CN102298323A - Adaptive control method of auto-leveling system - Google Patents

Abstract

The invention provides an adaptive control method of an auto-leveling system. The method provided in the invention is characterized in that the method comprises the following steps that: step1, a two pen recorder is used to record an input curve and an output curve of an auto-leveling system under the effect of a pseudo-code generator; step 2, discretization is carried out on the output curve recorded by the two pen recorder and a controllable autoregressive moving average model of the auto-leveling system is identified according to a generalized least squares method; step 3, a control input quantity uk at time k is calculated and obtained by taking a principle that a steady variance is minimum, wherein at the time k, the control input quantity uk enables a steady variance of an output yk+d of the auto-leveling system at time k+d to be minimum. According to the method provided in the invention, prediction can be carried out with d steps advanced, so that an adverse effect of a leveling dead zone of a closed loop system is reduced; and meanwhile, a feedback control effect of the closed loop system can be reserved. After the control method is utilized, the closed loop system has a strong anti-interference capability and interferences of various non-linear factors can also be eliminated basically, so that a uniformity for outputs of cotton slivers can be further improved.

Description

The self-adaptation control method of a kind of autoleveller system

Technical field

The present invention relates to the self-adaptation control method of a kind of autoleveller system, belong to the industrial control field of cotton spinning self-regulating technology.

Background technology

Autoleveller is as self-regulating a kind of form, and it can change the speed of input roller (or delivery roller) according to the line density of input sliver (or output sliver) and the difference of ratings, thereby correspondingly regulates the drafting multiple of drafting assembly.The weight that guarantees output sliver fluctuates in allowed limits.

The autoleveller system can be divided into open loop control, closed-loop control and hybrid ring control according to its control model at present.

1) open loop autoleveller system

The principle of work of open cycle system is " it is neat and well spaced to detect the back earlier ", promptly carries out neat and well spaced action by the variation that detects the feeding cotton stripline density, and this method need guarantee that the time delay of system is consistent by the time between check point and the neat and well spaced point with sliver.Open cycle system has regulating effect preferably to short-movie section sliver inequality.But open cycle system is only carried out the specific aim adjusting, can not appraise and decide the adjusting result.The deviation that each link parameter changes or external interference causes also can't be revised, and easily makes strip quantitatively produce deviation, so the less stable of open cycle system operation.

2) closed loop autoleveller system

Closed-loop control is by feedback principle work, and promptly earlier neat and well spaced back is detected, so its neat and well spaced dead band of existence, and this has just determined that closed-loop system mainly is neat and well spaced sliver inequality than long segment.Because the effect of closed-loop system backfeed loop can be revised the deviation that the various factors fluctuation is produced automatically, stability better.But it is not good to the disconnected even and orderly effect of short-movie, and the control specific aim is not strong.

3) hybrid ring autoleveller system

The hybrid ring system is that existing open loop has closed loop again in the drawing-off Adjustment System, has the advantage of the two concurrently.This in theory method is science the most, but because its complex structure is not easy control and cost is also higher.In addition, the hybrid ring system is 2 detections, and is a bit neat and well spaced, generally is to carry out fuzzy control on the basis of the fuzzy rule of a cover, and its prerequisite is exactly on certain error basis, rather than real-time response control.

Because the plucked of sliver is the irregular fluctuation of a kind of complexity, and the measuring accuracy of pick-up unit, also be subjected to various effect of non-linear easily, for example: give cotton speed, the fluctuation of electron device operating voltage, the work dead band of measuring sensor etc., thus make neat and well spaced effect often have bigger error.If adopt closed-loop system when neat and well spaced, control algolithm commonly used is " proportional-integral-differential " (being the PID method).This moment, PID played FEEDBACK CONTROL, promptly, the line density of output sliver is remained near the setting value according to the drafting multiple of the difference adjusting machine of the line density of neat and well spaced back sliver and ratings (ratings can be determined according to the specified drafting multiple of the setting value of output and input, output).For today sliver exporting speed up to the High-speed Drawing Frame of 600-1000m/s, the PID method is difficult to satisfy the control requirement.

