par la pulsation ω, ω_F du filtre du troisième ordre à l'instant considéré).This is why, in order to avoid such a situation, and more specifically to ensure that the inequality (imposed by the constraint n ° 3) is permanently satisfied: $\left|V_u\right|\le \frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}^{}}{\mathrm{at}}_{\mathit{MAX}},$

the treatment step (b) preferably comprises, according to a feature which may constitute a complete invention, a sub-step (b2) of preliminary saturation, during which the driving instruction V _u , V is applied to _JOY a first saturation law SAT1 which is calculated as a function of the pulsation ω, ω _F of the third order filter F3 (that is to say as a function of the instantaneous value taken by the pulsation ω, ω _F of the filter of the third order at the moment considered).

As illustrated in particular in the Figures 3 and 4 this first saturation law SAT1 can be implemented by a suitable first saturation module 15, forming a computer comprising, for example, an electronic circuit or a suitable computer program.

$$\mathit{SAT}1\left(V_u\right)=-\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}\mathrm{si}{V}_u<-\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}$$

$$\mathit{SAT}1\left(V_u\right)=+\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}\mathrm{si}{V}_u>\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}$$

avec

• V_u la consigne de pilotage (ici égale à la consigne de pilotage brute V_JOY),
• ω_F la pulsation (et plus particulièrement la pulsation filtrée) du filtre du troisième ordre F3,
• L la longueur du câble de suspension 6,
• g la gravité et
• a_MAX une valeur représentative de l'accélération maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1 (ladite valeur d'accélération maximale étant de préférence définie comme indiqué plus haut).

Preferably, the first saturation law SAT1 will be expressed by: $$\mathit{SAT}1\left(V_u\right)=V_u\mathrm{if}-\frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}\le V_u\le \frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}$$

$$\mathit{SAT}1\left(V_u\right)=-\frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}\mathrm{if}{V}_u<-\frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}$$

$$\mathit{SAT}1\left(V_u\right)=+\frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}\mathrm{if}{V}_u>\frac{\mathrm{<figure-callout\; id="3"\; label="g\; L\omega \; F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g\; </figure-callout>}}{{\mathit{L\omega }}_F}{\mathrm{at}}_{\mathit{MAX}}$$

with

• V _u the control setpoint (here equal to the raw control setpoint V _JOY ),
• ω _F the pulsation (and more particularly the filtered pulsation) of the third order filter F3,
• L the length of the suspension cable 6,
• g gravity and
• a _MAX represents a value representative of the maximum acceleration that the driving motor 7, 8 can give to the point of attachment H to which the suspension is suspended. load 1 (said maximum acceleration value being preferably defined as indicated above).

Preferably, as illustrated in the Figures 3 and 4 the first saturation law SAT1 is applied to the raw setpoint (in speed) V _JOY , before the third order filtering F3, so as to form (at the output of the first saturation module 15) the control setpoint V _u which is then sent to the third order filter F3.

peut dépasser la vitesse maximale admissible V_MAX, c'est-à-dire violer la contrainte n°4 (qui pose : |V_trol | ≤ V_MAX ), notamment si la consigne de pilotage V_u, et par conséquent la consigne de pilotage filtrée V_f qui en résulte, connaît des variations rapides, rapprochées dans le temps, et de forte amplitude.Moreover, in certain situations, when the length L of the suspension cable 6 is large, the execution instruction V _trol , and therefore the speed of the carriage 5, which is given by the conversion formula $V_{\mathit{trol}}=V_f+\frac{\mathrm{The}}{g}{\ddot{V}}_f,$

can exceed the maximum permissible speed V _MAX , that is to say violate the constraint n ° 4 (which poses: | V _trol | ≤ V _MAX ) , in particular if the control setpoint V _u , and consequently the instruction of Filtered driving V _f resulting, experiencing rapid variations, close together in time, and high amplitude.

The solution proposed by the inventors consists in limiting the execution setpoint V _trol when it reaches a predefined allowable limit (typically +/- V _MAX ), by suitably saturating the driving setpoint V _u .

The principle is to recalculate the control setpoint V _u when the execution instruction (and therefore the speed of the carriage 5) V _trol reaches the maximum permissible speed V _MAX , so that the absolute value of said execution instruction | V _trol | remains (at most) constant or even decreases; in other words, the control setpoint V _u is modified in order to cap the execution setpoint V _trol to its maximum allowable value V _MAX .

That is why the processing step (b) preferably comprises a sub-step (b3) of secondary saturation, which is intended to keep the execution instruction (ie the setpoint of speed of the point of attachment H ) V _trol when said performance instruction V _trol reaches substantially the maximum speed V _MAX that the drive motor 7, 8 can give to the point of attachment H (that is to say say in practice to the carriage 5).

et par conséquent ${\stackrel{⃛}{V}}_f=-\frac{g}{L}{\dot{V}}_f.$

Mathematically, if we want to keep the V _trol constant _setpoint , this amounts to asking V _trol = 0, so $0={\dot{V}}_{\mathit{trol}}={\dot{V}}_f+\frac{\mathrm{The}}{g}{\stackrel{⃛}{V}}_f,$

and therefore ${\stackrel{⃛}{V}}_f=-\frac{g}{\mathrm{The}}{\dot{V}}_f.$

• donc ${\stackrel{⃛}{V}}_f={\omega }_F{}^3\left(V_u-V_f-\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f-\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f\right)$
  
