WO2001033304A2 - Systeme de regulation pour organes de commande electriques et procede de regulation de trajectoire - Google Patents

Systeme de regulation pour organes de commande electriques et procede de regulation de trajectoire Download PDF

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Publication number
WO2001033304A2
WO2001033304A2 PCT/EP2000/010530 EP0010530W WO0133304A2 WO 2001033304 A2 WO2001033304 A2 WO 2001033304A2 EP 0010530 W EP0010530 W EP 0010530W WO 0133304 A2 WO0133304 A2 WO 0133304A2
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Prior art keywords
control
signal
drive
vector
control amplifier
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PCT/EP2000/010530
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German (de)
English (en)
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WO2001033304A3 (fr
Inventor
Eugen Saffert
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Eugen Saffert
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Publication date
Application filed by Eugen Saffert filed Critical Eugen Saffert
Publication of WO2001033304A2 publication Critical patent/WO2001033304A2/fr
Publication of WO2001033304A3 publication Critical patent/WO2001033304A3/fr

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Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path

Definitions

  • the present invention relates to a control system for electric drives, with an observer, which receives a first drive output signal and a first drive input signal and outputs a first state change signal and a second state change signal; and with a first, a second and a third control amplifier, the output signals of which are combined to form the drive input signal.
  • the invention further relates to a method for path control of electric drives, which is used to control a drive in order to cause the drive to follow a predetermined movement path.
  • the control system according to the invention has the advantage that, due to the more detailed modeling of the drive system in the observer and the use of additional control elements, the kinematic parameters of the movement sequences can be calculated with high accuracy from the measured position, without additional sensors being required. It is particularly advantageous that the measurement data within the cascade control structure according to the invention are used to correct errors in the kinematic parameters of the motion sequence before significant path errors and unsynchronities occur.
  • the observer delivers two further control signals which describe the state parameters of an elastic system.
  • the observer delivers two further control signals which describe the state parameters of an elastic system.
  • it is not sufficient to consider them as a point load mass. Rather, most systems have to be as one Mass-spring combination are described to take into account the elastic properties of the system. The respective deformation path and the deformation speed of the spring element must therefore be included in a more precise regulation.
  • nominal values for the speed and the acceleration are additionally fed into the control system and processed there in the manner according to the invention. This makes it possible to pre-control the dynamics of the operating system.
  • a further modified embodiment of the control system enables the acceleration pre-control to compensate for centrifugal forces that occur during the control of the drive system.
  • the acceleration is pre-selected to suit the centrifugal forces that occur.
  • This control system is particularly useful when circles or circular path segments are to be traversed by the drive system.
  • the inventive method for path control can advantageously be used in such control systems but also in a large number of other control systems.
  • the path control is carried out by transforming the control deviation into a co-moving coordinate system, as a result of which the manipulated variable vector can be determined particularly easily. After the control system vector has been determined by the control system, it is finally transformed back into the fixed coordinate system of the drive system.
  • FIG. 1 is a block diagram showing the general structure of a so-called observer in connection with a real system according to the prior art
  • Fig. 2 is a block diagram showing the general structure of an incremental state control according to the prior art
  • FIG. 3 shows a block diagram which represents a control system according to the invention in accordance with a first embodiment
  • FIG. 4 shows a block diagram of a second embodiment of the control system, in which the pilot control of the dynamics of the drive system is additionally possible;
  • FIG. 5 shows three diagrams which characterize the behavior of a drive system which is controlled without and with the control system according to FIG. 4;
  • FIG. 6 shows a block diagram of a modified embodiment of the control system, which is particularly suitable for controlling elastic systems
  • FIG. 7 shows a model representation of an elastic drive system for which the control system according to FIG. 6 can be used
  • FIG. 10 shows a block diagram of a control system which carries out the path control according to the invention
  • FIG. 11 is a schematic diagram of the course of the path control during the movement along a circular arc segment.
  • FIG. 1 shows a block diagram of a combination between a system to be controlled and a so-called observer, as is known from the prior art.
  • the system is a drive system, in particular an electric drive, and the movements carried out by the drive are understood as changes in the state of the system.
  • the measurable output variables of the system must be predicted in the control system (for example by means of a suitable calculation) and then compared with the actually measured output variables. In this way, an error is determined, which is then introduced into the control system as correction term K in order to reduce the error by taking this correction term into account.
  • the system shown in FIG. 1 can be defined mathematically by a discrete-time state space description as follows:
  • x x vector of the (fixed) xy coordinate system
  • y y vector of the (fixed) xy coordinate system
  • z z vector (direction vector) of the (moving) ze coordinate system
  • e e- Vector (deviation vector) of the (moving) ze coordinate system
  • the input variables are specified as vectors and the parameters of the system are represented by system matrices.
  • the estimated values A *, B * and C * which represent the system matrices A, B and C with certain deviations, must be determined and a correction vector K must also be determined.
