WO1992011117A1 - Method for controlling a motor-driven flexible mechanical system with variable configuration, such as a robot arm - Google Patents
Method for controlling a motor-driven flexible mechanical system with variable configuration, such as a robot arm Download PDFInfo
- Publication number
- WO1992011117A1 WO1992011117A1 PCT/FR1991/001044 FR9101044W WO9211117A1 WO 1992011117 A1 WO1992011117 A1 WO 1992011117A1 FR 9101044 W FR9101044 W FR 9101044W WO 9211117 A1 WO9211117 A1 WO 9211117A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- model
- components
- account
- trajectory
- control
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Ceased
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1635—Programme controls characterised by the control loop flexible-arm control
Definitions
- the invention relates to a method for controlling a flexible motorized mechanical system with variable configuration, of the type comprising at least one actuated actuator associated with at least one movable element to be displaced on a path in accordance with a setpoint.
- the invention applies in particular to all articulated and motorized mechanical systems, which are generally manipulators such as robots, cranes, overhead traveling cranes, solar panel orientation systems on satellite, etc.
- control means of these systems use control laws enabling the development of actuator control signals (such as electric motors and hydraulic cylinders) incorporated into these systems, from measurements of positions, speeds and / or accelerations of the moving elements of the systems.
- actuator control signals such as electric motors and hydraulic cylinders
- the invention aims to provide an effective solution to this problem. It relates to a method for controlling a flexible motorized system with variable configuration, allowing it to execute a movement or displacement instruction with maximum precision in minimum time.
- the invention provides a method for controlling a flexible motorized mechanical system with variable configuration, such as a robot arm for example, comprising at least one controlled actuator associated with at least one mobile element to be moved according to instructions of position and speed by means of a command taking into account deviations from these instructions, characterized in that it consists:
- This process makes it possible to define control laws which take account of the system's own flexibilities and to calculate in real time the commands of the actuators which make it possible to move the system over a determined trajectory without disturbing oscillations.
- this method consists, on the basis of the digital dynamic model of the system, of determining an optimal cinema of the mobile elements of the system, which takes account of the flexibilities of these elements, which is defined by positions, speeds and accelerations of these elements and which corresponds to the desired theoretical trajectory, then to determine ideal actions of the actuator or actuators corresponding to this optimal kinematics, in order to obtain the system control model.
- the method consists in taking into account any environmental constraints, such as example that obstacles placed on the trajectory, and to use a possible redundancy of the degrees of freedom of the components of the system to minimize a criterion of displacement such as time, an effort, a work, an energy or a combination time-effort for example .
- a verification of this choice can be carried out by a simulation, consisting in exciting the model of the open loop system and observing its response. According to another characteristic of
- control model is linearized at points on the trajectory, by mathematical calculation.
- the method consists in reducing in the linearized and simplified models, the number of variables characterizing flexibilities to the variables representing the vibrational modes. of the whole system. It suffices to keep in these models a summary of the overall vibrational behavior of the system, and not the detail of the origins of these vibrational modes.
- control laws of the system which are locally linear and of the state feedback type, can be defined by conventional control methods and include control gains associated with measurements of position deviations, displacement velocities, deformations and deformation velocities.
- the method then consists in calculating the values of these enslavement gains, in sampling the measurement signals supplied by the sensors, and to develop discrete real-time digital commands which are applied to the actuators at regular intervals, the order of magnitude of these intervals being a function of the dynamics of the actuators.
- this order of magnitude can range from milliseconds to tenths of a second.
- FIG. 1 is a theoretical representation of a very simple mechanical system to which the invention is applicable;
- Figure 2 is a more realistic representation of this system;
- Figure 3 is a flow diagram of the essential steps of the method according to the invention;
- FIG. 4 schematically represents a real mechanical system to which the invention has been applied;
- FIG. 5 is a graph representing the control and the displacement of this system as a function of time, according to a conventional control method;
- FIG. 6 is a graph representing the control and the displacement of this system as a function of time, in accordance with the invention.
- the system shown in FIG. 1 comprises a jack 10 whose cylinder 12 is fixed and whose piston rod 14 is connected to a load 16 to move it along the x axis of the piston rod 14.
- One or more caps - teurs not shown, make it possible to determine the posi ⁇ tion and possibly the speed of movement along the x axis.
- the classic law of servo-control of the jack 10 is written for example in the following way:
- the load oscillates more or less significantly when it reaches the end of the trajectory and that this oscillation is more or less rapidly, depending on the characteristics of the mechanical system and of the control. .
- This os ⁇ cillation is due in part to the lack of rigidity of the system, which has been shown schematically in a manner closer to reality in FIG. 2, in which an elastically deformable element 18 is interposed between the piston rod 14 of the cylinder 10 and the load 16.
- the presence of this element 18 schematically illustrates the ca ⁇ pacities of deformation and vibration of the system.
- the invention provides for taking these deformations into account by a control law which is of the following type:
- q (t) and q (t) are the amount of deformation and the rate of deformation of the element 18,
- K courseand Kg are the enslavement gains in deformation and speed of deformation.
- the amount of deformation and / or the rate of deformation of the element 18, or of the parameters depending on this amount or speed of deformation can be measured at any time by appropriate sensors, integrated into the mechanical system.
- FIG. 3 is a schematic flow diagram of the essential steps of the method according to the invention.
- the first step 20 of this process consists of a detailed and individual description of 'each component of the system, that is to say of all of its actuators, of all of its movable elements, as well as of their connections.
- This description also takes into account the uncontrolled external forces likely to act on the system (for example wind, gravity, etc.) as well as stiffness and concentrated damping, the characteristics of which are known.
- the description also takes into account the load to be transported, which can be defined directly or indirectly.
- the next step, represented in 22, will consist of a calculation of the vibratory modes of the components.
- these modes of components can be obtained by using conventional finite element modeling software, such as the code commercially available under the name "MSC NASTRAN”.
- the next step of the method according to the invention, represented in 24, consists in obtaining a digital dynamic model of the system: for this, the dynamic equations of the system in motion are established and resolved (taking into account its flexibility) to calculate generalized accelerations from which we can obtain by integrating velocities and positions of system components.
- Software which has been developed by the applicant and which is marketed under the name "ADAMEUS" can be used for this.
- the digital dynamic model thus obtained can itself be very complex when the controlled mechanical system is not extremely simple. It is therefore advantageous to reduce its complexity by retaining only the vibrational modes of the components which are sufficient to describe the behavior of the system. In practice, the vibration modes on which the actuators have no significant influence will not be modeled either.
- the method according to the invention then consists in establishing a system control model from this digital dynamic model, in the following manner:
- An optimal kinematics of the system are sought and determined (step 26), which takes account of the flexibility of the system and which is defined by numerical values of the positions, speeds and accelerations of the components of the system on a desired theoretical trajectory.
- This kinematics is optimized by taking into account any environmental constraints, such as obstacles placed on the trajectory, and by minimizing the work of the system on this trajectory, or by minimizing another criterion such as an effort, time, an energy or a time-effort combination, when a redundancy of the degrees of freedom presented by the components of the system allows this minimization.
- the flexibility characteristics of the elements of the system are taken into account as additional degrees of freedom of these elements, and are defined for each element individually and independently of the other elements.
- the effects of flexibilities elements on the kinematics can be corrected as if these elements were static.
- the next step 28 consists in defining the best forces and torques to be applied to the elements of the system, that is to say, the ideal actions of the actioners of the system, from the positions, speeds and acceleration determined in the previous step.
- M r or - M
- C, K are mass, damping, and stiffness matrices, respectively
- - the x, x, x are positions, speeds and linear accelerations
- - the ⁇ , ⁇ , ⁇ are positions, speeds and angular accelerations
- This linearization allows to move from a nonlinear system dynamics mechanical to a linear dynamic and is performed by numerical derivation.
- the next step of the process according to the invention designated by the reference 32 consists in simplifying and reduce these linearized control models to obtain control models that can be used by automated systems.
- This simplification and reduction step is based on the fact that the overall vibrational behavior of a mechanical system is a coupling of the elementary vibrational modes of the components of the system.
- the control model includes a summary of the overall vibrational behavior of the system. It is useless to know the detail and the origin of the elementary vi ⁇ bratory modes of the components.