• alors ${\dot{V}}_{\mathit{trol}}=0\iff V_u=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$
  
• le second membre de la dernière équation étant noté, par commodité, $$\mathrm{E}\left(\mathrm{t}\right):E\left(t\right)=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$$
  

Since, in application of the third order filter F3, we have: $$V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f+\frac{1}{{\omega }_F{}^3}{\stackrel{⃛}{V}}_f=V_u$$

• so ${\stackrel{⃛}{V}}_f={\omega }_F{}^3\left(V_u-V_f-\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f-\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f\right)$
  
• so ${\dot{V}}_{\mathit{trol}}=0\iff V_u=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$
  
• the second member of the last equation being noted, for convenience, $$\mathrm{E}\left(\mathrm{t}\right):E\left(t\right)=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$$
  

As indicated above, it is sought to keep the constant V _trol performance _set constant or to decrease it when it reaches the maximum permissible speed V _max . In addition, in practice, if the driving setpoint V _u is small, this indicates in principle that we are looking for a trolley speed, therefore a V _trol , low execution instruction, that is to say that there is then no reason to keep said constant V _trol performance instruction at its maximum value V _MAX , but rather to decrease it.

et $$\mathit{SAT}2\left(V_u\right)=\mathit{MAX}\left(E\left(t\right),V_u\right){\mathrm{si\; V}}_{\mathrm{trol}}<0,$$

avec :

• V_u la consigne de pilotage (laquelle est de préférence issue du premier module de saturation 15, après avoir subi la première loi de saturation SAT1, comme indiqué sur la figure 4),
• V_trol la consigne d'exécution (vitesse de chariot), estimée ici par la formule de conversion : $V_{\mathit{trol}}=V_f+\frac{L}{g}{\ddot{V}}_f$
  
  V_f la consigne de pilotage filtrée issue du filtre du troisième ordre F3,
  et $E\left(t\right)=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$
  
  avec
  • c₁, c₂ les coefficients, respectivement du premier ordre et du second ordre, utilisés par le filtre du troisième ordre F3 (typiquement, on aura c₁ = 2,15 et c₂ = 1,75),
  • ω_F la pulsation (ici plus particulièrement la pulsation filtrée) du filtre du troisième ordre F3,
  • L la longueur du câble de suspension 6 qui relie la charge suspendue 1 au point d'accroche H,
  • g la gravité.

Therefore, during the secondary saturation sub-step (b3), therefore, a second saturation law SAT2 is preferably applied to the control setpoint V _u , according to a characteristic which may constitute a complete invention. which is expressed by: $$\mathit{SAT}2\left(V_u\right)=\mathit{MIN}\left(E\left(t\right),V_u\right){\mathrm{if\; V}}_{\mathrm{trol}}>0$$

and $$\mathit{SAT}2\left(V_u\right)=\mathit{MAX}\left(E\left(t\right),V_u\right){\mathrm{if\; V}}_{\mathrm{trol}}<0,$$

with:

• V _u the control setpoint (which is preferably derived from the first saturation module 15, after having undergone the first saturation law SAT1, as indicated on FIG. figure 4 )
• V _trol the execution instruction (trolley speed), estimated here by the conversion formula: $V_{\mathit{trol}}=V_f+\frac{\mathrm{The}}{g}{\ddot{V}}_f$
  
  V _f the filtered control setpoint from the third order filter F3,
  and $E\left(t\right)=V_f+\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f+\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$
  
  with
  • c ₁ , c ₂ the coefficients, respectively of the first order and of the second order, used by the filter of the third order F3 (typically, we will have c ₁ = 2.15 and c ₂ = 1.75),
  • ω _F the pulsation (here more particularly the filtered pulsation) of the third order filter F3,
  • L the length of the suspension cable 6 which connects the suspended load 1 to the point of attachment H ,
  • g gravity.

As illustrated in particular in the figure 4 this second saturation law SAT2 may be implemented by a suitable second saturation module 16, forming a computer comprising, for example, an electronic circuit or a suitable computer program.

It will be noted that, for the sake of stability, the activation and deactivation of this second saturation law SAT2, in the vicinity of the maximum permissible speed V _MAX , may preferably be effected by hysteresis switching.

More particularly, the second saturation law SAT2 being initially inactive, it will be activated when the execution instruction V _{trol will} reach and exceed a threshold of engagement, slightly higher than V _MAX , and for example set at 1.04 * V _MAX (which reinforces the interest of choosing V _MAX slightly below the true physical speed limit of the driving motor 7, 8 concerned, typically between 95% and 98% of said physical limit), and being of again deactivated when the execution setpoint V _trol falls below an extinction threshold strictly below the switch-on threshold, and equal for example 1.01 * V _MAX .

Furthermore, the inventors have found that, even if the implementation of the first saturation law SAT1 described above generally made it possible to satisfy the constraint No. 3 (acceleration of the carriage having to remain below the maximum acceleration allowed at _MAX ), some very particular combinations of piloting instructions could still take this constraint n ° 3 in default.

