CN105068535A - Extraction method for first iteration control signals of XY motion platform - Google Patents

Abstract

The invention relates to an extraction method for first iteration control signals of an XY motion platform. The method comprises the following steps that 1) a reference locus similar to an expected tracking locus is searched in a base coordinate system of the XY motion platform; 2) the first iteration control signal of the jth segment ldj(x(t),y(t)) of the expected locus ld(x(t),y(t)) is extracted; and 3) the first iteration control signals of elements of the locus segment are transformed and spiced to obtain the first iteration control signal of ld(x(t),y(t)).

Description

A kind of first iterating control signal extracting method of XY motion platform

(1) technical field

The invention belongs to the application of iterative learning control technology in XY motion platform Trajectory Tracking Control.

(2) background technology

XY motion platform realizes reference locus by control XY spindle motor and follows the tracks of, and when carrying out repetitive operation task, iterative learning controls (IterativeLearningControl is called for short ILC) application of having succeeded; But current operation task was from task was different in the past, and the repeat property of conventional I LC limits its application.In fact, ILC is a kind of typically based on the control method of data-driven, is characterized in that the data learning (or approaching) from repeating operation generation goes out control signal; But no matter whether system repeats operation, the dynamic law of its inherence is necessarily buried in the data that operation process produces, especially with the data of current work similar process.XY motion platform reference locus can be in series by a series of track primitive, from the control signal of the track of operation learning accumulation in the past primitive, when facing new reference locus, carry out track primitive Optimized Matching, find similar track primitive successively, through the similar reference locus of series connection synthesis, extract its motion control signal and as the first iterating control signal of current work after carrying out signal transacting, analysis and compensation; This can be avoided directly going to find reference locus similar between whole operation area, also be zero (or other preset value) by changing the first iterating control signal of conventional I LC, between operation area and job task (or reference locus) change need the situation that relearns.Thus also can expand the application of ILC.

(3) summary of the invention

The present invention will overcome the above-mentioned shortcoming of prior art, provides a kind of first iterating control signal extracting method of XY motion platform,

The first iterating control signal extracting method of a kind of XY motion platform of the present invention, comprises the steps:

Step1. for an XY motion platform, the desired trajectory described under basis coordinates system (or { B} coordinate system) ^bl _dthe control signal of (x (t), y (t)) (wherein t ∈ [0, T]) can control to obtain by traditional iterative learning.Wherein

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Note: the track under basis coordinates system (or { B} coordinate system) ^bl _d(x (t), y (t)) can be abbreviated as l _d(x (t), y (t)), after relate to track under basis coordinates system all unification write a Chinese character in simplified form.

The similar reference locus expecting pursuit path need be found; If l _dj(x (t), y (t)) is desired trajectory l _dthe jth section track of (x (t), y (t)), l _j(x (t), y (t)) is one section of track primitive, wherein t ∈ (0, t in track storehouse _j); A given similarity ε >0, for track l _dj(x (t), y (t)) and l _j(x (t), y (t)), by rotational transform R _jwith translation transformation P _djORG, lowest mean square root error is between the two less than ε; Then claim under similarity ε, there is the similar reference locus expecting pursuit path, its jth section track is

l _dj(x(t),y(t))≈R _j· ^jl _j(x(t),y(t))+P _djORGj∈[1,n](2)

Wherein, P _djORGrepresent track l _djthe geocentric coordinate system of (x (t), y (t)) initial point of dj} relative to basis coordinates system the position of the initial point of B},

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Step2. desired trajectory l is extracted _dthe jth section track l of (x (t), y (t)) _djthe first iterating control signal of (x (t), y (t))

u _0dj(t)≈R _j· ^ju _j(t)+u{P _djORG}j∈[1,n](3)

Wherein, ^ju _jt () is track primitive l _j(x (t), y (t)) description under geocentric coordinate system ^jl _jthe control signal of (x (t), y (t)), u{P _djORGp _djORGcontrol signal;

Step3. the first iterating control signal of segmentation track primitive converted and spliced, obtaining l _dthe first iterating control signal of (x (t), y (t))

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Wherein u _0dxt () is x _dthe first iterating control signal of (t), u _0dyt () is y _dthe first iterating control signal of (t).