- the simplified linear models obtained at the end of step 32 make it possible to define the position, speed and / or acceleration and deformation sensors which must be integrated into the mechanical system, as shown in 34 in the figure. 3, and also to define the control laws of this system, as indicated in 36.
- the control laws which are locally linear state returns can be designed using proven methods known to specialist technicians. They are for example of the following type: x c (t) - ⁇ (t) xenfin ( t ) " x ()
- K 2 , K 3 , K 4 are the enslavement gains.
- the enslavement gains K lf K 2 , K 3 , K 4 are calculated by traditional methods known to the specialized technician (pole placement, optimal control with quadratic criterion for example) and which are found for example in l by T. Kailath "Linear Systems" 1980, Prentice-Hall. This step is shown at 38.
- the control thus designed and calculated is then implemented in real time by means of a digital calculator.
- a sampling of the measurement signals supplied by the sensors is carried out as indicated in 40, and the corresponding values of these measurements are supplied to the digital computer which periodically develops digital commands possibly formatted and applied to the actuators as indicated in 42.
- the steps for sampling the signals from the sensors and the step for discretizing the digital computer vary according to the dynamics of the actuators. In practice, they range from a millisecond to a tenth of a second, in most cases.
- FIG. 4 There is shown schematically in FIG. 4 a mechanical system of a relatively simple type, which has was used by the applicant to apply the method according to the invention.
- This mechanical system essentially comprises a torsion rod 46, which is oriented vertically and which is rotated about its axis, at its upper end, by an electric gear motor 48. At its lower end, the torsion rod 46 is connected to one end of a bending arm 50 horizon ⁇ tal, the other end of which carries a load 52. Bearings 54 guide the torsion rod 46 in its rotational movement.
- the load 52 When the motor 48 is energized, the load 52 is moved in a horizontal plane in rotation around the axis of the rod 46, to pass from the angular position shown in solid lines to the angular position 52c or setpoint position shown in dotted lines.
- the angular speed of the load when it arrives in its set position must be zero.
- FIG. 6 represents the corresponding curves of displacement of the actuator and of the load when this mechanical system is controlled in accordance with the invention.
- the results are spectacular: the load 52, the movement of which is represented by the solid line curve 60, reaches the set position in approximately one second, without any oscillation, neither during its movement nor when the actuator is stopped.
- the curve 62 in dotted lines represents the movement of the actuator.
- the method according to the invention consisted in mechanically describing each constituent element of the system (motor 48, torsion rod 46, bending arm 50, connection between the rod 46 and the arm 50, load 52) in terms of mass, inertia, position of the center of gravity, and vibrational modes.
- the mechanical variables are the angle of rotation of the motor 48, the first mode of deformation ql of the torsion rod 46 about its axis, the first mode of deformation q2 of the bending arm 50 in a plane perpenicular to axis of the rod 46, and the useful torque supplied by the motor 48.
- the first vibration mode of the torsion rod 46 and the first vibration mode of the bending arm are sufficient to reconstitute the first vibration mode of the whole system which is by far preponderant.
- the process steps described with reference to FIG. 3 make it possible to obtain a control model which will describe the evolution of the rotation angle of the motor and of the first overall vibration mode of the system (coupled deformation of the torsion rod 46 and flexion arm 50) as a function of the useful torque supplied by the motor.
- the sensors integrated into the mechanical system of FIG. 4 are for example sensors 64 of the position and speed of the actuator, and sensors giving information on the overall deformation and the overall deformation rate of the system , for example by means of the acceleration of the load 52 by means of a sensor 66 integrated into this load.
- Position sensors angular sensors
- speed sensors gyrometers
- accelerometers gyrometers
- strain gauges etc.
- the invention makes it possible to increase the precision and the speed of movement of a mechanical system with variable configuration, to use greater deflections, to lighten the structures and to increase the payload. It also provides instant stabilization of the system.
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Feedback Control In General (AREA)
Abstract
Description
PROCEDE DE COMMANDE D'UN SYSTEME MECANIQUE FLEXIBLE MOTORISE A CONFIGURATION VARIABLE. TEL QU'UN BRAS ROBOT METHOD FOR CONTROLLING A FLEXIBLE MOTORIZED MECHANICAL SYSTEM WITH VARIABLE CONFIGURATION. SUCH AS A ROBOT ARM
PAR EXEMPLE. 'invention concerne un procédé de commande d'un système mécanique flexible motorisé à configuration variable, du type comprenant au moins un actionneur com¬ mandé associé à au moins un élément mobile à déplacer sur une trajectoire conformément à une consigne.FOR EXAMPLE. The invention relates to a method for controlling a flexible motorized mechanical system with variable configuration, of the type comprising at least one actuated actuator associated with at least one movable element to be displaced on a path in accordance with a setpoint.
L'invention s'applique notamment à tous les systèmes mécaniques articulés et motorisés, qui sont en général des manipulateurs tels que des robots, des grues, des ponts roulants, des systèmes d'orientation de pan¬ neaux solaires sur satellite, etc..The invention applies in particular to all articulated and motorized mechanical systems, which are generally manipulators such as robots, cranes, overhead traveling cranes, solar panel orientation systems on satellite, etc.
Les moyens de commande de ces systèmes utili- sent des lois d'asservissement permettant d'élaborer des signaux de commande des actionneurs (tels que des moteurs électriques et des vérins hydrauliques) incorporés à ces systèmes, à partir de mesures des positions, des vitesses et/ou des accélérations des éléments mobiles des sys- tè es.The control means of these systems use control laws enabling the development of actuator control signals (such as electric motors and hydraulic cylinders) incorporated into these systems, from measurements of positions, speeds and / or accelerations of the moving elements of the systems.
On constate toutefois en pratique que les dé¬ placements de ces systèmes s'accompagnent d'oscillations parasites qui perturbent leur bon fonctionnement, nuisent à la précision de leurs déplacements, et diminuent éven- tuellement leur durée de vie. On est alors conduit à li¬ miter leurs vitesses de déplacement, et/ou leurs accélé¬ rations, pour atténuer ces inconvénients.However, it has been observed in practice that the displacements of these systems are accompanied by parasitic oscillations which disturb their proper functioning, impair the precision of their movements, and possibly decrease their lifespan. We are then led to limit their travel speeds, and / or their accelerations, to mitigate these drawbacks.
De façon générale, il en résulte une diminu¬ tion certaine des performances des systèmes motorisés à configuration variable.In general, this results in a certain decrease in the performance of motorized systems with variable configuration.
Cette limitation des performances est due à un manque de rigidité générale de ces systèmes, qui affecte leurs éléments mobiles, les liaisons entre ces éléments et leurs actionneurs, les procédés classiques d'asservissement étant basés sur l'hypothèse d'une rigi¬ dité parfaite de ces composants.This limitation in performance is due to a general lack of rigidity in these systems, which affects their mobile elements, the connections between these elements and their actuators, conventional servo-control methods being based on the assumption of perfect rigidity. of these components.
L'invention a pour but d'apporter une solution efficace à ce problème. Elle a pour objet un procédé de commande d'un système flexible motorisé à configuration variable, per¬ mettant de lui faire exécuter une consigne de mouvement ou de déplacement avec une précision maximale dans un temps minimal.The invention aims to provide an effective solution to this problem. It relates to a method for controlling a flexible motorized system with variable configuration, allowing it to execute a movement or displacement instruction with maximum precision in minimum time.
Elle a également pour objet un procédé de ce type, qui permette d'éviter et/ou d'amortir pendant le mouvement toutes vibrations ou oscillations parasites dues à la flexibilité du système et causées par des accé- lerations et décélérations ou par des influences ex¬ térieures, sans diminuer pour autant la précision et la vitesse de déplacement.It also relates to a process of this type, which makes it possible to avoid and / or dampen during the movement any parasitic vibrations or oscillations due to the flexibility of the system and caused by accelerations and decelerations or by ex influences ¬ later, without reducing the accuracy and speed of movement.
