Method and device for guiding the movement of a movable machine element of a machine

Abstract

The movement of a machine element of a machine that can be driven via a shaft with the aid of a motor can be guided by specifying a setpoint guidance variable describing a desired movement process of the machine element for the actuation of the motor and determining an actual pilot variable and/or an actual guidance variable from the setpoint guidance variable by subjecting the setpoint guidance variable to a digital path model which simulates the dynamic behavior of the machine element and the motor. The digital path model is parameterized by the total moment of inertia and the poles and zeros of the transfer function of the mechanical system consisting of motor, shaft and machine element.

Claims

1. A method for guiding a movement of a machine element of a machine driven via a shaft with the aid of a motor, comprising: specifying, for actuating the motor, a setpoint guidance variable describing a desired movement process of the machine element; subjecting the setpoint guidance variable to a digital path model which is parameterized by a total moment of inertia and poles and zeros of a transfer function of a mechanical system composed of the motor, the shaft and the machine element and which simulates a dynamic behavior of the machine element and the motor; transforming an output variable of the digital path model via a feedback variable, and forming an actual pilot variable by subtracting the transformed output variable from the setpoint guidance variable at an input summator of the digital model; forming an actual guidance variable by multiplying the output variable of the digital path model by a fitting vector; supplying the actual pilot variable and the actual guidance variable to a closed loop to set a level of current for the motor; and regulating the motor to actuate the movement of the machine element.

2. The method of claim 1, wherein the method is performed in real time during the movement of the machine element.

3. The method of claim 1, wherein the digital path model is a regulating path of a linearly regulated digital model.

4. The method of claim 1, wherein the setpoint guidance variable comprises a setpoint position, a setpoint velocity, or a setpoint acceleration of the machine element.

5. The method of claim 1, further comprising delaying the actual guidance variable according to a time delay of a power unit in the closed loop by a delay unit before supplying the actual guidance variable to the closed loop.

6. The method of claim 1, further comprising, for regulating the motor, supplying a difference between the actual guidance variable and a measured actual variable to a position regulator of the closed loop.

7. The method of claim 1, further comprising, for controlling the level of the motor current, adding an output signal of a velocity regulator of the closed loop to the actual pilot variable.

8. A machine, comprising: a motor; a shaft coupled to the motor; a movable machine element coupled to the shaft, with movement of the machine element controlled by the motor; and a numerical machine control device configured to: output a setpoint guidance variable describing a desired movement process of the machine element for actuating of the motor; subject the setpoint guidance variable to a digital path model, which is parameterized by a total moment of inertia and poles and zeros of a transfer function of the mechanical system composed of the motor, the shaft and the machine element and which simulates a dynamic behavior of the machine element and the motor; transform an output variable of the digital path model via a feedback variable, and form an actual pilot variable by subtracting the transformed output variable from the setpoint guidance variable at an input summator of the digital model; form an actual guidance variable by multiplying the output variable of the digital path model by a fitting vector; supply the actual pilot variable and the actual guidance variable to a closed loop to set a level of current for the motor; and regulate the motor to actuate the movement of the machine element.

9. A computer program product for numerical control of a machine, the computer program product embodied on a non-transitory computer-readable medium product and having computer-executable instructions, which, when loaded into a memory of a numerical machine control device and executed by a processor of the numerical machine control device, implement a method for guiding the movement of a machine element of the machine as set forth in claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) Other features and advantages of the present invention will be more readily apparent upon reading the following description of currently preferred exemplified embodiments of the invention with reference to the accompanying drawing, in which:

(2) FIG. 1 is a schematic representation of a two-mass vibrational system;

(3) FIG. 2 is a schematic representation of a device according to the invention for guiding the movement of a movable machine element of a machine;

(4) FIG. 3 is an information flow diagram to illustrate a general concept of the invention; and

(5) FIGS. 4a and b are flow diagrams of steps of a method according to the invention for guiding the movement of a movable machine element of a machine.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

(6) Throughout all the figures, same or corresponding elements may generally be indicated by same reference numerals. These depicted embodiments are to be understood as illustrative of the invention and not as limiting in any way, it should also be understood that the figures are not necessarily to scale and that the embodiments, may be illustrated by graphic symbols, phantom lines, diagrammatic representations and fragmentary views, in certain instances, details which are not necessary for an understanding of the present invention or which render other details difficult to perceive may have been omitted.

