US 11,494,465 B2 · Command value interpolation apparatus and servo driver

Abstract

Provided is an interpolation technique in which command values chronologically input can be interpolated without increasing a jerk and with less follow-up delay with respect to a command. A control unit (10) of a servo driver (20) has a function of sequentially generating, on the basis of four command values from x(k−2) to x(k+1), a kth interpolation function for calculating command values in a kth (≥3) time interval and a function of generating, as the kth interpolation function, a fifth-order equation with respect to time in which function values at a start time and an end time of the kth time interval match x(k) and x(k+1), respectively, and in which a second derivative value at a start time of the kth time interval matches a second derivative value at an end time of a (k−1)th time interval corresponding to a (k−1)th interpolation function.

A command value interpolation apparatus that interpolates a command value x(k) sequentially input (where k is an integer value indicating an order of input of the command value) at a predetermined cycle ts, the command value interpolation apparatus comprising a processor configured with a program to perform operations for driving a servo driver, the operations comprising:

generating a kth interpolation function yk(t) in which function values at a start time yk(t=0) and an end time yk(t=ts) of a kth time interval match a command value x(k) and a command value x(k+1), respectively, for each k value of greater than or equal to 1 in ascending order of k values;
and
repeating, in the ascending order of the k values, processing for calculating a plurality of command output values in the kth time interval by using the kth interpolation function yk(t), the command output values provided to the servo driver, wherein
generating the kth interpolation function yk(t) comprises generating, on the basis of four command values comprising a command value x(k−2) to a command value x(k+1), the kth (where k≥3) interpolation function yk(t),
the kth (where k≥3) interpolation function yk(t) is generated, using the four command values, as a fifth-order equation with respect to time such that function values at the start time yk(t=0) and the end time yk(t=ts) of the kth time interval match a command value x(k) and a command value x(k+1), respectively, and
the kth interpolation function yk(t) is generated such that a second derivative value of the generated kth interpolation function yk(t) at a start time of the kth time interval matches a second derivative value of a generated (k−1)th interpolation function yk−1(t) at an end time of a (k−1)th time interval, wherein the processor is configured with the program to perform operations such that;
generating, using the four command values, the kth (where k≥3) interpolation function yk(t) as the fifth-order equation with respect to time in which function values at the start time and the end time of the kth time interval match the command value x(k) and the command value x(k+1), respectively, comprises generating the kth interpolation function yk(t) such that a first derivative value and the second derivative value of the generated kth interpolation function yk(t) at the start time of the kth time interval respectively match a first derivative value and the second derivative value of the generated (k−1)th interpolation function yk−1(t) at the end time of the (k−1)th time interval;
generating, using the four command values, the kth (where k≥3) interpolation function yk(t) as the fifth-order equation comprises generating the fifth-order equation with respect to an elapsed time t from the start time of the kth time interval, by calculating coefficients a1 to a6 that satisfy an equation (1):
[
a
1
a
2
a
3
a
4
a
5
a
6
]
=
[
0
0
1
0
1
2
⁢
t
s
-
4
2
⁢
t
s
3
2
⁢
t
s
0
1
2
⁢
t
s
2
-
2
2
⁢
t
s
2
1
2
⁢
t
s
2
0
-
9
2
⁢
t
s
3
27
2
⁢
t
s
3
-
27
2
⁢
t
s
3
9
2
⁢
t
s
3
11
2
⁢
t
s
4
-
33
2
⁢
t
s
4
33
2
⁢
t
s
4
-
11
2
⁢
t
s
4
-
2
t
s
5
6
t
s
5
-
6
t
s
5
2
t
s
5
]
·
[
x
⁡
(
k
-
2
)
x
⁡
(
k
-
1
)
x
⁡
(
k
)
x
⁡
(
k
+
1
)
]
(
1
)
as zero-order to fifth-order coefficients, respectively.

166 more elements

Facts

Application

16/644,526Filed 2 Nov 2018

Priority

JP JP2017-2163179 Nov 2017

Published

US 2020/0285689 A110 Sep 2020

Granted

8 Nov 2022

Term ends

Not estimatedThe source records don’t support an estimate.

Classification7 codes

G05B 19/404
Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to…
G06F 17/175
Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method: of multidimensional data
G05B 19/4103
Characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and…:…
G06F 17/17
Complex mathematical operations: function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method

Command value interpolation apparatus and servo driver

Life of this patent

Command value interpolation apparatus and servo driver

Life of this patent

Abstract

Claims8