Summary of the invention

The purpose of this invention is to provide a kind of self-adaptation control method that suppresses closed-loop system neat and well spaced dead band influence.

In order to achieve the above object, technical scheme of the present invention has provided the self-adaptation control method of a kind of autoleveller system, it is characterized in that step is:

Step 1, be recorded under the pseudo-code generator effect input curve of autoleveller system and curve of output with two-pen recorder;

Step 2, the curve of output discretize that two-pen recorder is noted pick out the controlled autoregressive moving-average model of autoleveller system according to generalized least square method, are expressed as:

Wherein, d represents to import the retardation time to output, y _K+dThe expression k+d output of autoleveller system constantly, u _kExpression k input controlled quentity controlled variable constantly, ξ _K+dExpression k+d is white noise sequence constantly, A (z ^-1)=1-a ₁z ^-1-...-a _nz ^-n, B (z ^-1)=b ₀+ b ₁z ^-1+ ... + b _nz ^-n, C (z ^-1)=1+c ₁z ^-1+ ... + c _nz ^-n, wherein, u _kZ ^-n=u _K-n, ξ _K+dZ ^-n=ξ _K+d-n, be illustrated respectively in k-n constantly the input controlled quentity controlled variable and at k+d-n white noise sequence constantly, other by that analogy, a ₁To a _n, b ₀To b _nAnd c ₁To c _nBe respectively corresponding coefficient;

Step 3, be principle, obtain at k and make the autoleveller system constantly at the k+d output y of autoleveller system constantly with stable state variance minimum _K+dThe control input quantity u of stable state variance minimum _k,

Wherein, F (z ^-1) be

Merchant's formula, G (z ^-1) be

Residue multiply by z ^d, y _{M (k+d)}Be the k+d ideal output of autoleveller system constantly, y _kFor the k actual output of autoleveller system constantly, with k control input quantity u constantly _kCompensate random perturbation influence to the output of autoleveller system in the k+d moment.

Principle of work of the present invention is: controller exists the autoleveller system that d step lags behind to what identification was come out, and the d step is predicted in advance, calculates suitable regulating action according to predicted value then, with compensation since random perturbation at k+d constantly to the influence of output.Like this,, just can remain the stable state variance minimum of output quantity, also promptly keep the stable of output sliver line density by constantly sampling, forecast and controlling.

Method provided by the invention can shift to an earlier date d step to be predicted, has so both reduced the harmful effect in the neat and well spaced dead band of closed-loop system, keeps the FEEDBACK CONTROL effect of closed-loop system again.Closed-loop system has very strong antijamming capability after adopting this control algolithm, can eliminate the interference of various non-linear factors substantially, thereby the uniformity coefficient of output sliver is further improved.

Description of drawings

Fig. 1 is a DF-746 drawing frame closed-loop control system overall construction drawing;

Fig. 2 disturbs the control design sketch of method provided by the invention down for white noise;

Fig. 3 is that white noise disturbs PID control design sketch down.

Embodiment

For the present invention is become apparent, now with a preferred embodiment, and conjunction with figs. is described in detail below.

Present embodiment is an example with DF-746 drawing frame closed-loop control system as described in Figure 1, describes the self-adaptation control method of a kind of autoleveller provided by the invention system in detail, the steps include:

Step 1, be recorded under the pseudo-code generator effect input curve and the curve of output of DF-746 drawing frame closed-loop control system with two-pen recorder.Wherein, pseudo-code length, because the time constant of drafting system is not too big, pseudo-code length is difficult for selecting excessive, can select between 20 yards-50 yards when selecting.The pseudo-code amplitude, when selecting because the topworks that excessive amplitude may be damaged drawing frame, and non-linear factor also can increase accordingly, can be chosen in-scope of 1V-+1V in.Input curve is the pseudo-random code broken line that pseudo-code generator produces.Curve of output is that the situation of change of cotton stripline density is through the detected voltage of hydraucone pick-up unit (or electric current) curve of cyclical fluctuations.