  • the details of the construction and use of such an observer are known from the prior art, so that no further explanations are given here.
  • the state variables in the modeling on which the observer is based are selected so that they correspond to the auxiliary control variables to be influenced later by the control.
  • the rate of deformation and elasticity it is helpful to use the rate of deformation and elasticity as a state variable instead of the motor speed and position.
  • FIG. 2 shows a block diagram of an incremental state control according to the prior art, which uses an observer.
  • the general control problem is to have the position s (t) as a function of time follow a given function w (t).
  • the function w (t) is not explicitly specified but defined via the following constraints:
  • ⁇ r, max In a practical application, for example, a laser tool should travel along a piece of material at a certain speed in order to carry out corresponding machining operations (for example cutting, welding).
  • the specified control problem is solved in that, in a first step, the function w (t) is calculated by a so-called setpoint or path generator by solving the inverse kinematics. The controller used then has to carry out a follow-up control in order to implement the desired movement path through the drive system.
  • k M is the motor constant and i is the motor current.
  • the modeled system thus has the two states of speed v and position s.
  • the state vector v in the incremental state control known per se, the state vector v. but its change v ⁇ - V k-1
  • ⁇ k x ⁇ - X k-1 k-1 used.
  • ⁇ k i k - i k _ ! and ⁇ y k can be used.
  • An observer 1 receives two signals du and dy from two differentiating units 2.
  • observer 1 determines the corresponding change in state, which is output as acceleration signal a and speed signal v.
  • a first difference generator 3 forms a difference signal from the input variables y and w and outputs this difference signal to a first control amplifier 4.
  • the output signals of the observer v and a are sent to a second control amplifier 5 and a third control amplifier 6, respectively, the three control amplifiers 4, 5 and 6 delivering their output signals to a summer 7.
  • the difference generator 3, the control amplifiers 4, 5, 6 and the summer 7 implement the following controller equation in this circuit structure:
  • the first summer 7 supplies its output signal to a second summer 8, which as the further input signal
  • u k u k-1 + ⁇ u k under the constraint
  • FIG. 3 shows a block diagram of a control system according to the invention, which can also be referred to as virtual cascade control.
  • the elements that are already known from the block diagram shown in FIG. 2 have been given the same reference numerals.
  • the observer 1 does not deliver the output signals corresponding to the speed and the acceleration directly to the control amplifiers, but rather to a second difference former 11 (ev) or a third difference former 12 (ea).
  • the totalizer has been omitted since the control amplifiers are cascaded.
  • the signs of the inputs were interchanged, so that the latter now supplies the position error (ey) with a changed sign. The changed signs are taken into account by the newly inserted second and third difference formers 11, 12.
  • the first control amplifier 4 (ky) delivers an amplified position error which corresponds to a target speed vsoll.
  • the second control amplifier 6 (kv) delivers an amplified speed error, which corresponds to a target acceleration asoll and the third control amplifier 6 (ka) supplies the amplified acceleration error, which corresponds to the target pressure rsoll, ie the target change in acceleration.
  • the auxiliary variables of the control cascade a and v are provided by the observer, ie virtually.
  • the amplification factors of the three control amplifiers 4, 5, 6 have been designated in the block diagram shown for clarity with the quantities which they amplify. The following relationships apply:
  • a second limiter 13 receives the signal from the first control amplifier 4
  • a third limiter 14 receives the signal from the second control amplifier 5
  • a fourth limiter 15 receives the signal from the third control amplifier 6.
  • the limiters 13, 14 , 15 ensure that the setpoints supplied by the control amplifiers and thus the corresponding variables themselves comply with the constraints (see above).
  • FIG. 4 shows a block diagram of a modified embodiment of the control system according to the invention, which additionally has the possibility of a pilot control.
  • a pilot control current for the acceleration can be determined from the target acceleration a So ⁇ as follows:
  • Such a feedforward control is useful, for example, with regard to radial acceleration if the drive system is to perform circular trajectories.
  • the control loop must generate radial acceleration, although on the other hand the aim is for both the radial error and the radial speed to be zero. The following applies:
  • Acceleration pre-control is particularly useful if the path control according to the invention, which is shown in more detail below, is also used.
  • FIG. 5 shows three diagrams which illustrate the effect of the use of an additional pilot control according to the block diagram shown in FIG. 4 on the size of the following error.
  • Diagram a) shows the function of the position over time, the characteristic curve 20 indicating the course of the calculated target value, while the characteristic curve 21 represents the course of the position actually assumed by the drive system.
  • the amount of the following error is also shown by an auxiliary line 22, which results from the distance between the calculated target value and the position assumed at a certain point in time. It can be seen that the following error can amount to up to 30% of the total travel.
  • the following error is entered as a function of time when speed pre-control is carried out.
  • diagram c) the following error is again entered as a function of time, provided that a speed and an acceleration pre-control are fed into the control system. As can be seen from the diagram values, the following error is reduced to about 0.05% of the travel.
  • FIG. 6 shows the block diagram of a further embodiment of the control system.
  • the control system already explained in its basic structure was expanded in this embodiment in order to take into account the influences of the elastic behavior of a real drive system.
