Error compensation system and method for numerical control (NC) machine tool based on iterative learning control

An error compensation system for a numerical control (NC) machine tool based on iterative learning control, comprising:

• a trajectory generating module;
• a down-sampling module;
• a position controller;
• a first holder;
• a velocity-loop iterative learning controller;
• a velocity controller;
• a second holder;
• and
• a control plant;
• wherein the control plant comprises a motor and a mechanical transmission module;
• the trajectory generating module is configured to generate a desired trajectory command;
• the desired trajectory command comprises a first sampling command;
• the first sampling command is configured to be transmitted to the down-sampling module and the velocity-loop iterative learning controller;
• the first sampling command rf is down-sampled by the down-sampling module to obtain a second sampling command rs;
• a sampling rate of the first sampling command is larger than a sampling rate of the second sampling command;
• the velocity-loop iterative learning controller is configured to receive the first sampling command;
• the velocity-loop iterative learning controller is also configured to obtain a first sampling error compensation sequence according to a first sampling error sequence and a first sampling error compensation sequence of a previous iteration machining process stored in the velocity-loop iterative learning controller;
• the velocity-loop iterative learning controller comprises a memory and an iterative learning controller;
• the first sampling error sequence of the previous iteration machining process of the NC machine tool is expressed as ej-1;
• the first sampling command is expressed as rf;
• the first sampling error sequence ej-1 of previous iteration is a difference between the first sampling command rf and a displacement y of a sliding table of the NC machine tool;
• the first sampling error compensation sequence of the previous iteration is expressed as uj-1;
• the memory is configured to store the first sampling error sequence ej-1 and the first sampling error compensation sequence uj-1 of the previous iteration machining process;
• after the first sampling error sequence ej-1 and the first sampling error compensation sequence uj-1 are input to the iterative learning controller, the iterative learning controller is configured to obtain the first sampling error compensation sequence uj through iterative calculation using a proportional-derivative (PD) method, expressed as:
• u
• j
• =
• Q
• ⁡
• (
• u
• j
• -
• 1
• +
• Γ
• p
• ⁢
• e
• j
• -
• 1
• +
• Γ
• d
• ⁢
• de
• j
• -
• 1
• dt
• )
• ;
• (
• 1
• )
• wherein j is the number of iterations;
• Γp and Γd respectively represent an iterative learning gain;
• Q represents a low-pass filtering process;
• ej-1 is the first sampling error sequence;
• the position controller is configured to receive a difference between the second sampling command output by the down-sampling module and the displacement y of the sliding table of the NC machine tool, and output a velocity control signal, and the velocity control signal is held by the first holder, and input to the velocity controller after compared with real-time velocity of the sliding table of the NC machine tool;
• a mathematical realization expression of the first holder is shown as follows:
• Hu=HNSuN;
• wherein HN represents the second holder, which is configured as a zero-order holder;
• SuN represents an up-sampling process;
• and the zero-order holder is expressed as:
• H
• N
• =
• ∑
• f
• =
• 0
• N
• ⁢
• z
• -
• f
• ;
• the up-sampling process SuN is expressed as:
• S
• u
• N
• ⁢
• :
• ⁢
• u
• ⁡
• [
• n
• ]
• →
• u
• ′
• ⁡
• [
• n
• ]
• u
• ′
• ⁡
• [
• n
• ]
• =
• {
• u
• ⁡
• [
• n
• 1
• N
• ]
• ,
• when
• ⁢
• ⁢
• n
• i
• ∈
• n
• ⁢
• n
• i
• N
• ∈
• Z
• 0
• ;
• wherein Z is a time-shift operator;
• the velocity controller is configured to output a current signal;
• the current signal is configured to be superimposed on the first sampling error compensation sequence and transmitted to the second holder;
• the second holder is configured to drive the motor to rotate to drive the mechanical transmission module to move, such that the mechanical transmission module drives the sliding table of the NC machine tool to move to output an actual displacement y of the sliding table of the NC machine tool.