L'invention propose à cet effet un procédé de commande d'un système mécanique flexible motorisé a configuration variable, tel qu'un bras robot par exemple, comprenant au moins un actionneur commandé associé à au moins un élément mobile à déplacer selon des consignes de position et de vitesse au moyen d'une commande prenant en compte des écarts par rapport a ces consignes, caracté- risé en ce qu'il consiste :To this end, the invention provides a method for controlling a flexible motorized mechanical system with variable configuration, such as a robot arm for example, comprising at least one controlled actuator associated with at least one mobile element to be moved according to instructions of position and speed by means of a command taking into account deviations from these instructions, characterized in that it consists:
- à décrire les composants du système en termes de géométrie, masse, inertie, position du centre de gravité, de forces et de couples auxquels sont soumis ces composants, et de modes vibratoires, - à établir et résoudre les équations dyna¬ miques du mouvement du système en tenant compte de sa flexibilité, pour obtenir un modèle dynamique numérique de ce système,- to describe the components of the system in terms of geometry, mass, inertia, position of the center of gravity, forces and torques to which these components are subjected, and of vibrational modes, - to establish and solve the dynamic equations of motion of the system taking into account its flexibility, to obtain a dynamic digital model of this system,
- à établir à partir de ce modèle dynamique numérique un modèle de commande de déplacement du système sur une trajectoire théorique désirée,- to establish from this digital dynamic model a model for controlling the movement of the system on a desired theoretical trajectory,
- à simplifier ce modèle de commande par li¬ néarisation de ses variables et diminution de leur nombre, pour obtenir des modèles linéarisés simplifiés centrés en des points de ladite trajectoire,to simplify this control model by liarization of its variables and reduction in their number, in order to obtain simplified linearized models centered at points of said trajectory,
- à définir à partir de ces modèles linéarisés simplifiés l'int αtion au système de capteurs de posi- tion, de vitesse et/ou d'accélération, fournissant des informations sur le mouvement et les déformations du sys¬ tème, et à définir également des lois adaptées d'asservissement du système, - puis, à partir de ces lois et de mesures réalisées au moyen des capteurs, à déterminer en temps réel les commandes appliquées à chaque actionneur, assu¬ rant l'exécution optimale des consignes par le système et compensant ou prévenant des oscillations perturbatrices de ce système.- to define from these simplified linearized models the int αtion to the system of position sensors tion, speed and / or acceleration, providing information on the movement and the deformations of the system, and also to define adapted laws for controlling the system, - then, from these laws and measurements carried out by means of the sensors, to determine in real time the commands applied to each actuator, ensuring the optimal execution of the instructions by the system and compensating or preventing disturbing oscillations of this system.
Ce procédé permet de définir des lois d'asservissement qui tiennent compte des flexibilités propres du système et de calculer en temps réel les com¬ mandes des actionneurs qui permettent de déplacer le sys- tème sur une trajectoire déterminée sans oscillations perturbatrices.This process makes it possible to define control laws which take account of the system's own flexibilities and to calculate in real time the commands of the actuators which make it possible to move the system over a determined trajectory without disturbing oscillations.
Les résultats obtenus sont remarquables : le système se comporte comme s'il était non susceptible de vibrer. Selon une autre caractéristique de l'invention, les flexibilités des composants du système sont prises en compte comme des degrés de liberté supplé¬ mentaires et sont définies pour chaque composant de façon individuelle et indépendante des autres composants. Selon une autre caractéristique de l'invention, ce procédé consiste, à partir du modèle dy¬ namique numérique du système, à déterminer une cinéma¬ tique optimale des éléments mobiles du système, qui tient compte des flexibilités de ces éléments, qui est définie par des positions, vitesses et accélérations de ces élé¬ ments et qui correspond à la trajectoire théorique dési¬ rée, puis à déterminer des actions idéales du ou des ac¬ tionneurs correspondant à cette cinématique optimale, pour obtenir le modèle de commande du système. Pour optimiser la cinématique des éléments mo¬ biles du système, le procédé consiste à prendre en compte d'éventuelles contraintes d'environnement, telles par exemple que des obstacles placés sur la trajectoire, et à utiliser une éventuelle redondance des degrés de liberté des composants du système pour minimiser un critère de déplacement tel que le temps, un effort, un travail, une énergie ou une combinaison temps-effort par exemple.The results obtained are remarkable: the system behaves as if it were not likely to vibrate. According to another characteristic of the invention, the flexibilities of the components of the system are taken into account as additional degrees of freedom and are defined for each component individually and independently of the other components. According to another characteristic of the invention, this method consists, on the basis of the digital dynamic model of the system, of determining an optimal cinema of the mobile elements of the system, which takes account of the flexibilities of these elements, which is defined by positions, speeds and accelerations of these elements and which corresponds to the desired theoretical trajectory, then to determine ideal actions of the actuator or actuators corresponding to this optimal kinematics, in order to obtain the system control model. To optimize the kinematics of the mobile elements of the system, the method consists in taking into account any environmental constraints, such as example that obstacles placed on the trajectory, and to use a possible redundancy of the degrees of freedom of the components of the system to minimize a criterion of displacement such as time, an effort, a work, an energy or a combination time-effort for example .
Pour réduire la complexité du modèle dynamique numérique du système et pour réduire également les temps de calcul, il est avantageux de ne prendre en compte que les modes vibratoires des composants qui sont suscep- tibles d'être excités lors de l'exécution de la consigne par le système.To reduce the complexity of the digital dynamic model of the system and also to reduce the calculation times, it is advantageous to take into account only the vibratory modes of the components which are likely to be excited during the execution of the setpoint. by the system.
Une vérification de ce choix peut être réali¬ sée par une simulation, consistant à exciter le modèle du système en boucle ouverte et à observer sa réponse. Selon une autre caractéristique deA verification of this choice can be carried out by a simulation, consisting in exciting the model of the open loop system and observing its response. According to another characteristic of
1'invention, le modèle de commande est linéarisé sur des points de la trajectoire, par calcul mathématique.Invention, the control model is linearized at points on the trajectory, by mathematical calculation.
Selon une autre caractéristique de l'invention, visant également à réduire la complexité et la durée des calculs, le procédé consiste à réduire dans les modèles linéarisés et simplifiés, le nombre de va¬ riables caractérisant des flexibilités aux variables re¬ présentatives des modes vibratoires d'ensemble du sys¬ tème. II suffit en effet de conserver dans ces mo¬ dèles une synthèse du comportement vibratoire d'ensemble du système, et non le détail des origines de ces modes vibratoires.According to another characteristic of the invention, also aiming at reducing the complexity and the duration of the calculations, the method consists in reducing in the linearized and simplified models, the number of variables characterizing flexibilities to the variables representing the vibrational modes. of the whole system. It suffices to keep in these models a summary of the overall vibrational behavior of the system, and not the detail of the origins of these vibrational modes.
Les lois d'asservissement du système qui sont localement linéaires et du type à retour d'état, peuvent être définies par des méthodes classiques d'asservissement et comprennent des gains d'asservissement associés à des mesures d'écarts de posi¬ tions, de vitesses de déplacement, de déformations et de vitesses de déformation.The control laws of the system which are locally linear and of the state feedback type, can be defined by conventional control methods and include control gains associated with measurements of position deviations, displacement velocities, deformations and deformation velocities.
Le procédé consiste alors à calculer les va¬ leurs de ces gains d'asservissement, à échantillonner les signaux de mesure fournis par les capteurs, et à élaborer en temps réel et de façon discrète des commandes numé¬ riques qui sont appliquées aux actionneurs à intervalles réguliers, l'ordre de grandeur de ces intervalles étant fonction des dynamiques des actionneurs.The method then consists in calculating the values of these enslavement gains, in sampling the measurement signals supplied by the sensors, and to develop discrete real-time digital commands which are applied to the actuators at regular intervals, the order of magnitude of these intervals being a function of the dynamics of the actuators.
En pratique, cet ordre de grandeur peut aller de la milliseconde au dixième de seconde.In practice, this order of magnitude can range from milliseconds to tenths of a second.
L'invention sera mieux comprise et d'autres caractéristiques, détails et avantages de celle-ci appa- raitront plus clairement à la lecture de la description qui suit, faite à titre d'exemple en référence aux des¬ sins annexés dans lesquels : la figure 1 est une représentation théorique d'un système mécanique très simple auquel l'invention est applicable; la figure 2 est une représentation plus réa¬ liste de ce système; la figure 3 est un organigramme des étapes es¬ sentielles du procédé selon l'invention; la figure 4 représente schématiquement un sys¬ tème mécanique réel auquel l'invention a été appliquée; la figure 5 est un graphe représentant la com¬ mande et le déplacement de ce système en fonction du temps, selon un procédé classique d'asservissement; la figure 6 est un graphe représentant la com¬ mande et le déplacement de ce système en fonction du temps, conformément à l'invention.The invention will be better understood and other characteristics, details and advantages thereof will appear more clearly on reading the description which follows, given by way of example with reference to the appended drawings in which: Figure 1 is a theoretical representation of a very simple mechanical system to which the invention is applicable; Figure 2 is a more realistic representation of this system; Figure 3 is a flow diagram of the essential steps of the method according to the invention; FIG. 4 schematically represents a real mechanical system to which the invention has been applied; FIG. 5 is a graph representing the control and the displacement of this system as a function of time, according to a conventional control method; FIG. 6 is a graph representing the control and the displacement of this system as a function of time, in accordance with the invention.