  • This system is given here as an example for the more general case that more than two state variables have to be considered in the control system. are visible. Systems are also conceivable that have four, eight or more state variables. However, the controller structure will always have to be expanded in the same way as is shown below in relation to an elastic system.
  • Such an elastic system must be assumed in the case of a control that is as precise as possible in the case of a large number of drives which have been implemented in practice. Previous control systems, however, do not take this constellation into account or only insufficiently.
  • Elastic elements are already present in a drive system that uses a rotary motor that drives a load via an elastic spindle or an elastic toothed belt.
  • control system The particular advantage of this control system is that the inevitable deformations can be recorded in the control and taken into account by it.
  • the existing deformations lead to undesirable vibrations which are not actively compensated for by the control and, in particular, the possible speeds and accelerations of the regulated drive system.
  • the practical implementation in the control system is carried out by adding two further difference formers 50 and 51 and two further control amplifiers 52 and 53, which are inserted into the control cascade in the manner already explained. It is advisable to insert additional limiters 54 and 55 after each additional control amplifier in order to comply with the maximum specifications for the control variables.
  • the remaining structure of the control system corresponds to the previously described embodiments.
  • the path control according to the invention is based on the approach that all kinematic quantities of the movement of a system (both in the plane and in space), i.e. the position s, the speed v, the acceleration a, the jerk r etc., are vector quantities that attack at the center of gravity of the moving system.
  • these quantities which are actually defined in relation to the fixed coordinate system of the drive, can be transformed into any rotated or moving coordinate systems.
  • FIG. 8 illustrates the decomposition of a speed vector v into the components v x and v y in the fixed xy coordinate system, as well as the possible decomposition into the components v e and v z in one transformed, rotated ze coordinate system. Since the ordinate and the abscissa of the respective coordinate system are perpendicular to each other, the rotation of the moving ze coordinate system relative to the fixed xy coordinate system is clearly determined by specifying one of the two vectors z or e in the xy coordinate system. The other vector can be calculated by simply rotating it by 90 °.
  • the z-vector can be calculated from the e-vector.
  • the two coordinate vectors are expediently normalized so that their length is 1, or:
  • a first main step 60 the path must be described by reference points.
  • a suitable moving coordinate system is determined.
  • the control deviation is transformed into moving coordinates in the moving coordinate system.
  • a fourth main step 63 the necessary manipulated variables are determined by a direction controller and a deviation controller.
  • the determined manipulated variables are transformed back in a fifth main step 64 into fixed coordinates of the fixed coordinate system in order to then feed them to the drive system.
  • step 10 shows a more detailed flow chart of the path control, reference being made here to the mathematical relationships already set out above.
  • the main steps of the path control method set out in relation to FIG. 9 thus include the following sub-steps, the sequence and connection of which can be seen from FIG. 10.
  • the measuring system Control variables 65 (y) determined are fed to the observer 1 and the first difference former 3.
  • the difference former 3 also receives setpoints 66 (w) which serve to describe the path.
  • the vectors z and e of the moving coordinate system are calculated from the controlled variables 65 and the target values 66. It is thus possible in step 68 to transform the state vectors supplied by the observer from the fixed xy coordinate system to the moving ze coordinate system.
  • step 69 the path deviations (error vectors) can be transformed from the fixed xy coordinate system into the moving ze coordinate system.
  • step 70 is followed by the actual control, so that in step 71 it is possible to reverse transform the manipulated variable vector provided by the control from the moving ze coordinate system into the fixed xy coordinate system.
  • the manipulated variables (u) are finally delivered to the drive system in step 72.
  • the moving coordinate system ie the ze vectors, must be selected to match the desired trajectory.
  • the z-vector can be used as the target vector and the e-vector as the error vector be understood.
  • the moving coordinate system is to be defined in such a way that the target vector z in the respective reference point on the path always represents the tangent to the path of movement.
  • the target vector When moving along a straight line, the target vector will be aligned along the path.
  • the target vector When moving on a circular path, the target vector will represent the tangent at the respective reference point to the path of movement. This relationship can be represented mathematically as follows:
  • P A designate the starting point of the straight line segment.
  • the vector e is then calculated by rotating z according to the formula given above.
  • the error vectors ⁇ i, e, ..., e n _ ⁇ are each perpendicular to the target vector z and thus an error area or one Spanning (n-1) -dimensional error space perpendicular to the target vector z.
  • the (first) error vector e can be determined by dropping the plumb line onto the desired trajectory based on the actual position.
  • the target vector z perpendicular to this error vector e can be determined by simple calculation.
  • the further e-vectors i.e. error deviations in the other dimensions
  • the definition of the plumb line shows that the base point of the plumb line and the actual position lie on a straight line whose direction is perpendicular to the direction of the path.
  • the actual position corresponds to the sum of the base point and distance, multiplied by the error vector.
  • the remaining (n-2) error vectors will always be zero due to this definition of the (first) error vector.
  • the target component (index z) corresponds to the tangential component and the error component (index e) corresponds to the radial component of the movement.
  • the acceleration pre-control in the deviation control loop thus results from the speed (v z ) observed in the direction controller and the radius (r) of the circular path given by the reference points.