However, as indicated above, the application of a V _trol performance _instruction which does not respect the material limits, in particular the acceleration capacity, of the drive motors 7, 8, could lead to the execution of a motion not in accordance with the expected movement, and consequently the appearance of a dangling.

de la consigne de pilotage filtrée V_f une troisième loi de saturation SAT3 dont les seuils de saturation dépendent de l'accélération maximale a_MAX (typiquement telle que définie plus haut) que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1.This is particularly why, in order to secure the movement of the suspended load 1 and to guarantee the control and the precision of said movement, the step (b) of treatment preferably comprises, according to a characteristic which can constitute an invention in its own right. but which will preferably be implemented in addition to the first saturation law SAT1, a substep (b5) of saturation of the third derivative of the filtered control setpoint during which the third (temporal) derivative is applied ${\stackrel{⃛}{V}}_f$

the filtered control set V _f a third saturation law SAT3 whose saturation thresholds depend on the maximum acceleration a _MAX (typically as defined above) that the drive motor 7, 8 can confer at the point of hook H on which the load is suspended 1.

The implementation of this third saturation law SAT3 may advantageously add an additional precaution to that provided by the first saturation law SAT1, in order to optimize the security of the open-loop control according to the invention.

$$\mathrm{si}\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)\le {\stackrel{⃛}{V}}_f\le \frac{g}{L}\left(-{\dot{V}}_f+a_{\mathit{MAX}}\right),$$

$$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)\mathrm{si}{\stackrel{⃛}{V}}_f<\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)$$

et $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{L}\left(-{\dot{V}}_f+a_{\mathit{MAX}}\right)\mathrm{si}{\stackrel{⃛}{V}}_f>\frac{g}{L}\left(-{\dot{V}}_f+a_{\mathit{MAX}}\right)$$

avec :

• V_f la consigne de pilotage filtrée issue du filtre du troisième ordre F3,
• ω_F la pulsation (ici plus particulièrement la pulsation filtrée) du filtre du troisième ordre F3,
• c₁, c₂ les coefficients, respectivement du premier ordre et du second ordre, utilisés par le filtre du troisième ordre F3,
• L la longueur du câble de suspension 6 qui relie la charge suspendue 1 au point d'accroche H,
• g la gravité et
• a_MAX une valeur représentative de l'accélération maximale que le moteur d'entraînement 7, 8 peut conférer au point d'accroche H auquel est suspendue la charge 1, ladite valeur d'accélération maximale étant typiquement définie comme cela a été décrit plus haut.

More preferably, the third saturation law SAT3 can be expressed by: $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)={\omega }_{\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">F</figure-callout>}}{}^3\times \left(V_u-V_f-\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}{{\omega }_F}{\dot{V}}_f-\frac{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="imgf0001.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}{{\omega }_F{}^2}{\ddot{V}}_f\right)$$

$$\mathrm{if}\frac{g}{\mathrm{The}}\left(-{\dot{V}}_f-{\mathrm{at}}_{\mathit{MAX}}\right)\le {\stackrel{⃛}{V}}_f\le \frac{g}{\mathrm{The}}\left(-{\dot{V}}_f+{\mathrm{at}}_{\mathit{MAX}}\right),$$

$$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{\mathrm{The}}\left(-{\dot{V}}_f-{\mathrm{at}}_{\mathit{MAX}}\right)\mathrm{if}{\stackrel{⃛}{V}}_f<\frac{g}{\mathrm{The}}\left(-{\dot{V}}_f-{\mathrm{at}}_{\mathit{MAX}}\right)$$

and $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{\mathrm{The}}\left(-{\dot{V}}_f+{\mathrm{at}}_{\mathit{MAX}}\right)\mathrm{if}{\stackrel{⃛}{V}}_f>\frac{g}{\mathrm{The}}\left(-{\dot{V}}_f+{\mathrm{at}}_{\mathit{MAX}}\right)$$

with:

• V _f the filtered control setpoint from the third order filter F3,
• ω _F the pulsation (here more particularly the filtered pulsation) of the third order filter F3,
• c ₁ , c ₂ the coefficients, respectively of the first order and the second order, used by the third order filter F3,
• L the length of the suspension cable 6 which connects the suspended load 1 to the point of attachment H ,
• g gravity and
• a _MAX a value representative of the maximum acceleration that the driving motor 7, 8 can give to the point of attachment H to which the load 1 is suspended, said maximum acceleration value being typically defined as described above; .

As illustrated in particular in the figure 4 , the third saturation law SAT3 may be implemented by a third appropriate saturation module 17, forming a computer comprising for example an electronic circuit or a suitable computer program.

It will be noted that, advantageously, the reasoning and the equations proposed above are applicable if we consider the real situation, in three dimensions.

Indeed, if we consider the crane in a three-dimensional cartesian coordinate system (X, Y, Z), where Z represents the vertical axis, here confused with the mast 3, we can always write the law of Newton: M at _load = T + M g

et $\frac{P_{\mathit{trol}}{}^Y-P_{\mathit{load}}{}^Y}{L}=\frac{a_Y}{g-a_Z}$

avec a_X, a_Y et a_Z les L g-a_z L g-a_z composantes respectives en X, en Y et en Z de l'accélération de la charge suspendue 1.Assuming the small dangling angles, the X axis and the Y axis are respectively projected: $\frac{P_{\mathit{trol}}{}^X-P_{\mathit{load}}{}^X}{\mathrm{The}}=\frac{{\mathrm{at}}_X}{g-{\mathrm{at}}_Z}$

and $\frac{P_{\mathit{trol}}{}^Y-P_{\mathit{load}}{}^Y}{\mathrm{The}}=\frac{{\mathrm{at}}_Y}{g-{\mathrm{at}}_Z}$

with _X , _Y and _Z the L ga _z L ga _z respective components in X, Y and Z of the acceleration of the suspended load 1.

