SERVO CONTROL APPARATUS AND SERVO CONTROL METHOD

Abstract

A servo control apparatus includes an actual machine frequency characteristic measurer that calculates a frequency characteristic of an actual machine from a motor input signal and an output of a detector, and a parameter adjuster that finds a solution for a parameter of a controller, which sets a difference, between an open loop characteristic, calculated from a calculation result of the actual machine frequency characteristic measurer and a frequency characteristic of the controller, and an ideal open loop characteristic, to be less than or equal to a predefined reference, and that applies the obtained parameter to the controller.

Claims

1. A servo control apparatus which drives a load device by a servo motor, the servo control apparatus comprising: a command generator that generates a command value of the servo motor; a detector that detects a state quantity of the servo motor or the load device to be driven; a controller that controls a motor input signal such that the command value and an output of the detector coincide with each other; an actual machine frequency characteristic measurer that calculates a frequency characteristic of an actual machine from the motor input signal and the output of the detector; and a parameter adjuster that finds a solution for a parameter of the controller, which sets a difference, between an open loop characteristic, calculated from a calculation result of the actual machine frequency characteristic measurer and a frequency characteristic of the controller, and an ideal open loop characteristic, to be less than or equal to a predefined reference, and that applies the obtained parameter to the controller.

2. The servo control apparatus according to claim 1, wherein when the actual machine frequency characteristic measurer calculates the frequency characteristic of the actual machine, the actual machine frequency characteristic measurer changes a position of the load device to an arbitrary position and calculates a frequency characteristic of the actual machine for each position.

3. The servo control apparatus according to claim 1, wherein the parameter adjuster uses a plurality of the frequency characteristics of the actual machine calculated by the actual machine frequency characteristic measurer as the measurement value without modeling, to formulate, in an optimization problem, the open loop characteristic to which the controller is combined, and finds a solution for the optimization problem, to determine a parameter to be applied to the controller.

4. A servo control method for driving a load device by a servo motor, the method comprising: operating the servo motor according to a command value; detecting, with a detector, a state quantity of the servo motor or the load device to be driven; controlling, with a controller, a motor input signal so that the command value and an output of the detector coincide with each other; calculating a frequency characteristic of an actual machine from the motor input signal and the output of the detector; and finding a solution for a parameter of the controller, which sets a difference, between an open loop characteristic, calculated from the frequency characteristic of the actual machine and a frequency characteristic of the controller, and an ideal open loop characteristic, to be less than or equal to a predefined reference, and applying the obtained parameter to the controller.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0016] Embodiment(s) of the present disclosure will be described based on the following figures, wherein:

[0017] FIG. 1 is a block line diagram showing a structure of a servo control unit of a servo control apparatus;

[0018] FIG. 2 is a flowchart showing an operation of a servo control apparatus;

[0019] FIG. 3 is a diagram showing an example configuration of a typical machine tool; and

[0020] FIG. 4 is a diagram showing an example of variation of a frequency characteristic of an actual machine due to a position of a load device.

DESCRIPTION OF EMBODIMENTS FIG. 1 is a block line diagram showing a structure of a servo control unit of a servo control apparatus.

[0021] According to a program given from an operator or the like, a command generator 17 generates a movement command for a load device 16. A controller 13 controls a torque generated by a motor 15 so that the generated command and a value detected by a detector 14 coincide with each other. In addition, an actual machine frequency characteristic measurer 11 receives as inputs an output of the controller 13 and an output of the detector 14, calculates a frequency characteristic of a frequency characteristic measurement target part 18, and outputs the calculated frequency characteristic to a parameter adjuster 12. The parameter adjuster 12 finds a solution for an optimum parameter for the controller 13 based on the frequency characteristic calculated by the actual machine frequency characteristic measurer 11, and updates the controller 13. Each of the controller 13, the actual machine frequency characteristic measurer 11, and the parameter adjuster 12 is physically formed from a computer having one or more processors and a memory. The detector 14 detects a state quantity of the motor 15 or the load device 16, and is, for example, a position sensor, a vibration sensor, or the like.

[0022] FIG. 2 is a flowchart showing an operation of the servo control apparatus. S1 in FIG. 2 shows an operation of the actual machine frequency characteristic measurer 11 of FIG. 1, and S2 in FIG. 2 shows an operation of the parameter adjuster 12 of FIG. 1.