Three kinds of situations as shown in Figure 1 for occurring in track primitive stitching portion, front and back: 1., orbit segment intersects, 2., orbit segment is discontinuous, and 3., orbit segment is connected continuously.Therefore, in track primitive stitching portion, front and back, by linear interpolation method, transitional zone is introduced to control signal, realize control signal no-harass switch, obtain the first iterating control signal of desired trajectory;

Step31. 1. plant situation for, as shown in Figure 2, get l " _jthe end d of (x (t), y (t)) _jwith l " _j+1the top a of (x (t), y (t)) _j+1central point O, and with this point for the center of circle, r is transitional zone radius, meets at a c respectively _j, b _j+1.A _jl " _jthe top point of (x (t), y (t)), b _ja upper transitional zone and l " _jthe intersection point of (x (t), y (t)), c _j+1next transitional zone and l " _j+1the intersection point of (x (t), y (t)), d _j+1l " _j+1the distal point of (x (t), y (t)).

Then the time interval of transitional zone is:

T _j＝t _b(j+1)-t _cj(5)

Wherein, t _{b (j+1)}for a b _j+1at desired trajectory l _djmoment on (x (t), y (t)), t _cjfor a c _jat desired trajectory l _djmoment on (x (t), y (t)).

The error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is:

ΔT _j＝T _j-(t _cdj+t _ab(j+1))(6)

Wherein, t _cdjtrack l " _j(x (t), y (t)) upper some c _jwith a d _jbetween time interval length, t _{ab (j+1)}track l " _j+1(x (t), y (t)) upper some a _j+1with a b _j+1between time interval length.

Wherein,

l″ _j(x(t),y(t))＝R _j· ^jl _j(x(t),y(t))+P _djORG(7)

In the transition zone, c is put _jwith a b _j+1corresponding control signal is respectively u _cjand u _{b (j+1)}, then at control signal u _cjand u _{b (j+1)}no-harass switch is carried out by the method for linear interpolation.Treated control signal leaves u in _jf(t), t ∈ [0, T _j];

Wherein: u _jft () refers to the control signal of a jth transitional zone;

Step32. situation 2., is 3. planted for, as shown in Figure 3,4, similar, the time interval of transitional zone can be obtained such as formula shown in (5), the error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is such as formula shown in (6), but the Δ T that 1. plant situation _j<0, the Δ T 2. planting situation _j>0,3. the plant situation Δ T _j<0;

Step33. desired trajectory l _d(x (t), y (t)) by n section track primitive through the approximate acquisition of affined transformation, then the first iterating control signal of desired trajectory is:

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Wherein, u ₁(t), t ∈ [0, t _c1] be track l " ₁(x (t), y (t)), t ∈ [0, t _c1] control signal, u ₁(t), t ∈ [0, t _c1] be track l " ₁(x (t), y (t)), t ∈ [0, t _c1] control signal; the control signal u of first transitional zone _1f(t), t ∈ [0, T ₁] to right translation t _c1the control signal that time span obtains; track l " ₂(x (t), y (t)), t ∈ [t _b2, t _c2] to right translation (t _c1+ T ₁-t _b2) time span obtain control signal; the control signal u of second transitional zone _2f(t), t ∈ [0, T ₂] to right translation (t _c1+ T ₁+ t _c2-t _b2) time span obtain control signal; track l " ₃(x (t), y (t)), t ∈ [t _b3, t _c3] to right translation (t _c1+ T ₁+ t _c2-t _b2+ T ₂-t _b3) time span obtain control signal; track l " _n(x (t), y (t)), t ∈ [t _bn, t _cn] to right translation the control signal that time span obtains; mathematic(al) representation formula (9) shown in:

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The extracting method of the first iterating control signal that the iterative learning that the present invention proposes XY motion platform controls, effectively can solve the problem that first iterating control signal is zero (or other preset value), reference locus change needs relearn, improve learning efficiency, effectively decrease study number of times, and significantly can reduce the tracking error of first iteration control.