According to a first possibility of implementing the method according to the invention, it would be possible, in absolute terms, to keep, for the calculation of the execution instruction V _trol , and more particularly for the calculation of the Cartesian components V _trol ^X and V _trol ^Y of said execution instruction, expressions which show the vertical acceleration _Z of the suspended load 1, so as to also compensate for the potential effects of said vertical acceleration of the suspended load 1 on the generation of ballant .

However, according to a second preferred embodiment of the method according to the invention, it will be possible in practice to consider, by way of a simplifying hypothesis, that the acceleration of the load suspended at _Z is negligible with regard to the gravity g.

By simplifying the above expressions accordingly, we find: $$\frac{P_{\mathit{trol}}{}^X-P_{\mathit{load}}{}^X}{\mathrm{The}}\approx \frac{{\mathrm{at}}_X}{g}\mathrm{and}\frac{P_{\mathit{trol}}{}^Y-P_{\mathit{load}}{}^Y}{\mathrm{The}}\approx \frac{{\mathrm{at}}_Y}{g}.$$

Deriving (differentiating) then these expressions with respect to time, and considering, for realistic simplification, that the speed of variation dL / dt of the length L of the suspension cable 6 is negligible, we obtain: $$V_{\mathit{trol}}{}^X=V_{\mathit{load}}{}^X+\frac{\mathrm{The}}{\mathrm{<figure-callout\; id="2"\; label="g\; d"\; filenames="imgf0001.png"\; state="\{\{state\}\}">g\; </figure-callout>}}\frac{d^{}}{}\frac{{}^2}{{\mathit{dt}}^2}{V}_{\mathit{load}}{}^X\mathrm{and}{V}_{\mathit{trol}}{}^Y=V_{\mathit{load}}{}^Y+\frac{\mathrm{The}}{\mathrm{<figure-callout\; id="2"\; label="g\; d"\; filenames="imgf0001.png"\; state="\{\{state\}\}">g\; </figure-callout>}}\frac{d^{}}{}\frac{{}^2}{{\mathit{dt}}^2}{V}_{\mathit{load}}{}^Y$$

Furthermore, it will be noted that the method according to the invention is particularly versatile since it can be applied to any type of hoist 2, whatever the configuration of said hoist 2, insofar as said method advantageously allows in any case, to calculate the execution instruction V _trol in a simple way in a cartesian coordinate system, regardless of the coordinate system (Cartesian, cylindrical or spherical) specific to the hoist 2, in which is first expressed the driving instruction V _u , V _JOY when it is fixed by the driver of the machine, then in which the instruction V _trol must be expressed so that said execution instruction can be properly applied to driving motors 7, 8 concerned.

Indeed, it suffices first of all to convert into Cartesian coordinates, by means of a geometric transformation matrix (of the rotation matrix type), characteristic of the lifting gear 2 used, and which will be noted R _θ , the components of the control setpoint V _u , V _JOY initially expressed in the coordinate system specific to the hoist 2, then calculate the execution instruction V _trol in said Cartesian coordinate system, and finally to convert again , at by means of an inverse transformation matrix, which will be noted R- _θ , the Cartesian components of said V _trol performance _instruction in components expressed in the coordinate system specific to the lifting gear 2, applicable to 7, 8 which respectively manage the movement of said machine 2 (and more particularly of the carriage 5) according to each of said components.

Thus, in the case of a hoist 2 formed by a horizontal boom crane (tower crane with a horizontal boom), the most appropriate coordinate system of the machine 2 will be a cylindrical coordinate system in which the position of the considered object is marked by a radius r (along the arrow) and an azimuth angle θ (angle of lace around the axis of orientation), as shown on the figures 1 and 5 .

The control of the crane is carried out - in a fairly intuitive way for the driver - in distribution (modification of the radius r) and in orientation (modification of the azimuth θ), the driving setpoint V _u , V _JOY , as well as the execution instruction V _trol , will each comprise a distribution component, intended for the engine 7 distribution (which allows to act on the spoke) and an orientation component, for the motor 8 orientation (which allows to to act on the azimuth).

The first conversion (of the control setpoint V _u , V _JOY ) from the cylindrical system to the Cartesian system can be performed by means of a rotation matrix R _θ , while the second conversion (of the execution instruction V _trol ) from the Cartesian system to the cylindrical system can be operated by means of an inverse rotation matrix R- _θ .

Similarly, in the case of a hoist 2 formed by a luffing jib crane, the most appropriate coordinate system will be the spherical coordinate system, in which the position of the carriage 5 is located (and driven) by its azimuth (orientation of the luffing arrow in yaw), its declination (orientation of the luffing arrow in pitch) and its radius (distance from the carriage relative to the articulated base of the luffing jib).