Pour mieux faire comprendre l'invention, on va tout d'abord décrire brièvement, en référence aux figures 1 et 2, les problèmes qu'elle est destinée à résoudre.To better understand the invention, we will first briefly describe, with reference to Figures 1 and 2, the problems it is intended to solve.
Le système représenté en figure 1 comprend un vérin 10 dont le cylindre 12 est fixe et dont la tige de piston 14 est reliée à une charge 16 pour la déplacer le long de l'axe x de la tige de piston 14. Un ou des cap- teurs, non représentés, permettent de déterminer la posi¬ tion et éventuellement la vitesse de déplacement le long de 1'axe x. La loi classique d'asservissement du vérin 10 s'écrit par exemple de la façon suivante :The system shown in FIG. 1 comprises a jack 10 whose cylinder 12 is fixed and whose piston rod 14 is connected to a load 16 to move it along the x axis of the piston rod 14. One or more caps - teurs, not shown, make it possible to determine the posi¬ tion and possibly the speed of movement along the x axis. The classic law of servo-control of the jack 10 is written for example in the following way:
U (t) = Kp [xc(t) - x(t)] + Kv [ x c(t) - x (t)] avec : U(t) = débit de fluide alimentant le vérin, xc(t),xc(t) = position et vitesse de consigne de la charge x(t),x (t) = position et vitesse de la charge au temps t, Kp, Kv = gains d'asservissement en position et en vitesse. On constate en pratique que la charge oscille de façon plus ou moins importante lorsqu'elle atteint la fin de la trajectoire et que cette oscillation est a or- tie plus ou moins rapidement, en fonction des caractéris¬ tiques du système mécanique et de la commande. Cette os¬ cillation est due pour partie au manque de rigidité du système, qui a été représenté schématique ent d'une façon plus proche de la réalité en figure 2, dans laquelle un élément elastiquement deformable 18 est interposé entre la tige de piston 14 du vérin 10 et la charge 16. La pré¬ sence de cet élément 18 illustre schématiquement les ca¬ pacités de déformation et de vibration du système.U (t) = Kp [x c (t) - x (t)] + Kv [x c (t) - x (t)] with: U (t) = flow rate of fluid supplying the cylinder, x c (t ), x c (t) = position and speed of the load x (t), x (t) = position and speed of the load at time t, K p , K v = servo gain in position and in speed. In practice, it can be seen that the load oscillates more or less significantly when it reaches the end of the trajectory and that this oscillation is more or less rapidly, depending on the characteristics of the mechanical system and of the control. . This os¬ cillation is due in part to the lack of rigidity of the system, which has been shown schematically in a manner closer to reality in FIG. 2, in which an elastically deformable element 18 is interposed between the piston rod 14 of the cylinder 10 and the load 16. The presence of this element 18 schematically illustrates the ca¬ pacities of deformation and vibration of the system.
L'invention prévoit de prendre en compte ces déformations par une loi d'asservissement qui est du type suivant :The invention provides for taking these deformations into account by a control law which is of the following type:
U(t) = Kp[xc(t) - x(t)] + Kv[xc(t) - x (t)] + Kg[qc - q(t)] +K [q c - q (t)] où : - U(t), xc(t), xc(t), x(t), x(t), Kp et Kv ont la même signification que précédemment,U (t) = Kp [x c (t) - x (t)] + K v [x c (t) - x (t)] + K g [q c - q (t)] + K [q c - q (t)] where: - U (t), x c (t), x c (t), x (t), x (t), Kp and K v have the same meaning as before,
- q(t) et q (t) sont la quantité de dé¬ formation et la vitesse de déformation de l'élément 18,q (t) and q (t) are the amount of deformation and the rate of deformation of the element 18,
- qc et q c sont la déformation et la vi¬ tesse de déformation de consigne (en général, qc = constante et q c = 0) . K„ et Kg sont les gains d'asservissement en déformation et vitesse de déforma¬ tion.- q c and q c are the deformation and the speed of setpoint deformation (in general, q c = constant and q c = 0). K „and Kg are the enslavement gains in deformation and speed of deformation.
La quantité de déformation et/ou la vitesse de déformation de l'élément 18, ou des paramètres fonctions de cette quantité ou vitesse de déformation, peuvent être mesurés à tout moment par des capteurs appropriés, inté¬ grés au système mécanique.The amount of deformation and / or the rate of deformation of the element 18, or of the parameters depending on this amount or speed of deformation, can be measured at any time by appropriate sensors, integrated into the mechanical system.
Par exemple, il est possible de mesurer, non pas la vitesse de déplacement de la charge et la vitesse de déformation de l'élément 18, mais l'accélération de la charge pour définir la commande à appliquer au vérin 10.For example, it is possible to measure, not the speed of displacement of the load and the speed of deformation of the element 18, but the acceleration of the load to define the command to be applied to the jack 10.
Comme on va le voir ci-dessous en référence à la figure 3, l'invention permet, à partir d'un modèle dy- namique numérique d'un système mécanique, de définir des lois d'asservissement et de calculer des gains d'asservissement permettant au système mécanique d'être déplacé sur une trajectoire de consigne dans un minimum de temps, sans oscillations ni vibrations parasites. La figure 3 est un organigramme schématique des étapes es¬ sentielles du procédé selon l'invention.As will be seen below with reference to FIG. 3, the invention makes it possible, from a digital dynamic model of a mechanical system, to define control laws and to calculate gains of servo allowing the mechanical system to be moved on a set path in a minimum of time, without oscillations or parasitic vibrations. Figure 3 is a schematic flow diagram of the essential steps of the method according to the invention.
La première étape 20 de ce procédé consiste en une description détaillée et individuelle de' chaque com¬ posant du système, c'est-à-dire de tous ses actionneurs, de tous ses éléments mobiles, ainsi que de leurs liai¬ sons.The first step 20 of this process consists of a detailed and individual description of 'each component of the system, that is to say of all of its actuators, of all of its movable elements, as well as of their connections.
Cette description est faite en termes de caractéristiques des actionneurs (notamment les fonctions définissant les forces ou les couples utiles fournis par les actionneurs), ainsi qu'en termes de géométrie (dimensions), de masse, d'inertie, et de position du centre de gravité de chacun des éléments composant le système, et de caractéristiques de leurs liaisons.This description is made in terms of characteristics of the actuators (in particular the functions defining the forces or useful torques provided by the actuators), as well as in terms of geometry (dimensions), mass, inertia, and position of the center. the severity of each of the elements making up the system, and the characteristics of their connections.
Cette description prend également en compte les forces extérieures non commandées susceptibles d'agir sur le système (par exemple le vent, la gravité, etc..) ainsi que des raideurs et amortissements concentrés dont on connaît les caractéristiques.This description also takes into account the uncontrolled external forces likely to act on the system (for example wind, gravity, etc.) as well as stiffness and concentrated damping, the characteristics of which are known.
La description prend aussi en compte la charge à transporter, qu'on peut définir de façon directe ou in- directe.The description also takes into account the load to be transported, which can be defined directly or indirectly.
L'étape suivante, représentée en 22, va consister en un calcul des modes vibratoires des compo¬ sants. De façon classique, on peut obtenir ces modes vi¬ bratoires des composants en utilisant un logiciel clas- sique de modélisation par éléments finis, tel que le code disponible dans le commerce sous la dénomination "MSC NASTRAN" .The next step, represented in 22, will consist of a calculation of the vibratory modes of the components. Conventionally, these modes of components can be obtained by using conventional finite element modeling software, such as the code commercially available under the name "MSC NASTRAN".