Accompanying drawing explanation

Fig. 1 is three kinds of situations that track stitching portion occurs: 1., orbit segment intersects, and 2., orbit segment is discontinuous, and 3., orbit segment is connected continuously.

Fig. 2 is that the design drawing of transitional zone when 1. planting situation appears in track stitching portion, gets l " _jthe end d of (x (t), y (t)) _jwith l " _j+1the top a of (x (t), y (t)) _j+1central point O, and with this point for the center of circle, r is transitional zone radius, meets at a c respectively _j, b _j+1.A _jl " _jthe top point of (x (t), y (t)), b _ja upper transitional zone and l " _jthe intersection point of (x (t), y (t)), c _j+1next transitional zone and l " _j+1the intersection point of (x (t), y (t)), d _j+1l " _j+1the distal point of (x (t), y (t)).

Fig. 3 is that the design drawing of transitional zone when 2. planting situation appears in track stitching portion.

Fig. 4 is that the design drawing of transitional zone when 3. planting situation appears in track stitching portion.

Fig. 5 is that embodiment XY motion platform follows the tracks of desired trajectory l _d(x (t), y (t)).

Fig. 6 is segmentation desired trajectory and the geocentric coordinate system thereof that embodiment XY motion platform follows the tracks of desired trajectory.

Fig. 7 is the similar track primitive in embodiment.

Fig. 8 is that similar track primitive in embodiment is spliced similar desired trajectory.

Fig. 9 is the first iterating control signal of the X-axis desired trajectory extracted in embodiment.

Figure 10 is the first iterating control signal of the Y-axis desired trajectory extracted in embodiment.

Figure 11 is the first iteration control tracking error of X in embodiment, Y-axis.

The RMS comparison diagram that Figure 12 is X in embodiment, Y-axis adopts the error of the inventive method and conventional I LC method.

Embodiment

Below in conjunction with drawings and Examples, technical scheme of the present invention is further described.

If the displacement of each axle of XY motion platform and the linear dynamics of motor input current can be approximately such as formula the second order master pattern shown in (12).

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A first iterating control signal extracting method for XY motion platform, comprises the steps:

Step1. for the expectation pursuit path l as shown in Figure 5 that XY motion platform describes under basis coordinates system _d(x (t), y (t)), segmentation desired trajectory and geocentric coordinate system thereof as shown in Figure 6, wherein:

l _d(x(t),y(t))＝{l _d1(x(t),y(t)),l _d2(x(t),y(t)),l _d3(x(t),y(t))}(1)

Under the condition of similarity ε=0.1, similar track primitive as shown in Figure 7, wherein

Step2. desired trajectory l is extracted _dthe jth section track l of (x (t), y (t)) _djthe first iterating control signal of (x (t), y (t))

u _0dj(t)≈R _j· ^ju _j(t)+u{P _djORG}j∈[1,n](3)

Wherein: n=3, ^ju _jt () is track primitive l _j(x (t), y (t)) description under geocentric coordinate system ^jl _jthe control signal of (x (t), y (t)), u{P _djORGp _djORGcontrol signal;

Step3. the first iterating control signal of segmentation track primitive converted and spliced, obtaining l _dthe first iterating control signal of (x (t), y (t))

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Wherein: u _0dxt () is x _dthe first iterating control signal of (t), u _0dyt () is y _dthe first iterating control signal of (t).

Three kinds of situations as shown in Figure 1 for occurring in track primitive stitching portion, front and back: 1., orbit segment intersects, 2., orbit segment is discontinuous, and 3., orbit segment is connected continuously.Therefore, in track primitive stitching portion, front and back, by linear interpolation method, transitional zone is introduced to control signal, realize control signal no-harass switch, obtain the first iterating control signal of desired trajectory;

Step31. 1. plant situation for, as shown in Figure 2, get l " _jthe end d of (x (t), y (t)) _jwith l " _j+1the top a of (x (t), y (t)) _j+1central point O, and with this point for the center of circle, r is transitional zone radius, meets at a c respectively _j, b _j+1.A _jl " _jthe top point of (x (t), y (t)), b _ja upper transitional zone and l " _jthe intersection point of (x (t), y (t)), c _j+1next transitional zone and l " _j+1the intersection point of (x (t), y (t)), d _j+1l " _j+1the distal point of (x (t), y (t)).