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  • Engineering & Computer Science (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)
  • Control Of Multiple Motors (AREA)

Abstract

L'invention concerne un système de régulation pour des organes de commande électriques, comportant un élément d'observation (1), un premier amplificateur de régulation (4), un deuxième amplificateur de régulation (5) et un troisième amplificateur de régulation (6). Les signaux de sortie des amplificateurs de régulation sont combinés pour former un signal d'entrée d'organe de commande. A cet effet, un deuxième différenciateur (11) forme un signal de différence et achemine ce dernier au deuxième amplificateur de régulation (5), et un troisième différenciateur (12) forme un signal de différence et achemine ce dernier au troisième amplificateur de régulation (6). L'invention concerne également un procédé de régulation de trajectoire d'un organe de commande électrique, dont les trajectoires de déplacement possibles sont situés dans un système de coordonnées fixe de dimension n. Pour déterminer le vecteur de la grandeur de positionnement, une transformée est effectuée dans un système de coordonnées associé.
PCT/EP2000/010530 1999-10-31 2000-10-25 Systeme de regulation pour organes de commande electriques et procede de regulation de trajectoire WO2001033304A2 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE1999152388 DE19952388A1 (de) 1999-10-31 1999-10-31 Regelsystem für elektrische Antriebe und Verfahren zur Bahnregelung
DE19952388.6 1999-10-31

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WO2001033304A2 true WO2001033304A2 (fr) 2001-05-10
WO2001033304A3 WO2001033304A3 (fr) 2001-11-15

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102637011A (zh) * 2011-11-30 2012-08-15 沈阳工业大学 基于坐标变换和参数调整直接驱动数控平台鲁棒控制方法

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE19952389B4 (de) * 1999-10-31 2010-04-01 Eugen Saffert Verfahren zur Bestimmung der Parameter und/oder Strom-Weg-Kennlinie eines elektrisch angetriebenen Motorsystems
DE10303122B4 (de) 2002-09-27 2005-10-06 Koenig & Bauer Ag Verfahren zur Regelung der Bahnspannung eines Mehrbahnsystems
DE10321970A1 (de) 2003-05-15 2004-12-09 Siemens Ag Verfahren zur Bewegungsführung eines bewegbaren Maschinenelementes einer numerisch gesteuerten Werkzeug-oder Produktionsmaschine
DE102018208790A1 (de) * 2018-06-05 2019-12-05 Carl Zeiss Industrielle Messtechnik Gmbh Antriebseinrichtung für ein Koordinatenmessgerät, Koordinatenmessgerät und Verfahren zum Regeln einer solchen Antriebseinrichtung

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