L'étape suivante du procédé selon l'invention, représentée en 24, consiste à obtenir un modèle dynamique numérique du système : pour cela, on établit et on résout les équa¬ tions dynamiques du système en mouvement (en tenant compte de sa flexibilité) pour calculer des accélérations généralisées à partir desquelles on peut obtenir par in- tegration des vitesses et des positions des composants du système. On peut utiliser pour cela un logiciel qui a été développé par la déposante et qui est commercialisé sous la dénomination "ADAMEUS".The next step of the method according to the invention, represented in 24, consists in obtaining a digital dynamic model of the system: for this, the dynamic equations of the system in motion are established and resolved (taking into account its flexibility) to calculate generalized accelerations from which we can obtain by integrating velocities and positions of system components. Software which has been developed by the applicant and which is marketed under the name "ADAMEUS" can be used for this.
Le modèle dynamique numérique ainsi obtenu peut être lui-même très complexe lorsque le système méca¬ nique commandé n'est pas extrêmement simple. Il est donc avantageux de réduire sa complexité en ne retenant que les modes vibratoires des composants qui suffisent à dé¬ crire le comportement du système. En pratique, on ne mo- delisera pas non plus les modes vibratoires sur lesquels les actionneurs n'ont pas d'influence significative.The digital dynamic model thus obtained can itself be very complex when the controlled mechanical system is not extremely simple. It is therefore advantageous to reduce its complexity by retaining only the vibrational modes of the components which are sufficient to describe the behavior of the system. In practice, the vibration modes on which the actuators have no significant influence will not be modeled either.
Cette sélection des modes vibratoires est à la portée du technicien spécialisé en mécanique et/ou en as¬ servissement qui pourrait si nécessaire se reporter à l'un ou l'autre des ouvrages suivants : "Mathematical Models of Flexible Spacecraft Dynamics" par P.Th.L.M. Van Woer om, (Proceedings of the 10th IFAC Symposium, Automatic Control in Space, Toulouse, France, Juin 1985 - Pergamon Press); "Controller réduction by modal cost. Analysis" par A.Youssouf et R.E. Skelton, (I.E.E.E. Trans. on Autom. Control, vol.AC29, N'6, pages 520-530); "Réduction of large flexible spacecraft models using internai balancing theory", par C.Z. Gregory Jr (Journal of Guidance, Vol.7, N*6, Nov-Dec.1984, pages 725-732), les contenus de ces ouvrages étant incorporés ici par ré¬ férence. Il est par ailleurs possible de vérifier par une simulation si le choix des modes vibratoires retenus est correct. On procède pour cela à une excitation en boucle ouverte du modèle du système, permettant de vérifier si la suppression des modes vibratoires non retenus affecte ou non le comportement d'ensemble du système. Le logiciel ".ADAMEUS" permet cette simulation.This selection of vibratory modes is within the reach of a technician specialized in mechanics and / or servicing, who could if necessary refer to one or the other of the following works: "Mathematical Models of Flexible Spacecraft Dynamics" by P. Th.LM Van Woer om, (Proceedings of the 10 th IFAC Symposium, Automatic Control in Space, Toulouse, France, June 1985 - Pergamon Press); "Controller reduction by modal cost. Analysis" by A.Youssouf and RE Skelton, (IEEE Trans. On Autom. Control, vol.AC29, N'6, pages 520-530); "Reduction of large flexible spacecraft models using internai balancing theory", by CZ Gregory Jr (Journal of Guidance, Vol.7, N * 6, Nov-Dec.1984, pages 725-732), the contents of these works being incorporated here by reference. It is also possible to verify by a simulation if the choice of the vibratory modes retained is correct. For this, an open loop excitation of the system model is carried out, making it possible to verify whether the suppression of the non-retained vibrational modes affects or not the overall behavior of the system. The ".ADAMEUS" software allows this simulation.
Le procédé selon l'invention consiste ensuite à établir un modèle de commande du système à partir de ce modèle dynamique numérique, de la façon suivante :The method according to the invention then consists in establishing a system control model from this digital dynamic model, in the following manner:
- on recherche et on détermine (étape 26) une cinématique optimale du système, qui tient compte de la flexibilité du système et qui est définie par des valeurs numériques des positions, vitesses et accélérations des composants du système sur une trajectoire théorique dési¬ rée. Cette cinématique est optimisée par prise en compte des contraintes éventuelles d'environnement, telles que des obstacles placés sur la trajectoire, et par une minimisâtion du travail du système sur cette trajectoire, ou par minimisation d'un autre critère tel qu'un effort, le temps, une énergie ou une combinaison temps-effort, lorsqu'une redondance des degrés de liberté présentés par les composants du système permet cette minimisation.- An optimal kinematics of the system are sought and determined (step 26), which takes account of the flexibility of the system and which is defined by numerical values of the positions, speeds and accelerations of the components of the system on a desired theoretical trajectory. This kinematics is optimized by taking into account any environmental constraints, such as obstacles placed on the trajectory, and by minimizing the work of the system on this trajectory, or by minimizing another criterion such as an effort, time, an energy or a time-effort combination, when a redundancy of the degrees of freedom presented by the components of the system allows this minimization.
Les caractéristiques de flexibilité des élé¬ ments du système sont prises en compte comme des degrés de liberté supplémentaires de ces éléments, et sont défi- nies pour chaque élément de façon individuelle et indé¬ pendante des autres éléments. Les effets des flexibilités des éléments sur la cinématique peuvent être corrigés comme si ces éléments étaient statiques.The flexibility characteristics of the elements of the system are taken into account as additional degrees of freedom of these elements, and are defined for each element individually and independently of the other elements. The effects of flexibilities elements on the kinematics can be corrected as if these elements were static.
- l'étape suivante 28 consiste à définir les meilleures forces et couples à appliquer aux éléments du système, c'est-à-dire, les actions idéales des action¬ neurs du système, à partir des positions, vitesses et ac¬ célérations déterminées dans 1'étape précédente.the next step 28 consists in defining the best forces and torques to be applied to the elements of the system, that is to say, the ideal actions of the actioners of the system, from the positions, speeds and acceleration determined in the previous step.
On obtient ainsi un modèle de commande de dé¬ placement du système sur une trajectoire désirée.This gives a control model for moving the system over a desired path.
Comme indiqué en 30, on procède ensuite à une linéarisation de ce modèle de commande en des points pré¬ déterminés de la trajectoire désirée. Cette linéarisation permet d'obtenir des modèles du second ordre, qui sont caractérisés par trois matrices de masse, d'amortissement et de raideur auxquelles on adjoint des raideurs et des amortissements artificiels par l'intermédiaire des com¬ mandes appliquées aux actionneurs. Ces modèles linéari¬ sés, valables chacun pour un point déterminé de la tra¬ jectoire, sont par exemple du type :As indicated in 30, a linearisation of this control model is then carried out at predetermined points on the desired trajectory. This linearization makes it possible to obtain second-order models, which are characterized by three matrices of mass, damping and stiffness to which are added stiffness and artificial damping by means of the commands applied to the actuators. These linear models, each valid for a determined point on the trajectory, are for example of the type:
M = r
- T est un vecteur de commande,- T is a control vector,
- les x, x, x sont des positions, vitesses et accélérations linéaires, - les θ, θ, θ sont des positions, vitesses et accélérations angulaires,- the x, x, x are positions, speeds and linear accelerations, - the θ, θ, θ are positions, speeds and angular accelerations,
- les q, q, q caractérisent les modes vibratoires des composants du système.- the q, q, q characterize the vibratory modes of the components of the system.
Cette linéarisation permet de passer d'une dy- namique non linéaire du système' mécanique à une dynamique linéaire et est réalisée par dérivation numérique.This linearization allows to move from a nonlinear system dynamics mechanical to a linear dynamic and is performed by numerical derivation.