Then the time interval of transitional zone is:

T _j＝t _b(j+1)-t _cj(5)

Wherein, t _{b (j+1)}for a b _j+1at desired trajectory l _djmoment on (x (t), y (t)), t _cjfor a c _jat desired trajectory l _djmoment on (x (t), y (t)).

The error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is:

ΔT _j＝T _j-(t _cdj+t _ab(j+1))(6)

Wherein, t _cdjtrack l " _j(x (t), y (t)) upper some c _jwith a d _jbetween time interval length, t _{ab (j+1)}track l " _j+1(x (t), y (t)) upper some a _j+1with a b _j+1between time interval length.

Wherein,

l″ _j(x(t),y(t))＝R _j· ^jl _j(x(t),y(t))+P _djORG(7)

In the transition zone, c is put _jwith a b _j+1corresponding control signal is respectively u _cjand u _{b (j+1)}, then at control signal u _cjand u _{b (j+1)}no-harass switch is carried out by the method for linear interpolation.Treated control signal leaves u in _jf(t), t ∈ [0, T _j];

Wherein: u _jft () refers to the control signal of a jth transitional zone;

Step32. situation 2., is 3. planted for, as shown in Figure 3,4, similar, the time interval of transitional zone can be obtained such as formula shown in (5), the error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is such as formula shown in (6), but the Δ T that 1. plant situation _j<0, the Δ T 2. planting situation _j>0,3. the plant situation Δ T _j<0;

Step33. desired trajectory l _d(x (t), y (t)) by n section track primitive through the approximate acquisition of affined transformation, then the first iterating control signal of desired trajectory is:

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Wherein, u ₁(t), t ∈ [0, t _c1] be track l " ₁(x (t), y (t)), t ∈ [0, t _c1] control signal, u ₁(t), t ∈ [0, t _c1] be track l " ₁(x (t), y (t)), t ∈ [0, t _c1] control signal; the control signal u of first transitional zone _1f(t), t ∈ [0, T ₁] to right translation t _c1the control signal that time span obtains; track l " ₂(x (t), y (t)), t ∈ [t _b2, t _c2] to right translation (t _c1+ T ₁-t _b2) time span obtain control signal; the control signal u of second transitional zone _2f(t), t ∈ [0, T ₂] to right translation (t _c1+ T ₁+ t _c2-t _b2) time span obtain control signal; track l " ₃(x (t), y (t)), t ∈ [t _b3, t _c3] to right translation (t _c1+ T ₁+ t _c2-t _b2+ T ₂-t _b3) time span obtain control signal; mathematic(al) representation formula (9) shown in:

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Transitional zone in stitching portion as shown in Figure 8.Wherein, r ₁=0.85, r ₂=1.52.In addition, the method proposed by the present invention, the X of extraction, the control signal of Y-axis desired trajectory are as shown in Fig. 9,10.

Carry out Iterative Learning Control Simulation experiment; 1st iterative learning, as shown in figure 11, tracking error is 0.112 to the maximum to the first tracking error of X, Y-axis, and the first tracking error tracking error of Y-axis is 0.093 to the maximum.In addition, the first iterating control signal extract the method adopting the present invention to propose and the first iterating control signal of classic method have done contrast, as shown in figure 12; In fig. 12, desired trajectory x _dthe RMS of the 1st secondary tracking error of t method that () adopts the present invention to propose is 0.152, is 0.035 at the 3rd time; The RMS adopting the 1st secondary tracking error of classic method is 4.500, and the 5th is 0.038; Desired trajectory y _d(t) adopt method in this paper first time tracking error RMS be 0.160, third time be 0.039; The RMS adopting the 1st secondary tracking error of classic method is 2.234, and the 5th is 0.043.