Here again, the conversions to and from the Cartesian system will be performed by appropriate geometrical transformation matrices, so as to be able to manage the azimuth drive motor (yaw) of the arrow, the drive motor in declination (pitch) of the boom, and the drive motor on the spoke (translation along the arrow).

In the case of a hoist 2 of the traveling crane type, designed to perform linear movements of translation along an axis (X), or along two axes perpendicular to each other (X and Y), the instruction can be directly expressed in a Cartesian coordinate system (X, Y), and therefore will not require any coordinate conversion.

• la position de la charge suspendue 1 est donnée dans un système de coordonnées adapté à l'engin de levage 2, ici préférentiellement en coordonnées cylindriques : r_load, θ_load ;
• la consigne de pilotage (brute) V_JOY est exprimée par le conducteur de l'engin (via le joystick 11) sous forme d'une consigne de vitesse de charge suspendue V_load, dont les composantes correspondent au système de coordonnées considéré ; ici ladite consigne de vitesse de charge suspendue V_load, comprend (est décomposée en) une composante de vitesse de charge radiale souhaitée V_load ^r et une composante de vitesse de charge angulaire souhaitée V_load ^θ ;
• les composantes de la consigne de vitesse de charge suspendue V_load sont alors régularisées C³, et plus particulièrement filtrées à cet effet par le filtre du troisième ordre F3 ;
• ainsi, la première composante de la consigne de vitesse de charge suspendue, ici la composante de vitesse de charge radiale souhaitée V_load ^r, est régularisée C³, et plus particulièrement filtrée par le filtre du troisième ordre F3 (module de filtrage 12), pour obtenir une consigne de vitesse de charge radiale filtrée V_load ^rf (c'est-à-dire la première composante de la consigne de pilotage filtrée V_f) ;
• de même, la seconde composante de la consigne de vitesse de charge suspendue, ici la composante de vitesse de charge angulaire souhaitée V_load ^θ, est régularisée C³, et plus particulièrement est filtrée par le filtre du troisième ordre F3 (module de filtrage 12), pour obtenir une consigne de vitesse de charge angulaire filtrée, puis elle est multipliée par le rayon r_load, qui correspond à la distance à laquelle la charge suspendue 1 se trouve de l'axe de rotation vertical (ZZ'), de manière à obtenir une consigne de vitesse tangentielle (orthoradiale) filtrée V_load ^θf (c'est-à-dire la seconde composante de la consigne de pilotage filtrée V_f) ;
• la consigne de vitesse de charge filtrée (consigne de pilotage filtrée V_f), dont les composantes, ici radiale et tangentielle, sont désormais connues, est alors exprimée dans un repère cartésien en appliquant une matrice de transformation géométrique, ici la matrice de rotation R_θload qui correspond à la position angulaire en lacet θ_load de la charge suspendue 1 : (V_load ^Xf, V_load ^Yf) = R_θload (V_load ^rf, V_load ^θf) ;
• sur chaque axe X et Y dudit repère cartésien, on peut alors déterminer, grâce à la formule de conversion (module de conversion 13), la composante correspondante de la consigne d'exécution (consigne de vitesse de chariot) V_trol : V_trol ^X = V_load ^Xf + $\frac{L}{g}{\ddot{V}}_{\mathit{load}}{}^{\mathit{Xf}}$
  
  et $V_{\mathit{trol}}{}^Y=V_{\mathit{load}}{}^{\mathit{Yf}}+\frac{L}{g}{\ddot{V}}_{\mathit{load}}{}^{\mathit{Yf}};$
  
• la consigne d'exécution (consigne de vitesse de chariot) V_trol, disponible en coordonnées cartésiennes est alors exprimée dans le système de coordonnées adapté à l'engin de levage, en l'espèce en coordonnées cylindriques, en appliquant une matrice de transformation géométrique inverse, ici une matrice de rotation inverse R-_θtrol qui correspond à la position angulaire en lacet θ_trol du chariot 5 : (V_trol ^r, V_trol ^θ) = R-_θtrol (V_trol ^X, V_trol ^Y) ;
• les composantes de la consigne d'exécution V_trol sont alors appliquées chacune à leur moteur d'entraînement 7, 8 respectif; ainsi, la composante radiale V_trol ^r de la consigne d'exécution V_trol est alors appliquée au moteur de distribution 7,
• tandis que la composante tangentielle V_trol ^θ de ladite consigne d'exécution V_trol est convertie en consigne de vitesse angulaire de chariot, par multiplication par 1/r_trol, où r_trol représente la distance du chariot 5 à l'axe de rotation vertical (ZZ'), puis appliquée au moteur d'orientation (giration en lacet) 8.