L'étape suivante du procédé selon 1'invention désignée par la référence 32, consiste à simplifier et à réduire ces modèles de commande linéarisés pour obtenir des modèles de commande utilisables par des automati- ciens. Cette étape de simplification et de réduction est basée sur le fait que le comportement vibratoire d'ensemble d'un système mécanique est un couplage des modes vibratoires élémentaires des composants du système. Pour maîtriser le comportement d'ensemble du système, il suffit que le modèle de commande comprenne une synthèse du comportement vibratoire d'ensemble du système. Il est inutile de connaître le détail et l'origine des modes vi¬ bratoires élémentaires des composants. On passe donc des modèles linéarisés obtenus à l'issue de l'étape 30 à des modèles linéarisés simplifiés par remplacement des modes vibratoires des composants par des modes vibratoires d'ensemble lorsque cela est possible. Là également, il est à la portée du technicien spécialisé en asservisse¬ ment d'opérer une sélection parmi les modes vibratoires d'ensemble, pour ne retenir que ceux qui sont pré¬ pondérants. (Cette sélection de modes vibratoires d'ensemble faisant appel aux mêmes principes que ceux dé¬ crits dans les ouvrages de référence cités plus haut. )The next step of the process according to the invention designated by the reference 32, consists in simplifying and reduce these linearized control models to obtain control models that can be used by automated systems. This simplification and reduction step is based on the fact that the overall vibrational behavior of a mechanical system is a coupling of the elementary vibrational modes of the components of the system. To master the overall behavior of the system, it suffices that the control model includes a summary of the overall vibrational behavior of the system. It is useless to know the detail and the origin of the elementary vi¬ bratory modes of the components. We therefore go from the linearized models obtained at the end of step 30 to simplified linearized models by replacing the vibrational modes of the components with overall vibrational modes when possible. Here also, it is within the reach of the technician specialized in slaving to make a selection from among the overall vibratory modes, so as to retain only those which are predominant. (This selection of overall vibration modes using the same principles as those described in the reference works cited above.)
Les modèles linéaires simplifiés obtenus à l'issue de l'étape 32 permettent de définir les capteurs de position, de vitesse et/ou d'accélération et de défor- mation qu'il faut intégrer au système mécanique, comme indiqué en 34 en figure 3, et de définir également des lois d'asservissement de ce système, comme indiqué en 36. Les lois d'asservissement qui sont localement des retours d'état linéaires (pour des portions de la trajectoire ou en fonction de la configuration du système) , peuvent être conçues à partir de méthodes éprouvées, connues des tech¬ niciens spécialisés. Elles sont par exemple du type sui¬ vant : xc(t) - χ(t) x„(t) " x( ) The simplified linear models obtained at the end of step 32 make it possible to define the position, speed and / or acceleration and deformation sensors which must be integrated into the mechanical system, as shown in 34 in the figure. 3, and also to define the control laws of this system, as indicated in 36. The control laws which are locally linear state returns (for portions of the trajectory or according to the configuration of the system) can be designed using proven methods known to specialist technicians. They are for example of the following type: x c (t) - χ (t) x „ ( t ) " x ()
= K, + K* + K3 [qc-q(t)]= K, + K * + K 3 [q c -q (t)]
C θc(t) - θ(t) θc(t) - θ(t) + K4 [qc-q(t)] où : - F et C sont les forces linéaires et les couples fournis par les actionneurs,C θ c (t) - θ (t) θ c (t) - θ (t) + K 4 [q c -q (t)] where: - F and C are the linear forces and the torques provided by the actuators,
- x, xc, θ, θc, ont la même signification que précédemment, - g, qc caractérisent des modes vibratoires,- et leurs valeurs de consigne,- x, x c , θ, θ c , have the same meaning as before, - g, q c characterize vibratory modes, - and their set values,
- κ1#a K2, K3, K4 sont les gains d'asservissement. Les gains d'asservissement Klf K2, K3, K4 sont calculés par des méthodes traditionnelles connues du technicien spécialisé (placement de pôles, commande opti¬ male à critère quadratique par exemple) et que l'on trouve par exemple dans l'ouvrage de T. Kailath "Linear Systems"1980, Prentice-Hall. Cette étape est représentée en 38.- κ 1 # a K 2 , K 3 , K 4 are the enslavement gains. The enslavement gains K lf K 2 , K 3 , K 4 are calculated by traditional methods known to the specialized technician (pole placement, optimal control with quadratic criterion for example) and which are found for example in l by T. Kailath "Linear Systems" 1980, Prentice-Hall. This step is shown at 38.
Les lois de commande ci-dessus sont à temps continu. Il est cependant possible de transformer les mo¬ dèles linéarisés simplifiés en modèles à temps discret par des méthodes connues, pour obtenir des lois de com¬ mande à temps discret.The above control laws are continuous time. It is however possible to transform the simplified linearized models into discrete time models by known methods, in order to obtain laws of discrete time control.
L'asservissement ainsi conçu et calculé est alors mis en oeuvre en temps réel au moyen d'un calcula¬ teur numérique. Un échantillonnage des signaux de mesure fournis par les capteurs est réalisé comme indiqué en 40, et les valeurs correspondantes de ces mesures sont four¬ nies au calculateur numérique qui élabore périodiquement des commandes numériques éventuellement mises en forme et appliquées aux actionneurs comme indiqué en 42. Les pas d'échantillonnage des signaux des cap¬ teurs et le pas de discrétisation du calculateur numé¬ rique (période d'élaboration des commandes numériques destinées aux actionneurs) varient en fonction des dyna¬ miques des actionneurs. En pratique, ils vont de la mil- liseconde au dixième de seconde, dans la plupart des cas.The control thus designed and calculated is then implemented in real time by means of a digital calculator. A sampling of the measurement signals supplied by the sensors is carried out as indicated in 40, and the corresponding values of these measurements are supplied to the digital computer which periodically develops digital commands possibly formatted and applied to the actuators as indicated in 42. The steps for sampling the signals from the sensors and the step for discretizing the digital computer (period of development of the digital commands intended for the actuators) vary according to the dynamics of the actuators. In practice, they range from a millisecond to a tenth of a second, in most cases.
On a représenté schématiquement en figure 4 un système mécanique d'un type relativement simple, qui a été utilisé par la déposante pour appliquer le procédé selon 1'invention.There is shown schematically in FIG. 4 a mechanical system of a relatively simple type, which has was used by the applicant to apply the method according to the invention.
Ce système mécanique comprend essentiellement une tige de torsion 46, qui est orientée verticalement et qui est entraînée en rotation autour de son axe, à son extrémité supérieure, par un moto-réducteur électrique 48. A son extrémité inférieure, la tige de torsion 46 est reliée à une extrémité d'un bras de flexion 50 horizon¬ tal, dont l'autre extrémité porte une charge 52. Des pa- liers 54 guident la tige de torsion 46 dans son mouvement de rotation.This mechanical system essentially comprises a torsion rod 46, which is oriented vertically and which is rotated about its axis, at its upper end, by an electric gear motor 48. At its lower end, the torsion rod 46 is connected to one end of a bending arm 50 horizon¬ tal, the other end of which carries a load 52. Bearings 54 guide the torsion rod 46 in its rotational movement.
Lorsque le moteur 48 est excité, la charge 52 est déplacée dans un plan horizontal en rotation autour de l'axe de la tige 46, pour passer de la position angu- laire représentée en trait plein à la position angulaire 52c ou position de consigne représentée en trait poin¬ tillé. La vitesse angulaire de la charge à son arrivée dans sa position de consigne doit être nulle.When the motor 48 is energized, the load 52 is moved in a horizontal plane in rotation around the axis of the rod 46, to pass from the angular position shown in solid lines to the angular position 52c or setpoint position shown in dotted lines. The angular speed of the load when it arrives in its set position must be zero.
Lorsque le système est commandé par un asser- vissement classique prenant en compte uniquement la posi¬ tion et la vitesse angulaire du moteur (loi du type C(t)When the system is controlled by a conventional servo control taking into account only the position and the angular speed of the motor (law of type C (t)
= Kτ [θ(t)-θo] + K2 [θ(t)], θo étant la position angulaire de consigne et C(t) le couple fourni par le moteur), on obtient le déplacement angulaire représenté par la courbe en trait plein 56 de la figure 5, dans laquelle la courbe 58 en trait pointillé représente le mouvement de l'actionneur, c'est-à-dire la variation dans le temps de la position angulaire de l'arbre de sortie du moteur 48. On voit que cet arbre de sortie atteint très rapidement la position de consigne, en une seconde environ, alors que la charge 52 oscille largement autour de cette posi¬ tion de consigne, en raison de la torsion de la tige 46 et de la flexion du bras 50.= K τ [θ (t) -θo] + K 2 [θ (t)], θo being the set angular position and C (t) the torque supplied by the motor), we obtain the angular displacement represented by the curve in solid line 56 of FIG. 5, in which the curve 58 in dotted line represents the movement of the actuator, that is to say the variation over time of the angular position of the output shaft of the motor 48 We see that this output shaft very quickly reaches the set position, in about a second, while the load 52 oscillates widely around this set position, due to the torsion of the rod 46 and the bending arm 50.