Step 2, the curve of output discretize that two-pen recorder is noted pick out the controlled autoregressive moving-average model (English abbreviates the CARMA dynamic model as) of DF-746 drawing frame closed-loop control system according to generalized least square method, and the form of this model is:

y _k=a ₁y _K-1+ ... + a _ny _K-n+ b ₀u _K-d+ b ₁u _K-d-1+ ... + b _nu _K-d-n+ ξ _k+ c ₁ξ _K-1+ ... + c _nξ _K-n(1), wherein, y _kTo y _K-nRepresent k respectively constantly to the output of k-n drawing frame closed-loop control system constantly, i.e. cotton stripline density, ξ _kTo ξ _K-nRepresent that respectively k is constantly to k-n white noise sequence constantly, u _K-dTo u _K-d-nRepresent that respectively k-d is constantly to k-d-n input controlled quentity controlled variable constantly, a ₁To a _n, b ₀To b _nAnd c ₁To c _nBe respectively corresponding coefficient.

Formula (1) is expressed as transport function: A (z ^-1) y _k=z ^-dB (z ^-1) u _k+ C (z ^-1) ξ _k(2), wherein,

A(z ^-1)＝1-a ₁z ^-1-…-a _nz ^-n(3)，B(z ^-1)＝b ₀+b ₁z ^-1+…+b _nz ^-n(4)，C(z ^-1)＝1+c ₁z ^-1+…+c _nz ^-n(5)。For present embodiment, d is taken as 1, then A (z ^-1)=1-1.402z ^-1+ 0.524z ^-2, B (z ^-1)=0.0117z ^-1+ 0.00202z ^-2, C (z ^-1)=1-0.159z ^-1+ 0.0149z ^-2

D is the retardation time of output to input, main reflection since the existence in neat and well spaced dead band and testing agency, topworks's hysteresis quality in time to the influence of system.ξ _kBe that average is zero, variance is σ ²Independent random variable.Input after arrangement can be written as:

By formula (6) control action (u of slave controller as can be known _k) begin to act on and exist d step on the output sliver and postpone to actuator, promptly at the input delay k+d of system that k adds constantly constantly just at the output y of system _K+dIn display.

Utilize the Diophantine equation that the disturbance term in the formula (6) is resolved into two parts below:

$\frac{C\left(z^{-1}\right)}{A\left(z^{-1}\right)}=F\left(z^{-1}\right)+z^{-d}\frac{G\left(z^{-1}\right)}{A\left(z^{-1}\right)}---\left(7\right)$

With

C(z ^-1)＝A(z ^-1)F(z ^-1)+z ^-dG(z ^-1)?(8)

Wherein, F (z ^-1), G (z ^-1) be respectively d-1 time and n-1 order polynomial, i.e. F (z ^-1) be

Merchant's formula, z ^-dG (z ^-1) be

Residue.

F (z is multiply by on formula (6) both sides ^-1), have:

F(z ^-1)A(z ^-1)y _k+d＝F(z ^-1)B(z ^-1)u _k+F(z ^-1)C(z ^-1)ξ _k+d?(9)

By formula (8) a little conversion get:

A(z ^-1)F(z ^-1)＝C(z ^-1)-z ^-dG(z ^-1)?(10)

Formula (10) substitution formula (9) is got:

C(z ^-1)y _k+d-z ^-dG(z ^-1)y _k+d＝F(z ^-1)B(z ^-1)u _k+F(z ^-1)C(z ^-1)ξ _k+d?(11)

To following formula a little conversion get:

$y_{k+d}=\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k+F\left(z^{-1}\right){\mathrm{\ξ}}_{k+d}---\left(12\right).$

Step 3, be principle, obtain at k and make the autoleveller system constantly at the k+d output y of autoleveller system constantly with stable state variance minimum _K+dThe control input quantity u of stable state variance minimum _k, the steps include:

Utilize the Diophantine equation that the disturbance term in the formula (6) is resolved into two parts:

$\frac{C\left(z^{-1}\right)}{A\left(z^{-1}\right)}=F\left(z^{-1}\right)+z^{-d}\frac{G\left(z^{-1}\right)}{A\left(z^{-1}\right)}---\left(7\right)$

With

C (z ^-1)=A (z ^-1) F (z ^-1)+z ^-dG (z ^-1) (8), wherein, F (z ^-1), G (z ^-1) be respectively d-1 time and n-1 order polynomial, i.e. F (z ^-1) be

Merchant's formula, z ^-dG (z ^-1) be

Residue.