[0023] First, in step S11 and step S12, a frequency characteristic of an actual machine of the frequency characteristic measurement target part 18 shown in FIG. 1 is measured while changing a position of the load device. Here, a value n means a number of measurement points, and is a value determined in advance so as to maximize a variation width of the characteristic variation. For example, when the load device is the table 37 shown in FIG. 3, a difference in the motor axis equivalent inertia of the portion of the ball screw 34 is the maximum between a case in which the load device is positioned near a positive end in a movable range and a case in which the load device is positioned near a negative end. In addition, because an elastic deformation of the portion of the ball screw 34 is the maximum when the load device is positioned near a center of the movable range, desirably, 3 points are employed, including a point near the positive end, a point near the negative end, and a point near the center of the movable range. After the process of step S11, in step S12, a number of measurements m is incremented from 0, and, when the number of measurements m becomes greater than or equal to the number of measurement points n, the process proceeds to step S21.

[0024] In step S21, a structure of a velocity controller C(s) is determined based on the frequency characteristic of the actual machine obtained in steps S11 and S12. In the present example configuration, examples of elements of a compensator included in the structure of the velocity controller C(s) include, for example, a PID compensator, a PI compensator, a PD compensator, a P compensator, a phase advancement/delay compensator, a notch filter, an all-pass filter, a low-pass filter, and a high-pass filter. In the present embodiment, there is exemplified a structure which is described as the following formula (1) and in which a PI compensator and an X-stage notch filter C.sub.k(s) are combined. The notch filter C.sub.k(s) can be expressed as the following formula (2).

[0025] The number of stages X of the notch filter may be defined in advance in consideration of the calculation capabilities of the DSP and the number of resonance characteristics which usefully act on the widening of the bandwidth of the notch filter, or the like, and may alternatively be suitably changed in the step S21, in correspondence to the resonance characteristic of the frequency characteristic of the actual machine.

[00001]$\begin{array}{cc}C\left(s\right)=\left(K_p+\frac{K_i}{s}\right).Math.\stackrel{K}{\underset{k=1}{.Math.}}{C}_k\left(s\right)& \mathrm{formula}\left(1\right)\end{array}$$\begin{array}{cc}{C}_k\left(s\right)=\frac{s^2+2{\alpha }_k{\zeta }_k{\omega }_{k}s+{\omega }_k^2}{s^2+2{\zeta }_k{\omega }_{k}s+{\omega }_k^2}& \mathrm{formula}\left(2\right)\end{array}$

[0026] In these formulae, K.sub.p and K.sub.i are parameters of the PI compensator, and α.sub.k, ζ.sub.k, and ω.sub.k are parameters of the notch filter. In addition, s represents a Laplacian operator, and corresponds to a product of a unit imaginary number j and an angular frequency ω. Therefore, the controller C(s) may be expressed in a complex number, as shown below in formula (3).

[00002]$\begin{array}{cc}C\left(j\omega \right)=\left(K_p+\frac{K_i}{j\omega }\right).Math.\underset{k=1}{\overset{X}{.Math.}}\left(\frac{{\left(j\omega \right)}^2+2{\alpha }_k{\zeta }_k{\omega }_k\left(j\omega \right)+{\omega }_k^2}{{\left(j\omega \right)}^2+2{\zeta }_k{\omega }_k\left(j\omega \right)+{\omega }_k^2}\right)& \mathrm{formula}\left(3\right)\end{array}$

[0027] In step S22, open loop characteristics L.sub.1(jω, L.sub.2(jω), . . . , L.sub.n(jω) are designed based on the frequency characteristic of the actual machine measured in steps S11 and S12, and the controller C(s) designed in step S21.

[0028] When the frequency characteristics of the actual machine measured in steps S11 and S12 are P.sub.1(jω), P.sub.2(jω), . . . , P.sub.n(jω), the open loop characteristics L.sub.1(jω), L.sub.2(jω), . . . , L.sub.n(jω) in respective frequency characteristics of the actual machine may be represented by the following formula (4).

[00003]$\begin{array}{cc}\left[\begin{array}{c}{L}_1\left(j\omega \right)\\ L_2\left(j\omega \right)\\ .Math.\\ L_n\left(j\omega \right)\end{array}\right]=\left(K_p+\frac{K_i}{j\omega }\right).Math.\underset{k=1}{\overset{X}{.Math.}}\left(\frac{{\left(j\omega \right)}^2+2{\alpha }_k{\zeta }_k{\omega }_k\left(j\omega \right)+{\omega }_k^2}{{\left(j\omega \right)}^2+2{\zeta }_k{\omega }_k\left(j\omega \right)+{\omega }_k^2}\right)\left[\begin{array}{c}{P}_1\left(j\omega \right)\\ P_2\left(j\omega \right)\\ .Math.\\ P_n\left(j\omega \right)\end{array}\right]& \mathrm{formula}\left(4\right)\end{array}$

[0029] With the complex-number expression using jω as in formula (4) rather than the transfer function expression using the Laplacian operator s, it becomes possible to determine the open loop characteristic without modeling the frequency characteristic of the actual machine.