La figure 6 représente les courbes correspon- dantes de déplacement de l'actionneur et de la charge lorsque ce système mécanique est commandé conformément à l'invention. Les résultats sont spectaculaires : la charge 52, dont le mouvement est représenté par la courbe en trait plein 60, atteint la position de consigne en un temps d'environ une seconde, sans aucune oscillation, ni pendant son mouvement, ni à l'arrêt de l'actionneur. La courbe 62 en trait pointillé représente le mouvement de 1'actionneur.FIG. 6 represents the corresponding curves of displacement of the actuator and of the load when this mechanical system is controlled in accordance with the invention. The results are spectacular: the load 52, the movement of which is represented by the solid line curve 60, reaches the set position in approximately one second, without any oscillation, neither during its movement nor when the actuator is stopped. The curve 62 in dotted lines represents the movement of the actuator.
Tout se passe comme si le système était non susceptible de vibrer.Everything happens as if the system was not likely to vibrate.
Dans le cas de cette application, le procédé selon l'invention a consisté à décrire mécaniquement chaque élément constitutif du système (moteur 48, tige de torsion 46, bras de flexion 50, liaison entre la tige 46 et le bras 50, charge 52) en termes de masse, d'inertie, de position du centre de gravité, et de modes vibra- toires. Les variables mécaniques sont l'angle de rotation du moteur 48, le premier mode de déformation ql de la tige de torsion 46 autour de son axe, le premier mode de déformation q2 du bras de flexion 50 dans un plan perpen¬ diculaire à l'axe de la tige 46, et le couple utile fourni par le moteur 48. Le premier mode vibratoire de la tige de torsion 46 et le premier mode vibratoire du bras de flexion sont suffisants pour reconstituer le premier mode vibratoire d'ensemble du système qui est de très loin prépondérant. Les étapes de procédé décrites en référence à la figure 3 permettent d'obtenir un modèle de commande qui va décrire l'évolution de l'angle de rotation du mo¬ teur et du premier mode vibratoire d'ensemble du système (déformation couplée de la tige de torsion 46 et du bras de flexion 50) en fonction du couple utile fourni par le moteur. Dans ce cas particulier, le modèle de commande est déjà du type linéaire du second ordre et se présente sous la forme suivante : θ + αè + βθ = γ C q + 2δ ω q + ω2q = ε C où : - α, β, γ traduisent l'influence d'un sys¬ tème non rigide sur l'entraînement moteur, - ω est la pulsation propre du mode vi¬ bratoire d'ensemble q,In the case of this application, the method according to the invention consisted in mechanically describing each constituent element of the system (motor 48, torsion rod 46, bending arm 50, connection between the rod 46 and the arm 50, load 52) in terms of mass, inertia, position of the center of gravity, and vibrational modes. The mechanical variables are the angle of rotation of the motor 48, the first mode of deformation ql of the torsion rod 46 about its axis, the first mode of deformation q2 of the bending arm 50 in a plane perpenicular to axis of the rod 46, and the useful torque supplied by the motor 48. The first vibration mode of the torsion rod 46 and the first vibration mode of the bending arm are sufficient to reconstitute the first vibration mode of the whole system which is by far preponderant. The process steps described with reference to FIG. 3 make it possible to obtain a control model which will describe the evolution of the rotation angle of the motor and of the first overall vibration mode of the system (coupled deformation of the torsion rod 46 and flexion arm 50) as a function of the useful torque supplied by the motor. In this particular case, the command model is already of the second order linear type and is presented in the following form: θ + αè + βθ = γ C q + 2δ ω q + ω 2 q = ε C where: - α, β, γ reflect the influence of a non-rigid system on the motor drive, - ω is the proper pulsation of the overall vi¬ bratory mode q,
- δ est son amortissement,- δ is its depreciation,
- ε représente 1'excitation de ce mode par le couple appliqué C,- ε represents the excitation of this mode by the applied torque C,
- θ est l'angle de rotation du moteur. L'asservissement s'écrit alors de la façon suivante :- θ is the angle of rotation of the motor. The servo is then written as follows:
C(t) = Kj_ [θ(t) - θ0] + K2 [è(t)] + K3 [q(tî] + K4 [q(t)] où θ0 est la position angulaire de la charge au point de consigne.C (t) = K j _ [θ (t) - θ 0 ] + K 2 [è (t)] + K 3 [q (tî] + K 4 [q (t)] where θ 0 is the angular position load to set point.
Les capteurs intégrés au système mécanique de la figure 4 sont par exemple des capteurs 64 de position et de vitesse de l'actionneur, et des capteurs donnant des informations sur la déformation d'ensemble et la vi¬ tesse de déformation d'ensemble du système, par exemple par l'intermédiaire de l'accélération de la charge 52 au moyen d'un capteur 66 intégré à cette charge. On peut utiliser pour cela des capteurs de position (capteurs an- gulaires) , des capteurs de vitesse (gyrometres), des ac- céléromètres, des jauges de contrainte, etc..The sensors integrated into the mechanical system of FIG. 4 are for example sensors 64 of the position and speed of the actuator, and sensors giving information on the overall deformation and the overall deformation rate of the system , for example by means of the acceleration of the load 52 by means of a sensor 66 integrated into this load. Position sensors (angular sensors), speed sensors (gyrometers), accelerometers, strain gauges, etc. can be used for this.
Dans le système de la figure 4, on a utilisé un moteur à courant continu CE.M. PARVEX F12 M2 associé à une génératrice tachymétrique CE.M.- F9T et un réduc- teur au 1/130 pour entraîner une charge dont la masse est de 2,6 kg et l'inertie 0,3 kg.m2. Les premiers modes vi¬ bratoires de la tige de torsion, du bras de flexion et d'ensemble du système sont respectivement aux environs de 2Hz, 1Hz et 1,2Hz. Dans ce cas précis, les gains d'asservissement sont :In the system of Figure 4, a CE.M. DC motor was used. PARVEX F12 M2 associated with a CE.M.- F9T tachometer generator and a 1/130 reducer to drive a load whose mass is 2.6 kg and the inertia 0.3 kg.m 2 . The first modes of vibration of the torsion rod, of the flexion arm and of the system as a whole are respectively around 2 Hz, 1 Hz and 1.2 Hz. In this specific case, the enslavement gains are:
K-i≈ 13,8 V/rad K3= - 60,3 V/rad K2= - 0,576 V/rad.s-1 K4= 1,48 V/rad.s-1 Les variables nécessaires au calcul de l'asservissement ne peuvent en général être toutes direc- tement mesurées. Elles sont alors remplacées par leurs estimations qui sont obtenues au moyen de techniques traditionnelles dites de l'observateur, à partir des me- sures de paramètres effectivement disponibles et des mo¬ dèles linéarisés simplifiés du système.Ki≈ 13.8 V / rad K 3 = - 60.3 V / rad K 2 = - 0.576 V / rad.s -1 K 4 = 1.48 V / rad.s -1 The variables required to calculate l In general, all of the servo cannot be directly measured. They are then replaced by their estimates which are obtained by means of traditional techniques known as of the observer, from the safe parameters actually available and simplified linearized models of the system.
De façon générale, l'invention permet d'augmenter la précision et la vitesse de déplacement d'un système mécanique à configuration variable, d'utiliser des débattements plus importants, d'alléger les structures et d'augmenter la charge utile. Elle as¬ sure également une stabilisation instantanée du système.In general, the invention makes it possible to increase the precision and the speed of movement of a mechanical system with variable configuration, to use greater deflections, to lighten the structures and to increase the payload. It also provides instant stabilization of the system.
Elle s'applique aux systèmes existants sans modifications particulières de ces derniers, et permet la conception et la définition de nouveaux systèmes à per¬ formances exceptionnelles. It applies to existing systems without any particular modification of the latter, and allows the design and definition of new systems with exceptional performance.