F (z is multiply by on formula (6) both sides ^-1), have:

F(z ^-1)A(z ^-1)y _k+d＝F(z ^-1)B(z ^-1)u _k+F(z ^-1)C(z ^-1)ξ _k+d?(9)

By formula (8) a little conversion get:

A(z ^-1)F(z ^-1)＝C(z ^-1)-z ^-dG(z ^-1)?(10)

Formula (10) substitution formula (9) is got:

C(z ^-1)y _k+d-z ^-dG(z ^-1)y _k+d＝F(z ^-1)B(z ^-1)u _k+F(z ^-1)C(z ^-1)ξ _k+d?(11)

To following formula a little conversion get:

$y_{k+d}=\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k+F\left(z^{-1}\right){\mathrm{\ξ}}_{k+d}---\left(12\right)$

Want to make the output sliver line density as far as possible consistent, just need find (by the effect of input controlled quentity controlled variable) optimum d step to forecast Y _K+d|k, make the variance minimum of prediction error, that is:

$J=E\left[{(y_{k+d}-y_{k+d|k})}^2\right]{|}_{Y_{k+d|k}}\→\min ---\left(13\right)$

Meaning of formula (13): ask for cotton stripline density predicted value y _K+d|kWith the actual input of cotton stripline density y _K+dSquare error and make its minimum, as the cardinal rule of adaptive control, just can make cotton stripline density basicly stable according to this principle, improve the sliver quality.

With formula (12) substitution formula (13),

$E\left[{(y_{k+d}-y_{k+d|k})}^2\right]=E\left\{{[\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k+F\left(z^{-1}\right){\mathrm{\ξ}}_{k+d}-y_{k+d|k}]}^2\right\}---\left(14\right)$

White noise sequence ξ in the formula (14) _K+d, ξ _K+d-1..., ξ _K+1With the measured value y that has learnt _k, y _K-1..., u _K-1, u _K-2... uncorrelated.So in the formula (14) right side preceding two and the 3rd be linearity independently, thereby have

$E\left[{(y_{k+d}-y_{k+d|k})}^2\right]=E\left\{{[\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k{-y}_{k+d|k}]}^2\right\}+E\left\{{\left[F\left(z^{-1}\right){\mathrm{\ξ}}_{k+d}\right]}^2\right\}---\left(15\right)$

Can select to make the minimum optimum precursor of cotton stripline density fluctuation to be:

$Y_{k+d|k}=\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k---\left(16\right)$

Formula (16) is the optimum precursor in d step forward, and it is at inputoutput data y _k, y _K-1..., u _K-1, u _K-2... the basis on the optimum forecast of square error minimum in the linear prediction that k+d is exported constantly.

Set k+d ideal constantly at this and be output as y _{M (k+d)}, can make desirable output y generally speaking _{M (k+d)}Equal the value Y of optimum precursor _K+d|k, in the hope of optimal control law.That is:

$y_{m(k+d)}=\frac{G\left(z^{-1}\right)}{C\left(z^{-1}\right)}{y}_k+\frac{F\left(z^{-1}\right)B\left(z^{-1}\right)}{C\left(z^{-1}\right)}{u}_k---\left(17\right)$

The anti-u that separates _k, can try to achieve optimal control law:

Tried to achieve the control law that makes the square error minimum this moment.

In the present embodiment, the output valve of setting control procedure be 0 (also can be other constant, easyly be made as 0), then y in the formula (18) at this for calculating _{M (k+d)}Value be zero, formula (18) can be rewritten as:

$u_k=-\frac{G\left(z^{-1}\right)y_k}{F\left(z^{-1}\right)B\left(z^{-1}\right)}---\left(19\right).$

Utilizing coefficient of comparison to find the solution the Diophantine equation gets: F (Z ^-1)=1, G (Z ^-1)=1.243-0.5091z ^-1

Optimal control policy is:

$u_k=-\frac{1.243-0.5091z^{-1}{y}_k}{0.0117z^{-1}+0.00202z^{-2}}---\left(20\right)$

At last this example is carried out simulated experiment under the disturbed condition, the disturbance that in operational process, is subjected to white noise sequence simulation drawing frame.And to set noise intensity be 0.1, and the emulation step number was defined as for 400 steps.The input and output analog result of method provided by the invention as shown in Figure 2.Y among Fig. 2 _r(k) (dotted line) expression desired output signal, y (k) (solid line) is illustrated in the real output signal under the interference effect.