Therefore, the method that the present invention proposes is practicable, the first iterating control signal extracted is approximately the desired control signal of track, effectively can solve the problem that first iterating control signal is zero (or other preset value), reference locus change needs relearn, improve learning efficiency, effectively decrease study number of times, and significantly can reduce the tracking error of first iteration control.

Claims (2)

1. a first iterating control signal extracting method for XY motion platform, comprises the steps:

Step1. for the expectation pursuit path that XY motion platform describes under basis coordinates system

$l_d\left(x\right(t),y(t\left)\right)=\left[\begin{array}{c}{x}_d\left(t\right)\\ y_d\left(t\right)\end{array}\right]---\left(1\right)$

The similar reference locus expecting pursuit path need be found; If l _dj(x (t), y (t)) is desired trajectory l _dthe jth section track of (x (t), y (t)), l _j(x (t), y (t)) is one section of track primitive, wherein t ∈ (0, t in track storehouse _j); A given similarity ε >0, for track l _dj(x (t), y (t)) and l _j(x (t), y (t)), by rotational transform R _jwith translation transformation P _djORG, lowest mean square root error is between the two less than ε; Then claim under similarity ε, there is the similar reference locus expecting pursuit path, its jth section track is

l _dj(x(t),y(t))≈R _j· ^jl _j(x(t),y(t))+P _djORGj∈[1,n](2)

Wherein, P _djORGrepresent track l _djthe geocentric coordinate system of (x (t), y (t)) initial point of dj} relative to basis coordinates system the position of the initial point of B},

$R_j=\left[\begin{array}{cc}cos\mathrm{\&theta;}& -sin\mathrm{\&theta;}\\ sin\mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right];$

Step2. desired trajectory l is extracted _dthe jth section track l of (x (t), y (t)) _djthe first iterating control signal of (x (t), y (t))

u _0dj(t)≈R _j· ^ju _j(t)+u{P _djORG}j∈[1,n](3)

Wherein, ^ju _jt () is track primitive l _j(x (t), y (t)) description under geocentric coordinate system ^jl _jthe control signal of (x (t), y (t)), u{P _djORGp _djORGcontrol signal;

Step3. the first iterating control signal of segmentation track primitive converted and spliced, obtaining l _dthe first iterating control signal of (x (t), y (t))

$u_{0d}\left(t\right)=\left[\begin{array}{c}{u}_{0dx}\left(t\right)\\ u_{0dy}\left(t\right)\end{array}\right]---\left(4\right)$

Wherein u _0dxt () is x _dthe first iterating control signal of (t), u _0dyt () is y _dthe first iterating control signal of (t).

2. the first iterating control signal extracting method of XY motion platform as claimed in claim 1; it is characterized in that: described in Step3, be spliced into the first iterating control signal method of desired trajectory by segmentation track primitive control signal; three kinds of situations for occurring in track primitive stitching portion, front and back: 1., orbit segment intersects; 2. before and after, orbit segment is discontinuous, and 3., orbit segment is connected continuously.By linear interpolation method, transitional zone is introduced to control signal, realize control signal no-harass switch, obtain the first iterating control signal of desired trajectory;

Step31. 1. plant situation for the, the time interval of setting transitional zone is:

T _j＝t _b(j+1)-t _cj(5)

Wherein, t _{b (j+1)}for a b _j+1at desired trajectory l _djmoment on (x (t), y (t)), t _cjfor a c _jat desired trajectory l _djmoment on (x (t), y (t));

The error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is:

ΔT _j＝T _j-(t _cdj+t _ab(j+1))(6)

Wherein, t _cdjtrack l " _j(x (t), y (t)) upper some c _jwith a d _jbetween time interval length, t _{ab (j+1)}track l " _j+1(x (t), y (t)) upper some a _j+1with a b _j+1between time interval length;

Wherein,

l″ _j(x(t),y(t))＝R _j· ^jl _j(x(t),y(t))+P _djORG(7)