Claims
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| FR9016092A FR2670705B1 (en) | 1990-12-21 | 1990-12-21 | METHOD AND CONTROL OF A FLEXIBLE MOTORIZED MECHANICAL SYSTEM WITH VARIABLE CONFIGURATION, SUCH AS A ROBOT ARM FOR EXAMPLE. |
| FR90/16092 | 1990-12-21 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| WO1992011117A1 true WO1992011117A1 (en) | 1992-07-09 |
Family
ID=9403526
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/FR1991/001044 Ceased WO1992011117A1 (en) | 1990-12-21 | 1991-12-20 | Method for controlling a motor-driven flexible mechanical system with variable configuration, such as a robot arm |
Country Status (2)
| Country | Link |
|---|---|
| FR (1) | FR2670705B1 (en) |
| WO (1) | WO1992011117A1 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110802602A (en) * | 2019-11-29 | 2020-02-18 | 东北大学 | Mechanical arm flexible joint pose transformation vibration suppression method based on PI control strategy |
| CN110977969A (en) * | 2019-11-29 | 2020-04-10 | 东北大学 | Resonance suppression method of flexible load servo drive system based on pose transformation of mechanical arm |
| CN111421530A (en) * | 2020-03-27 | 2020-07-17 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Rope-driven flexible manipulator microgravity experimental platform |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP4390415B2 (en) * | 1999-12-16 | 2009-12-24 | パナソニック株式会社 | Robot positioning control method and positioning control device |
| DE10016137C2 (en) * | 2000-03-31 | 2003-08-21 | Iveco Magirus | Drehleiter |
| DE10016136C2 (en) * | 2000-03-31 | 2003-08-21 | Iveco Magirus | Turntable ladder control |
| AT504536B1 (en) | 2006-10-30 | 2009-03-15 | Ehrenleitner Franz | METHOD FOR MOVING LOADS, TOOLS AND THE LIKE |
| ITUD20080057A1 (en) * | 2008-03-17 | 2009-09-18 | Cifa Spa | PROCEDURE FOR CHECKING THE VIBRATIONS OF AN ARTICULATED ARM FOR CONCRETE PUMPING AND ITS DEVICE |
| CN103092129B (en) * | 2013-01-29 | 2014-10-22 | 电子科技大学 | Predictive control method for complex digital control system |
| CN108789418B (en) * | 2018-08-03 | 2021-07-27 | 中国矿业大学 | Control method of flexible manipulator |
-
1990
- 1990-12-21 FR FR9016092A patent/FR2670705B1/en not_active Expired - Fee Related
-
1991
- 1991-12-20 WO PCT/FR1991/001044 patent/WO1992011117A1/en not_active Ceased
Non-Patent Citations (6)
| Title |
|---|
| IECON '90 16TH ANNUAL CONFERENCE OF IEEE INDUSTRIAL ELECTRONICS SOCIETY, PACIFIC GROVE, CALIFORNIA, US, 27-30 NOVEMBRE 1990 vol. 1, pages 273 - 278; ARAKAWA ATSUSHI & FUKUDA TOSHIO: 'Vibration Control of a Flexible Robotic Arm -- Experiments and Relationship between Sensitivity Analysis and H Control Method --' * |
| PROCEEDINGS OF THE 1989 AMERICAN CONTROL CONFERENCE, PITTSBURG, US, JUNE 21-23, 1989 vol. 3, pages 2352 - 2359; ASADA HARUHIDO & ZHENG-DONG MA: 'INVERSE DYNAMICS OF FLEXIBLE ROBOTS' * |
| PROCEEDINGS OF THE 28TH IEEE CONFERENCE ON DECISION AND CONTROL, TAMPA, FLORIDA, US, DECEMBER 13-15, 1989 vol. 3, pages 2141 - 2146; KANEKO JUNJI & KANO HIROYUKI: 'MODAL CONTROL OF FLEXIBLE ONE-LINK ARMS WITH RANDOM DISTURBANCES' * |
| PROCEEDINGS OF THE 29TH IEEE CONFERENCE ON DECISION AND CONTROL, HONOLULU, HAWAII, US, DECEMBER 5-7, 1990 vol. 4, pages 1995 - 2000; YURKOVITCH, HILLSLEY & TZES: 'IDENTIFICATION AND CONTROL FOR A MANIPULATOR WITH TWO FLEXIBLE LINKS' * |
| PROCEEDINGS OF THE 29TH IEEE CONFERENCE ON DECISION AND CONTROL, HONOLULU, HAWAII, US, DECEMBER 5-7, 1990 vol. 4, pages 2566 - 2567; GUANRONG CHEN: 'EXACT CLOSED-FORM OPTIMAL SOLUTION FOR CONSTRAINED TRAJECTORY CONTROL OF SINGLE LINK FLEXIBLE-JOINT MANIPULATOR' * |
| THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH vol. 6, no. 4, 1987, CAMBRIDGE, MA, US pages 3 - 19; DANIEL M. ROVNER & ROBERT H. CANNON JR: 'EXPERIMENTS TOWARD ON-LINE IDENTIFICATION AND CONTROL OF A VERY FLEXIBLE ONE-LINK MANIPULATOR' * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110802602A (en) * | 2019-11-29 | 2020-02-18 | 东北大学 | Mechanical arm flexible joint pose transformation vibration suppression method based on PI control strategy |
| CN110977969A (en) * | 2019-11-29 | 2020-04-10 | 东北大学 | Resonance suppression method of flexible load servo drive system based on pose transformation of mechanical arm |
| CN110802602B (en) * | 2019-11-29 | 2023-01-10 | 东北大学 | Mechanical arm flexible joint pose transformation vibration suppression method based on PI control strategy |
| CN111421530A (en) * | 2020-03-27 | 2020-07-17 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Rope-driven flexible manipulator microgravity experimental platform |
Also Published As
| Publication number | Publication date |
|---|---|
| FR2670705B1 (en) | 1993-04-09 |
| FR2670705A1 (en) | 1992-06-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP2569129B1 (en) | Method for controlling an automated work cell | |
| WO1992011117A1 (en) | Method for controlling a motor-driven flexible mechanical system with variable configuration, such as a robot arm | |
| JP4249902B2 (en) | Singularity avoidance in satellite attitude control | |
| CN106055753B (en) | The steering engine of electrohydraulic load simulator redundant force instructs Dynamic Compensation Control Method | |
| JP2005242794A (en) | Robot control apparatus and robot control method | |
| JP6305283B2 (en) | Power system control system | |
| EP0321579A1 (en) | Articulated robot controller | |
| CN105406797A (en) | Control device and speed reducer system | |
| WO2005062143A1 (en) | Method and device for controlling displacements of the movable part of a multiaxis robot | |
| CN112792813A (en) | Robot control method, control device and robot with automatic parameter optimization | |
| WO2017220900A1 (en) | Method for compensating for coriolis, centrifugal and gravitational couples in a movement simulator and system comprising a movement simulator | |
| CN106873383A (en) | A kind of On-Line Control Method for reducing industrial robot vibration | |
| FR3016872A1 (en) | ANTI-BALLING CONTROL METHOD WITH ADJUSTABLE ASSISTANCE FOR TRANSPORTING A SUSPENDED LOAD | |
| WO2009065808A1 (en) | Device and method for regulating the displacement of a suspended load | |
| De Luca | Flexible robots | |
| EP1894067A1 (en) | Device for automatically adjusting servo controls of a movement mechanical simulator and an associated device | |
| WO2020043851A1 (en) | Method for automatic load compensation for a cobot or an upper limb exoskeleton | |
| FR3031959A1 (en) | METHOD AND DEVICE FOR CONJUGATING CONTROL RODS | |
| JPH0991004A (en) | Method for estimating load weight | |
| CN111015661A (en) | Active vibration control method and system for flexible load of robot | |
| EP2741893B1 (en) | Method of controlling a machine with redundant parallel actuation, associated control device and machine | |
| Farah et al. | A model-based control law for vibration reduction of serial robots with flexible joints | |
| EP0085008A1 (en) | Analogous control system for servoloops controlling the rotational position of a motor with a variable inertial load | |
| Wu et al. | Control of hybrid machines with 2-DOF for trajectory tracking problems | |
| JPH10249763A (en) | Friction parameter control method for robot manipulator |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| AK | Designated states |
Kind code of ref document: A1 Designated state(s): BR CA JP KR US |
|
| AL | Designated countries for regional patents |
Kind code of ref document: A1 Designated state(s): AT BE CH DE DK ES FR GB GR IT LU MC NL SE |
|
| DFPE | Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101) | ||
| 122 | Ep: pct application non-entry in european phase | ||
| NENP | Non-entry into the national phase |
Ref country code: CA |