[0030] Next, in step S23, a computation process is performed for an optimization problem for determining the parameters of the velocity controller C(s) based on the open loop characteristic of formula (4). In this process, as an optimization algorithm to be used, it is necessary to include a constraint condition using a gain margin and a phase margin, for the purpose of achieving an operation without an unusual sound and vibration. Thus, the optimization algorithm may be an algorithm for which a constraint formula may be provided. In addition, when the velocity controller C(s) is expressed in a linear form with respect to the solved parameter, formulation is possible by linear matrix inequality (LMI). In the present example configuration, because the open loop characteristic of formula (4) is expressed in a nonlinear form, a configuration will be described exemplifying the formulation of the optimization problem by sequential quadratic programming (SQP). After the formulation by the SQP, the following formula (5) may be obtained.

[00004]$\begin{array}{cc}\underset{K_p,K_i,{\alpha }_k,{\zeta }_k,{\omega }_k}{\min }\underset{q=1}{\overset{n}{.Math.}}\underset{t=1}{\overset{T}{.Math.}}.Math.L_d\left(j{\omega }_t\right)-L_q\left(j{\omega }_t\right).Math.& \mathrm{formula}\left(5\right)\end{array}$$\mathrm{subject}\mathrm{to}:$$-20{\log }_{10}.Math.L_q\left(j{\omega }_p\right).Math.\ge \mathrm{GM}\left(q=1,2,.Math.,n\right)$${\tan }^{-1}\left(L_q\left(j{\omega }_g\right)\right)-\left(-180°\right)\ge \mathrm{PM}$

[0031] Here, L.sub.d(s) represents an ideal open loop characteristic, and may be arbitrarily determined based on the performance demanded by the designer for the control system. When the widening of the bandwidth is simply targeted, for example, a form such as that shown below in formula (6) may be employed. Here, α and β are arbitrary coefficients. In addition, while the open loop characteristics using the frequency characteristic of the actual machine exist in a number corresponding to the number of measurement points n, there is only one ideal open loop characteristic L.sub.d(s).

[00005]$\begin{array}{cc}{L}_d\left(s\right)=\alpha \frac{s+\beta }{s^2}& \mathrm{formula}\left(6\right)\end{array}$

[0032] In formula (5) described above, ω.sub.p represents an angular frequency when a phase characteristic becomes −180°, and the gain margin GM shows a gain characteristic of the open loop characteristic when the angular frequency becomes ω.sub.p. A parameter ω.sub.g shows an angular frequency at which the gain characteristic becomes 0 dB, and the phase margin PM is a phase characteristic of the open loop characteristic when the angular frequency becomes ω.sub.g. A parameter T is a number of data points of the frequency characteristics used for the formulation of the optimization problem, and may be set to any arbitrary value within the number of data points measured in step S11.

[0033] The gain margin GM, the phase margin PM, and the ideal open loop characteristic L.sub.d(s) must be determined in advance, when formula (5) is formulated.

[0034] In formula (5), determination variables of the optimization problem for setting differences between the ideal open loop characteristic L.sub.d(s) and the open loop characteristics L.sub.1(jω), L.sub.2(jω), . . . , L.sub.n(jω) in the frequency characteristics of the actual machine to be less or equal to a predefined reference are K.sub.p, K.sub.i, α.sub.k, ζ.sub.k, ω.sub.k (k=1, 2, . . . , X). When optimum solutions for these (2+3X) determination parameters can be obtained, the optimum open loop characteristic and the controller parameter can be determined.

[0035] In step S24, the velocity controller parameter is updated to the parameter solved in step S23, so that the load device 16 can be controlled with the optimum controller.

[0036] With this process, a controller which enables widening of the bandwidth is designed in all frequency characteristics when the load device is positioned at any arbitrary point, and in a state satisfying the gain margin and the phase margin. As such, even in cases where the frequency characteristic of the actual machine varies due to the position of the load device, a stable high-speed and high-precision control can be enabled, which does not cause unusual sound or vibration. At the same time, because the data of the frequency characteristic of the actual machine can be formulated to the optimization problem without any processing, there is no effort for modeling, and a controller can be designed in consideration of all of the resonance characteristics.

[0037] In the present example configuration, a machine tool having a shaft for driving a table from a motor via a ball screw is exemplified. However, the technique of the present disclosure is also applicable to a shaft in which the load device is a spindle head, or to a machine tool driven by a linear motor, and is also applicable to industrial machines other than the machine tool. In addition, in the above description, the embodiment described above is described exemplifying a velocity control system, but the structure of the velocity control system is not important, and the technique is also applicable to a position control system, and a cascaded control system in which the position and velocity control systems are combined.