In the transition zone, c is put _jwith a b _j+1corresponding control signal is respectively u _cjand u _{b (j+1)}, then at control signal u _cjand u _{b (j+1)}between carry out no-harass switch by the method for linear interpolation; Treated control signal leaves u in _jfin (t), t ∈ [0, T _j];

Wherein: u _jft () refers to the control signal of a jth transitional zone;

Step32. situation 2., is 3. planted for, similar with Step31, the time interval of transitional zone can be obtained such as formula shown in (5), the error of the time span of the approximate trajectories after transitional zone process and the time span of desired trajectory is such as formula shown in (6), but the Δ T that 1. plant situation _j<0, the Δ T 2. planting situation _j>0,3. the plant situation Δ T _j<0;

Step33. the first iterating control signal of desired trajectory is:

$u_{0d}=\{u_1\left(t\right),\stackrel{\&OverBar;}{u_{1f}\left(t\right)},\stackrel{\&OverBar;}{u_2\left(t\right)},\stackrel{\&OverBar;}{u_{2f}\left(t\right)},\stackrel{\&OverBar;}{u_3\left(t\right)},...,\stackrel{\&OverBar;}{u_n\left(t\right)}\}---\left(8\right)$

Wherein, u ₁(t), t ∈ [0, t _c1] be track l " ₁(x (t), y (t)), t ∈ [0, t _c1] control signal; the control signal u of first transitional zone _1f(t), t ∈ [0, T ₁] to right translation t _c1the control signal that time span obtains; track l " ₂(x (t), y (t)), t ∈ [t _b2, t _c2] to right translation (t _c1+ T ₁-t _b2) time span obtain control signal; the control signal u of second transitional zone _2f(t), t ∈ [0, T ₂] to right translation (t _c1+ T ₁+ t _c2-t _b2) time span obtain control signal; track l " ₃(x (t), y (t)), t ∈ [t _b3, t _c3] to right translation (t _c1+ T ₁+ t _c2-t _b2+ T ₂-t _b3) time span obtain control signal; track l " _n(x (t), y (t)), t ∈ [t _bn, t _cn] to right translation the control signal that time span obtains; mathematic(al) representation formula (9) shown in:

$\begin{array}{c}\stackrel{\&OverBar;}{u_{1f}\left(t\right)}=u_{1f}\left(t-t_{c1}\right),t\&Element;(t_{c1},t_{c1}+T_1\&rsqb;\\ \stackrel{\&OverBar;}{u_2\left(t\right)}=u_2\left(t-\left(t_{c1}+T_1-t_{b2}\right)\right),t\&Element;(t_{c1}+T_1,t_{c1}+T_1+t_{c2}-t_{b2}\&rsqb;\\ \stackrel{\&OverBar;}{u_{2f}\left(t\right)}=u_{2f}\left(t-\left(t_{c1}+T_1+t_{c2}-t_{b2}\right)\right),\\ t\&Element;\left(t_{c1}+T_1+t_{c2}-t_{b2},t_{c1}+T_1+t_{c2}-t_{b2}+T_2\right),\\ \stackrel{\&OverBar;}{u_3\left(t\right)}=u_3\left(t-\left(t_{c1}+T_1+t_{c2}-t_{b2}+T_2-t_{b3}\right)\right),\\ t\&Element;\left(t_{c1}+T_1+t_{c2}-t_{b2}+T_2,t_{c1}+T_1+t_{c2}-t_{b2}+T_2+t_{c3}-t_{b3}\right)\\ .\\ .\\ .\\ \stackrel{\&OverBar;}{u_n\left(t\right)}=u_n\left(t-\underset{j=1}{\overset{n-1}{\mathrm{\&Sigma;}}}\left(t_{cj}+T_j-t_{b\left(j+1\right)}\right)\right)\\ t\&Element;\left(\underset{j=1}{\overset{n-1}{\mathrm{\&Sigma;}}}\left(t_{cj}+T_j-t_{b\left(j+1\right)}\right)+t_{bn},T\right)\end{array}---\left(9\right)$