(7) Turning now to the drawing, and in particular to FIG. 1, there is shown a schematic representation of a two-mass vibrational system which includes a motor 16, which is connected or coupled to a load 18 via a shaft. The load 18 can, for example, be a machine element of a machine which can be driven by the motor. The motor 16 has a motor inertia J.sub.M and a motor torque M.sub.M. The load 18 or the machine element 18 has a load inertia J.sub.L. The connection along the shaft between the motor 16 and the load 18 has a stiffness c and a damping d. The connection can, for example, be present in the form of a gear unit, a drive shaft or a drive train.

(8) If the rotor position angle x.sub.M of the rotor of the motor 16 changes, because of the finite torsional stiffness, in particular in dynamic cases, the load position x.sub.L does not change as would have been expected from a pure change in the rotor position angle x.sub.M, rather the load position x.sub.L vibrates with respect to the position actually to be expected in static cases in dependence on the rotor position angle x.sub.M.

(9) The system dynamics of the two-mass vibrational system depicted in FIG. 1 can be described mathematically by a linear system of differential equations with the aid of customary transformation methods, such as Lagrange-methods, Newton-Euler methods and the like.
M.Math.{umlaut over (X)}+D.Math.{dot over (X)}+K.Math.X=T.Math.f.sub.M,(1)
wherein M is the mass matrix, D is the damping matrix, K is the torsion stiffness matrix, T is a transformation matrix, X is the state vector and f.sub.M is the input control vector of the motor 16. Together with the holonomic equation
u.sub.Mot=T.sup.T.Math.X(2)
with the output variable vector u.sub.Mot, which can, for example, be the rotor position angle x.sub.M. Since the two-mass vibrational system is causal or implementable and the number m of zeros of the transfer function is lower than the number n of poles of the transfer function, after transition to the state-space representation by decomposing the nth order system differential equation into n first order differential equations, the state-space model with the following state equation results
{dot over (X)}=[1 0]X[0]f.sub.Mot(3)
and the output equation
u.sub.Mot=[ ]X(4)

(10) To transfer a path model into a digital path model, it is necessary to discretize the state-space model of the equations (3) and (4). However, this discretization is very computationally intensive, since inversions of matrices are necessary in the state-space regulation. However, this kind of parameterization of the state matrix can result in numerical problems as the system order increases. In some circumstances, this results in unwanted instabilities due to rounding or overflow errors which can thus lead to uncontrolled movements of the machine shaft.

(11) Therefore, it is provided according to the invention that the path model is transferred into the digital path model by parameterization via the total moment of inertia and the poles and zeros of the transfer function H.sub.Mot=u.sub.Mot/f.sub.Mot of the mechanical system comprised of motor 16, shaft and machine element 18. Herein, the machine shaft of the machine is formed by the motor 16, the load 18 and the connection between the motor 16 and the load 18 with a stiffness c and a damping d. This machine shaft has a total moment of inertia J.sub.G.

(12) With this parameterization, the discrete-time transfer function can be written directly from the parameters, i.e., the i=1 . . . m conjugate-complex zero pairs z.sub.i, the j=1 . . . n (>m) conjugate-complex pole pairs p.sub.j and the total moment of inertia J.sub.G of the machine shaft:

(13) $H_{\mathrm{Mot}}=\frac{{.Math.}_{i=1}^m\left(z-z_i\right)\left(z-{\tilde{z}}_i\right)}{({J_G\left(z-1\right)}^2{.Math.}_{j=1}^n\left(z-p_j\right)\left(z-{\tilde{p}}_j\right)}$