In practice, and as illustrated in the figure 6 , the method according to the invention may therefore comprise successively the following operations:

• the position of the suspended load 1 is given in a coordinate system adapted to the hoist 2, here preferably in cylindrical coordinates: r _load , θ _load ;
• the driving instruction (gross) V _JOY is expressed by the driver of the machine (via the joystick 11) in the form of a suspended _load speed instruction V _load , the components of which correspond to the coordinate system considered; Here, said suspended _load speed setpoint V _load comprises (is decomposed into) a desired radial load speed component V _load ^r and a desired angular load speed component V _load ^θ ;
• the components of the suspended _load speed instruction V _load are then regularized C ³ , and more particularly filtered for this purpose by the third order filter F3;
• thus, the first component of the suspended charge speed instruction, here the desired radial load speed component V _load ^r , is regularized C ³ , and more particularly filtered by the third order filter F ³ (filter module 12), to obtain a filtered radial load speed reference V _load ^rf (that is to say the first component of the filtered control setpoint V _f );
• likewise, the second component of the suspended charge speed instruction, here the desired angular charge velocity component V _load ^θ , is regularized C ³ , and more particularly is filtered by the third order filter F3 (filter module 12 ), to obtain a filtered angular load speed instruction, then it is multiplied by the radius r _load , which corresponds to the distance at which the suspended load 1 is from the vertical axis of rotation (ZZ '), so obtaining a filtered (orthoradial) tangential velocity instruction V _load ^θf (that is to say the second component of the filtered control setpoint V _f );
• the filtered charge speed reference (filtered piloting setpoint V _f ), whose components, here radial and tangential, are now known, is then expressed in a Cartesian frame by applying a geometric transformation matrix, here the rotation matrix R _θload which corresponds to the angular position in yaw θ _load of the suspended load 1: (V _load ^Xf , V _load ^Yf ) = R _θload (V _load ^rf , V _load ^θf ) ;
• on each X and Y axis of said Cartesian coordinate system, it is then possible to determine, by means of the conversion formula (conversion module 13), the corresponding component of the execution instruction (trolley speed reference) V _trol : V _trol ^X = V _load ^Xf + $\frac{\mathrm{The}}{g}{\ddot{V}}_{\mathit{load}}{}^{\mathit{Xf}}$
  
  and $V_{\mathit{trol}}{}^Y=V_{\mathit{load}}{}^{\mathit{yf}}+\frac{\mathrm{The}}{g}{\ddot{V}}_{\mathit{load}}{}^{\mathit{yf}};$
  
• the execution instruction (trolley speed reference) V _trol , available in Cartesian coordinates is then expressed in the coordinate system adapted to the hoist, in this case in cylindrical coordinates, by applying a geometric transformation matrix inverse, here an inverse rotation matrix R- _θtrol which corresponds to the angular position in yaw θ _trol of the carriage 5: (V _trol ^r , V _trol ^θ ) = R- _θtrol (V _trol ^X , V _trol ^Y );
• the components of the V _trol instruction _set are then each applied to their respective drive motor 7, 8; thus, the radial component V _trol ^r of the execution instruction V _trol is then applied to the distribution motor 7,
• while the tangential component V _trol ^θ of said execution instruction V _trol is converted into trolley angular speed reference, by multiplication by 1 / r _trol , where r _trol represents the distance of the carriage 5 to the vertical axis of rotation (ZZ '), then applied to the orientation motor (yaw gyration) 8.

Note also that the cylindrical coordinates of the carriage 5 (point of attachment H ) can be easily known (in real time), for example by means of a part of an angular position sensor which provides information on the angular position in yaw of the arrow 4 with respect to the mast 3, that is to say on the angular position yaw θ _trol of the carriage 5, and secondly by means of a position sensor, for example associated with the engine d distribution drive 7, which makes it possible to know the position of the carriage 5 (in translation) along the arrow 4, and consequently the radial distance r _trol at which said carriage 5 is located on the vertical axis of rotation (ZZ ').

Similarly, the length L of the suspension cable 6 can be known in real time by means of a sensor measuring the absolute rotation of the winch or the hoisting motor which generates the winding of said suspension cable 6.

The angular position in yaw θ _load of the suspended load 1, as well as the (radial) distance r _load of said suspended load with respect to the vertical axis of gyration (ZZ ') can be estimated by integration (over time) of the components of the filtered control setpoint V _f , since said components respectively correspond to the filtered _load radial velocity V _load ^rf and the filtered _load angular velocity V _load ^θf .

Thus, more particularly, it will be possible to evaluate an estimated radial position r _load _ _estimate of the suspended load 1 as: $$r_{\mathit{load}\_\mathit{estimated}}\left(t\right)={\displaystyle {\int }_0^t{V}_{\mathit{load}}{}^{\mathit{rf}}\mathit{dt}+r_{\mathit{load}}\left(0\right)}$$

It will be noted in this respect that, when the hoist 2, and more particularly the suspended load 1, is at rest, so that said suspended load 1 hangs substantially vertically from the carriage 5, the angular position in yaw and the distance to the axis of gyration of the suspended load 1 are respectively identical to the angular position in yaw and the distance to the axis of gyration of the carriage 5, themselves measured as indicated above.

We can therefore set, as an initial condition (and thus as a calibration parameter) of the aforementioned integral computation: r _load (0) = r _trol (0), where "0" corresponds to an initial moment when the system is at rest .

If necessary, to improve the accuracy of the estimation of the radial position of the suspended load 1, it will be possible to use an observer (observation matrix) involving an additional measurement of the radial position of the carriage 5.

Furthermore, it will be noted that the regularization C ³ , and more particularly the third-order filtering F3, can be applied to a (single) characteristic movement of the hoist 2 (typically the gyration movement in orientation or the translation movement in distribution in the preferred example illustrated on the figures 1 and 6 ), that is to say to only one of the components of the control set V _u , V _JOY , or to several of said characteristic movements (that is to say to several of said components), or, preferably , all of said characteristic movements (that is to say all the components of the control set).