In order to make two kinds of control effects have comparability, when adopting pid control algorithm that the input and output of this example are simulated, noise intensity still is made as 0.1, and step-length still was made as for 400 steps.The input and output analog result as shown in Figure 3 during PID control.Y among Fig. 3 _r(k) (dotted line) expression desired output signal, y (k) (solid line) is illustrated in the real output signal under the interference effect.

When adopting traditional PID control, the real output value of sliver is very big with the deviation of expectation output valve, and the stable extreme difference of actual output as can be seen.When adopting method provided by the invention, the amplitude fluctuations of the actual output of sliver reduces, and shows stability preferably.

This example has illustrated the system for the such large time delay of High-speed Drawing Frame, strong disturbance, method provided by the invention can effectively weaken the interference of various non-linear factors, and because this algorithm has the function of prediction in advance, it has also reduced the influence of the neat and well spaced dead band of drawing frame to control system.Therefore, the MVC control method serves as the control principle with the stability of output sliver line density, can greatly improve the neat and well spaced degree of output sliver, shows good recurrence performance.And under equal conditions, for traditional PID control method, it has great advantage.

Claims (5)

1. the self-adaptation control method of an autoleveller system is characterized in that, step is:

Step 1, be recorded under the pseudo-code generator effect input curve of autoleveller system and curve of output with two-pen recorder;

Step 2, the curve of output discretize that two-pen recorder is noted pick out the controlled autoregressive moving-average model of autoleveller system according to generalized least square method, are expressed as:

Wherein, d represents to import the retardation time to output, y _K+dThe expression k+d output of autoleveller system constantly, u _kExpression k input controlled quentity controlled variable constantly, ξ _K+dExpression k+d is white noise sequence constantly, A (z ^-1)=1-a ₁z ^-1-...-a _nz ^-n, B (z ^-1)=b ₀+ b ₁z ^-1+ ... + b _nz ^-n, C (z ^-1)=1+c ₁z ^-1+ ... + c _nz ^-n, wherein, u _kZ ^-n=u _K-n, ξ _K+dZ ^-n=ξ _K+d-n, be illustrated respectively in k-n constantly the input controlled quentity controlled variable and at k+d-n white noise sequence constantly, other by that analogy, a ₁To a _n, b ₀To b _nAnd c ₁To c _nBe respectively corresponding coefficient;

Step 3, be principle, obtain at k and make the autoleveller system constantly at the k+d output y of autoleveller system constantly with stable state variance minimum _K+dThe control input quantity u of stable state variance minimum _k,

Wherein, F (z ^-1) be

Merchant's formula, G (z ^-1) be

Residue multiply by z ^d, y _{M (k+d)}Be the k+d ideal output of autoleveller system constantly, y _kFor the k actual output of autoleveller system constantly, with k control input quantity u constantly _kCompensate random perturbation influence to the output of autoleveller system in the k+d moment.

2. the self-adaptation control method of a kind of autoleveller as claimed in claim 1 system is characterized in that the pseudo-code length of described pseudo-code generator is 20 yards-50 yards.

3. the self-adaptation control method of a kind of autoleveller as claimed in claim 1 system is characterized in that, the pseudo-code amplitude of described pseudo-code generator is in the scope of-1V-+1V.

4. the self-adaptation control method of a kind of autoleveller as claimed in claim 1 system is characterized in that, the input curve of described autoleveller system is the pseudo-random code broken line that pseudo-code generator produces.

5. the self-adaptation control method of a kind of autoleveller as claimed in claim 1 system is characterized in that, the curve of output of described autoleveller system is the curve of cyclical fluctuations of the situation of change of cotton stripline density through detected voltage of hydraucone pick-up unit or electric current.

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