(14) The transfer function (5) can be used to calculate the coefficients of the transfer function a.sub.i and b.sub.i which can be used to derive the transfer function directly into the state-space model. Either the controllable canonical form or the observable canonical form can be used for this purpose. As an example, the general controllable canonical form is shown below with the state differential equation:

(15) $\begin{array}{cc}\stackrel{.}{X}=\left(\begin{array}{ccccc}0& 1& .Math.& 0& 0\\ 0& 0& .Math.& 0& 0\\ 0& .Math.& & .Math.& .Math.\\ 0& 0& .Math.& 0& 1\\ -b_0& -b_1& .Math.& -b_{N-2}& -b_{N-1}\end{array}\right)X+\left(\begin{array}{c}0\\ 0\\ .Math.\\ 0\\ 1\end{array}\right)f_{\mathrm{Mot}}& \left(6\right)\end{array}$
and the algebraic output equation
u.sub.Mot=(a.sub.0a.sub.Nb.sub.0a.sub.1a.sub.Nb.sub.1 . . . a.sub.N-2a.sub.Nb.sub.N-2a.sub.N-1a.sub.Nb.sub.N-1)X+a.sub.Nf.sub.Mot (7)

(16) The advantage with this controllable canonical form is that no matrices need to be inverted and numerical stability is always ensured. In addition, the parameters of the parameterization can be converted directly into the discrete-time coefficients of the state differential equation (6) and the output equation (7).

(17) The new parameterization simplifies digital path modeling because every feature of the transfer function H.sub.Mot=u.sub.Mot/f.sub.Mot is uniquely parameterized. Accordingly, no expert knowledge regarding the effects of the mass matrix, the damping matrix or the torsion stiffness matrix is absolutely necessary for modeling or adjusting the modeling when there is a change to physical properties of the shaft, the motor 16 and/or the machine element 18, for example when a more rigid or more inert machine element 18 is installed. Moreover, the complexity of the state-space model (6)(7) does not increase with the system order because, no matter how many frequencies the model includes, the system matrix of the state differential equation (6) always only needs to be filled element-by-element.

(18) The new type of parameterization using the total moment of inertia and the poles and zeros of the transfer function H.sub.Mot=u.sub.Mot/f.sub.Mot makes it possible to automatically identify the poles and zeros with the aid of a measured frequency response and to ascertain the total inertia. This automation of the main feature identification also enables the digital path modeling to be automated. Herein, for example, iterative optimization of the model parameters can be performed by adapting the modeled frequency response to the measured frequency response, for example by minimizing the least square deviation across the frequencies.

(19) FIG. 2 is a schematic representation of a device according to the invention for guiding the movement of a movable machine element of a machine. Herein, the device can, for example, be present in the form of a numerical machine control device and/or a regulating device of the machine. The device has guidance-variable generating means 17, which generates a setpoint guidance variable y.sub.setp, as seen in FIG. 4b, step 401, describing the desired movement process of the machine element 18, for example a setpoint guide position, a setpoint guide velocity or a setpoint guide acceleration and sends it to a model 2 as an input variable seen in FIG. 4b, step 402. The guidance-variable generating means 17 can, for example, be present as a commercially available component of the numerical control in machines, such as, for example, machine tools, production machines and/or robots. Herein, the setpoint guidance variable y.sub.setp is a variable that is normally supplied directly as a setpoint variable to a downstream closed loop 26 which regulates the movement process of the machine element 18 in accordance with the prespecified setpoint guidance variable y.sub.setp.

(20) According to the invention, a model 2 for determining an actual guidance variable y.sub.act and/or an actual pilot variable M.sub.pilot is now interposed between the setpoint guidance-variable generating means 17 and the closed loop 26. The actual pilot variable M.sub.pilot is, for example, present as a pilot torque and the actual guidance variable y.sub.act can, for example, be an actual position model variable. Herein, the model 2 has the above-described digital path model 3 and a state regulator, which is implemented in the form of a feedback vector 6 and a fitting element 1. The model 2 furthermore has a fitting vector w (see reference symbol 5).