The invention furthermore relates, of course, as such to the use of a C ³ regularization, and more particularly to the use of a third order filter F ³ , and where appropriate, the use of one and / or the other saturation laws SAT1, SAT2, SAT3, in the determination of a V _trol execution _setpoint intended to be applied to a drive motor 7, 8 to move a load suspended 1 to a hoist 2, according to one or the other of the methods described in the foregoing.

As such, it should be noted that the invention as such relates to the implementation of a regularization C ³ , and more particularly to the implementation of the third order filter F ³ , respectively of all or some of the laws of saturation, regardless of the type of calculation used to determine the components of the V _trol execution _instruction .

Claims (14)

1. A method for controlling the displacement of a load (1) suspended to a point of attachment (H) of a lifting machine (2), said method comprising a piloting setpoint acquisition step (a), during which a setpoint called « piloting setpoint » (V_u) is acquired and which is representative of a displacement speed (V_load) that the operator of the lifting machine wishes to confer on the suspended load (1), then a processing step (b) during which a setpoint called « execution setpoint » (V_trol), which is intended to be applied to at least one drive motor (7, 8) in order to displace the suspended load (1), is elaborated from said piloting setpoint (V_u), the method being characterized in that the processing step (b) includes a C³ smoothing substep (b4) during which the piloting setpoint (V_u) is processed so as to confer to said piloting setpoint (V_u) properties of third differentiability with respect to time and continuity with respect to time, in order to generate, from said piloting setpoint (V_u), a filtered piloting setpoint (V_f) which is of class C³, then the execution setpoint (V_trol) is defined from said filtered piloting setpoint (V_f).
2. The method according to claim 1, characterized in that the execution setpoint (V_trol) expresses the speed setpoint that the point of attachment (H) must reach, and is defined as follows: $$V_{\mathit{trol}}=V_f+\frac{L}{g}{\ddot{V}}_f$$

   

   with:

   V_f the filtered piloting setpoint,

   L the length of the suspension cable (6) which links the suspended load (1) to the point of attachment (H),

   g gravity.
3. The method according to claim 1 or 2, characterized in that, during the C³ smoothing substep (b4), use is made, to generate the filtered piloting setpoint (V_f), of a parameter (ω, ω ₀) which is representative of the maximum acceleration (a_MAX) that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended, so that the execution setpoint (V_trol) which results from said filtered piloting setpoint (V_f) depends on said maximum acceleration so as to be achievable by said drive motor (7, 8).
4. The method according to any of the preceding claims, characterized in that, during the C³ smoothing substep (b4), a third-order filter (F3) is applied to the piloting setpoint (V_u) in order to generate the filtered piloting setpoint (V_f) which is of class C³.
5. The method according to claims 3 and 4, characterized in that the processing step (b) comprises a substep (b1) of setting the pulsation of the third-order filter (F3), during which the pulsation (ω, ω₀) of said third-orderfilter (F3) is calculated from a value (a_MAX) which is representative of the maximum acceleration that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended
6. The method according to claim 4 or 5, characterized in that the processing step (b) comprises a substep (b1) of setting the pulsation (ω, ω ₀ , ω_F ) of the third-order filter (F3), during which the pulsation (ω, ω ₀ , ω_F ) of the third-order filter (F3) is adapted according to the value of the piloting setpoint (V_u) applied by the operator of the lifting machine at the considered time, and more preferably the value of the pulsation (ω, ω ₀ , ω_F ) of the third-order filter (F3) is modified depending on whether the piloting setpoint (V_u) is lower or on the contrary higher than a reference speed (V_thresh) which is defined from the maximum speed value (V_MAX) that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended.
7. The method according to any of claims 4 to 6, characterized in that the processing step (b) comprises a substep (b1) of setting the pulsation of the third-order filter, during which the pulsation (ω) of the third-order filter (F3) is calculated from a calculated pulsation (ω ₀) determined as follows:

   we choose V_thresh = k * V_MAX, with 0<k<1, for example k=0.5;

   if V_u≤V_thresh, then we define the calculated pulsation (ω ₀) to a high value of $${\omega }_0={\omega }_{\mathit{high}}={\left(\frac{a_{\mathit{MAX}}\mathit{xg}}{V_{\mathit{thresh}}\mathit{xL}}\right)}^{\frac{1}{3}}$$

   

   if V_u>V_thresh, then we define the calculated pulsation (ω ₀) to a low value of $${\omega }_0={\omega }_{\mathit{low}}={\left(\frac{a_{\mathit{MAX}}\mathit{xg}}{V_{\mathit{MAX}}\mathit{xL}}\right)}^{\frac{1}{3}}$$

   

   with:

   V_u the piloting setpoint,

   L the length of the suspension cable (6) which links the suspended load (1) to the point of attachment (H),

   g gravity,

   V_MAX a value representative of the maximum speed that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended, and

   a_MAX a value representative of the maximum acceleration that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended.
8. The method according to claim 7, characterized in that, during the substep (b1) of setting the pulsation of the third-order filter (F3), a second-order filter (F2) is applied to the calculated value (ω, ω₀), so that the third-order filter uses a filtered calculated pulsation (ω_F ), said filtered calculated pulsation (ω_F ) thus being preferably defined as: $${\omega }_F\left(p\right)=\frac{1}{1+2m\frac{p}{{\omega }_X}+\frac{p^2}{{\omega }_X{}^2}}{\omega }_0\left(p\right)$$