(21) The model 2 can, for example, be a linearly regulated path model in which an output variable of the digital path model 3 modified by means of a feedback vector 6 is fed back to an input variable of the path model 3, s seen in FIG. 4b, step 403. The output variable of the digital path model 3 is the state vector y. The digital path model 3 is used to simulate the mechanical behavior of the motor 16, the machine element 18 and the mechanical connection between the motor 16 and the machine element 18. The dynamic behavior of this system is parameterized via the total moment of inertia and the poles and zeros of the transfer function H.sub.Mot=u.sub.Mot/f.sub.Mot.

(22) The state regulator enables undesired properties of the elements involved in the movement to be corrected in advance. Herein, the actual pilot variable M.sub.pilot and the actual guidance variable y.sub.act are determined, as seen in FIG. 4b steps 404 and 405. The feedback vector r can have individual feedback coefficients r1, r2, r3 and r4 (see reference symbol 6) and leads back to a scalar variable s=yrT by multiplication with the state vector y.

(23) The fitting vector w required to generate the scalar actual guidance variable y.sub.act which, multiplied by the state vector y, produces the scalar actual guidance variable y.sub.act can have w1=1 and w2 . . . N=0 as fitting coefficients, so that y.sub.act=ywT.

(24) Herein, the feedback vector r can, for example, be selected such that one single or more natural oscillation frequencies of the digital path model 3 are damped. The fitting element 1, for example a prefilter, can be used to influence the overall gain of the model 2. Thus, in the simplest case, the fitting element 1 can include a multiplication of the setpoint guidance variable y.sub.setp with a constant factor (for example 1.5). A subtractor 4 is used to subtract the output variable y modified by means of the feedback variable r, i.e., the state vector, of the digital path model 3 from the setpoint guidance variable y.sub.setp modified by the fitting element 1 with a subtractor 4. This results in the actual pilot variable M.sub.pilot, which is supplied to the digital path model 3 as an input variable. This outputs the state vector y as an output variable, wherein the scalar actual guidance variable y.sub.act is then generated by means of the fitting vector w.

(25) A delay unit connected downstream of the digital path model 3 enables the behavior of a power unit (for example a converter) that actuates the motor 16 and possibly further delays not taken into account in the model to be introduced independently of the design of the digital path model 3. In the example in FIG. 2, the downstream delay unit 9 is used to delay the actual guidance variable y.sub.act as seen in FIG. 4b, step 406 according to the delay of the power unit 15, i.e., the time required by the power unit 15 to build up the current I, and to output it at the output of the delay unit 9. However, the delay does not necessarily have to be performed.

(26) The actual pilot variable M.sub.pilot and the possibly delayed actual guidance variable y.sub.act are fed into the closed loop 26 for regulating the motor 16 as seen in FIG. 4b, steps 407 and 408. A subtractor 10 is used to subtract the delayed actual guidance variable y.sub.act from an actual variable y.sub.mact measured, for example, by a sensor. The measured actual variable y.sub.mact can, for example be the rotor position angle of the motor 16. The calculated difference is then supplied from the subtractor 10 to a differentiator 12, which ascertains the time derivative and forwards it to a position regulator 11. The output variables of the differentiator 12 and the position regulator 11 are inverted in each case and added with the aid of an adder 25. The output variable of the adder 25 is supplied to a velocity regulator 13 as an input variable.

(27) The output variable of the velocity regulator 13 is then filtered with the aid of an optional filter 14 in order to filter out any undesirable properties that may still occur in the frequency response. The filter 14 outputs the actual regulator torque M.sub.v, which is added to the actual pilot variable M.sub.pilot, i.e., the pilot torque, by an adder 19, in order to obtain the setpoint torque M.sub.setp. The setpoint torque M.sub.setp is then supplied to the power unit 15 as an input variable, which can, for example, be present in the form of a converter with associated actuation electronics. The power unit 15 is actuated according to the setpoint M.sub.setp in order to set the level of the motor current I. As a result, the motor 16 actuates the movement process of the machine element 18 in a dynamically corrected manner.