   

   with:

   ω ₀ the calculated pulsation, before the second-order filtering (F2),

   ω_X the natural pulsation of the second-order filter (F2), for example equal to 4 rad/s,

   m the damping coefficient of the second-order filter (F2), preferably equal to 0.7.
9. The method according to any of claims 4 to 8, characterized in that the processing step (b) comprises a preliminary saturation substep (b2), during which a first saturation law (SAT1) is applied to the piloting setpoint (V_u) and which is calculated according to the pulsation (ω, ω_F ) of the third-order filter (F3).
10. The method according to claim 9, characterized in that the first saturation law (SAT1) is expressed by: $$\mathit{SAT}1\left(V_u\right)=V_u\mathrm{if}-\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}\le V_u\le \frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}$$

    

    $$\mathit{SAT}1\left(V_u\right)=-\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}\mathrm{if}{V}_u<-\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}$$

    

    $$\mathit{SAT}1\left(V_u\right)=+\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}\mathrm{if}{V}_u>\frac{g}{{\mathit{L\omega }}_F{}^3}{a}_{\mathit{MAX}}$$

    

    with

    V_u the piloting setpoint,

    ω_F the pulsation of the third-order filter (F3),

    L the length of the suspension cable (6) which links the suspended load (1) to the point of attachment (H),

    g gravity, and

    a_MAX a value representative of the maximum acceleration that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended.
11. The method according to any of the preceding claims, characterized in that the processing step (b) comprises a secondary saturation substep (b3), which is intended to maintain constant or to make the execution setpoint (V_trol) decrease when said execution setpoint substantially reaches the maximum speed (V_MAX) that the drive motor (7, 8) can confer to the point of attachment (H).
12. The method according to claims 11 and 4, characterized in that, during the secondary saturation substep (b3), as second saturation law (SAT2) is applied to the piloting setpoint (V_u) and is expressed by: $$\mathit{SAT}2\left(V_u\right)=\mathit{MIN}\left(E\left(t\right),V_u\right){\mathrm{if\; V}}_{\mathrm{trol}}>0,$$

    

    and $$\mathit{SAT}2\left(V_u\right)=\mathit{MAX}\left(E\left(t\right),V_u\right){\mathrm{if\; V}}_{\mathrm{trol}}<0,$$

    

    with:

    V_u the piloting setpoint

    V_trol the execution setpoint, estimated by: $V_{\mathit{trol}}=V_f+\frac{L}{g}{\ddot{V}}_f$

    

    V_f the filtered piloting setpoint coming from the third-order filter (F3), and $E\left(t\right)=V_f+\frac{c_1}{{\omega }_F}{\dot{V}}_f+\frac{c_2}{{\omega }_F{}^2}{\ddot{V}}_f-\frac{g}{{\mathit{L\omega }}_F{}^3}{\dot{V}}_f$

    

    with

    c₁, c₂ respectively the first-order and second-order coefficients, used by the third-order filter (F3),

    ω_F the pulsation of the third-order filter (F3),

    L the length of the suspension cable (6) which links the suspended load (1) to the point of attachment (H),

    g gravity.
13. The method according to any of the preceding claims, characterized in that the processing step (b) comprises a substep (b5) of saturation of the third derivative of the filtered piloting setpoint during which a third saturation law (SAT3) is applied to the third derivative $\left({\stackrel{⃛}{V}}_f\right)$

    

    of the filtered piloting setpoint (V_f) and whose saturation thresholds depend on the maximum acceleration (a_MAX) that the drive motor (7, 8) can confer to the point of attachment (H) of the suspended load (1).
14. The method according to claims 13 and 14, characterized in that the third saturation law (SAT3) is expressed by: $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)={\omega }_F{}^{3}x(V_u-V_f-\frac{c_1}{{\omega }_F}{\dot{V}}_f-\frac{c_2}{{\omega }_F{}^2}{\ddot{V}}_f$$

    

    $$\mathrm{if}\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)\le {\stackrel{⃛}{V}}_f\le \frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right),$$

    

    $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)\mathrm{if}\stackrel{⃛}{V}<\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right),$$

    

    and $$\mathit{SAT}3\left({\stackrel{⃛}{V}}_f\right)=\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)\mathrm{if}{\stackrel{⃛}{V}}_f>\frac{g}{L}\left(-{\dot{V}}_f-a_{\mathit{MAX}}\right)$$

    

    with

    V_f the filtered piloting setpoint coming from the third-order filter (F3),

    ω_F the pulsation of the third-order filter (F3),

    c₁, c₂ respectively the first-order and second-order coefficients, used by the third-order filter (F3),

    L the length of the suspension cable (6) which links the suspended load (1) to the point of attachment (H),

    g gravity, and

    a_MAX a value representative of the maximum acceleration that the drive motor (7, 8) can confer to the point of attachment (H) to which the load (1) is suspended.

Images