(28) The system shown in FIG. 2 with the model 2 and the closed loop 26 can, for example, be implemented for a plurality of machine shafts of a machine, wherein the specific dynamic behavior of the different shafts can be depicted in the different parameters of the digital path models 3. Herein, the setpoint guidance-variable generating means 17 can generate an associated setpoint guidance variable y.sub.setp for each machine shaft and specify it as an input variable for the respective associated model 2.

(29) FIG. 3 is a schematic information flow diagram for the general case in which the individual machine shafts can be coupled to one another. For example, a change in position of a machine shaft can automatically cause a change in position of other machine shafts, such as in a robot arm with a plurality of joints. A setpoint generating means 17 specifies single or more setpoint guidance variables such as, for example, a setpoint position x.sub.setp, a setpoint velocity v.sub.setp and/or a setpoint acceleration a.sub.setp, to a model 2 as input variables. Herein, the individual variables can be present as vectors corresponding to the number of machine shafts to be moved. Herein, the model 2 ascertains for the individual machine shafts of the machine single or more actual guidance variables such as, for example, an actual torque variable M.sub.act, an actual velocity variable v.sub.act and/or an actual acceleration variable a.sub.act. These variables can also be present as vectors. They are delayed with the aid of a delay unit 9 according to the time delay of the power unit 15.

(30) At the motor 16 and/or from another location, measured variables such as, for example, a measured actual position variable x.sub.mact, a measured actual velocity variable v.sub.mact and/or measured actual acceleration variable a.sub.mact, wherein the variables can also be present as vectors, are deducted from the delayed guidance variables calculated by the model 2 by means of a subtractor 10 and the difference supplied to a regulator 20. These ascertain the regulator torque M.sub.V as the output variable, wherein then the pilot variable M.sub.pilot from the regulating torque M.sub.V is added by means of an adder 19 and in this way a setpoint torque M.sub.setp is determined and supplied to a power unit 15 as an input variable (herein, M.sub.pilot, M.sub.V and M.sub.setp can also be present as vectors). Herein, the power unit 15 supplies the currents I for the individual motors 16 for moving the machine shaft of the machine. Hence, the general inventive approach can also be implemented with machines in which coupled machine shafts are present with the aid of a model 2 that also takes account of the couplings of the machine shafts.

(31) As can be seen in Figure FIG. 4a, M1 represents specifying, for actuating the motor, a setpoint guidance variable describing a desired movement process of the machine element. M2 represents determining an actual pilot variable or an actual guidance variable from the setpoint guidance variable by subjecting the setpoint guidance variable to a digital path model which is parameterized by a total moment of inertia and poles and zeros of a transfer function of a mechanical system composed of the motor, the shaft and the machine element and which simulates a dynamic behavior of the machine element and the motor.

(32) The invention enables the principle of model-based control to improve the dynamic behavior of the movement of machine elements, to be operated more easily, to be adapted without expert knowledge and to become more effective due to the better model quality.

(33) In the preceding detailed description, various features for improving the stringency of the presentation have been summarized in one or more examples. However, herein, it should be clear that the above description is merely illustrative and in no way restrictive in nature. It serves to cover all alternatives, modifications and equivalents of the various features and exemplary embodiments. In the light of the above description, many other examples will be immediately and directly apparent to those skilled in the art on the basis of their specialist knowledge.

(34) The exemplary embodiments were selected and described in order to be able to present the principles underlying the invention and its possible applications in practice in the best possible way. As a result, those skilled in the art will be able to optimally modify and utilize the invention and its different exemplary embodiments in respect of the intended use. In the claims and the description, the terms including and having are used as neutral language terms for the corresponding term comprising. Furthermore, the use of the terms a and an is not in principle intended to exclude a plurality of features and components described in this way.

(35) While the invention has been illustrated and described in connection with currently preferred embodiments shown and described in detail, it is not intended to be limited to the details shown since various modifications and structural changes may be made without departing in any way from the spirit and scope of the present invention. The embodiments were chosen and described in order to explain the principles of the invention and practical application to thereby enable a person skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated.