CN102749844A - Prediction control method for non-self-balancing system - Google Patents

Abstract

The invention relate to the design of a prediction control method for a non-self-balancing system and mainly aims to solve the problems of difficult control on the non-self-balancing system, difficult modeling for the non-self-balancing system, difficult guarantee for the stability of a control system and irregular adjustment on parameters of a controller in the prior art. A single controller is adopted to only perform a step response test on a controlled target to obtain a prediction model of the target, and a prediction control algorithm is built by constructing control input of single freedom degree and introducing the concept of a rotation factor into a performance index by using a special error feedback correction method. The prediction control algorithm comprises the following steps of (1) building control input of single freedom degree: selecting future system control input which consists of one primary function weighing; (2) performing step signal excitation on the controlled target to obtain a process model; (3) building a future system expected performance index, and introducing the concept of the rotation factor into a performance index function; (4) deducing future prediction output; (5) building the special error feedback correction; and (6) ensuring the stability of the control system and tracing set value. Due to the adoption of the technical scheme, the problems are better solved, and the method can be used for operation control of the non-self-balancing system.

Description

Non-forecast Control Algorithm from balance system

Technical field

The present invention relates to a kind of non-forecast Control Algorithm from balance system.

Background technology

In actual industrial process control is used, widely apply based on the predictive control algorithm of step response and impulse response is existing to stabilization process, the steady production that improves device has been brought into play vital role.But in actual Chemical Manufacture, a common class object, promptly under the situation of system's generation input signal excitation, controlled system can not oneself reach new balance, and its process output valve will increase always or reduce down, claims that this type systematic is non-from balance system.The common non-liquid level that comprises devices such as rectification column, distillation column, stripping tower from the object that weighs, thus can liquid level that these devices of better controlled in practical operation reduce the influence of downstream unit very crucial.

Control to this type systematic mainly is the correct application to conventional PID regulator at present; The Majhi professor is at document " Modified smith predictor and controller for processes with time delay " (IEE Proc.-ControlTheory Appl.1999; 140 (5); 359-366) proposed to control new method to the PID of this type systematic; Follow-up have other similar methods to occur again, but the shortcoming of these class methods still shows to non-and need just can guarantee system stability by the regulator more than 2 from balance system, and it is too much to have caused regulating in the control method parameter; And these regulate the transfer function model of parameter great majority based on gained, and limitation is bigger.In addition, the PID regulator belongs to passive adjusting strategy, normally takes place to disturb in the external world and just regulates the control input after perhaps systematic parameter perturbs; Thereby make that control corresponding system robust performance is bad; Be difficult to provide excellent control effect, be controlled to concrete tower liquid level under the situation of external interference existence, can not in time eliminate ectocine; Cause the tower level fluctuation, influence downstream and produce.

The major reason why Model Predictive Control achieves success in practical application is that control engineering teacher can conveniently obtain needed forecast model through the test signal incentive object.Though from balance system, system can't oneself reach new balance after applying extraneous test interference, under the situation that does not influence ordinary production, test us through the step signal of appropriate time section and still can obtain to characterize the model of its characteristic for non-.Therefore, has realistic meaning by the non-predictive control algorithm of step signal method of testing design from balance system.

Summary of the invention

Technical matters to be solved by this invention is to exist in the prior art non-ly to be difficult to control from balance system, and modeling difficulty, control system stability are difficult to guarantee that controller parameter is regulated irregular problem.This method has the control system robust stability of assurance and follows the tracks of setting value bias free, the advantage that controller parameter is easy to adjust.

In order to solve the problems of the technologies described above, the technical scheme that the present invention adopts is following: a kind of non-forecast Control Algorithm from balance system, according to non-characteristics from balance system; Utilization is implemented the step signal excitation to non-from balance system; Gather the actual production data and set up step response model,, introduce the Error Feedback bearing calibration of becoming privileged through making up single-degree-of-freedom control input; Build algorithm of predictive functional control, may further comprise the steps:

(1) sets up single-degree-of-freedom control input: select system in future control input to form by a basis function weighting;

u(k)＝u(k+j)＝μ ₁(k) (j＝1，2，…，H _i-1)

(2) controlled device is implemented the excitation procurement process model of step signal;

(3) set up system in future expected performance index, in performance index function, introduce the notion of twiddle factor;

(4) derivation of future anticipation output;

The Error Feedback of (5) building particularization is proofreaied and correct;

(6) stability of control system guarantees and follows the tracks of the setting value zero-deviation;

Wherein u (k) is the current control input of system, and u (k+j) is the following expectation input of system, μ ₁(k) be control input weighting coefficient.

In the technique scheme, non-following from the balance system characteristic:

The single output of single input is non-to can be described as from balance system:

$y_P\left(k\right)=\underset{i=1}{\overset{\∞}{\mathrm{\Σ}}}({\stackrel{\‾}{a}}_i-{\stackrel{\‾}{a}}_{i-1})u(k-i)$

Wherein

Be step-response coefficients, y _P(k) be process output, u (k) is the process input; Note

Then

$y_P\left(k\right)=\underset{i=1}{\overset{\∞}{\mathrm{\Σ}}}{\stackrel{\‾}{s}}_{i}u(k-i)$

Notice that step-response coefficients

will or reduce with fixing speed increase behind a certain step-length N, then

$y_P\left(k\right)={\stackrel{\‾}{s}}_{1}u(k-1)+\·\·\·{\stackrel{\‾}{s}}_{i}u(k-i)\·\·\·+{\stackrel{\‾}{s}}_{N}u(k-N)+{\stackrel{\‾}{s}}_N\underset{i=1}{\overset{\∞}{\mathrm{\Σ}}}u(k-N-i)$

Wherein ${\stackrel{\‾}{s}}_N={\stackrel{\‾}{a}}_N-{\stackrel{\‾}{a}}_{N-1}.$

Following formula is transformed to the Z territory, have

$y_P\left(z\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{s}}_i{z}^{-i}u\left(z\right)+{\stackrel{\&OverBar;}{s}}_N{z}^{-1-\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HSA00000477552500011.png,HSA00000477552500012.png"\; state="\{\{state\}\}">N</figure-callout>}}\frac{1}{1-z^{-1}}u\left(z\right)=G_P\left(z\right)u\left(z\right)=\frac{G_{P_1}\left(z\right)}{1-z^{-1}}u\left(z\right)$

The non-steady component of

expression in the formula, and

from the balance system transport function

Following formula is done equivalence transformation, get non-step response model from balance system

$y_P\left(k\right)=y_P(k-1)+{\stackrel{\&OverBar;}{s}}_{1}u(k-1)+\underset{i=2}{\overset{N}{\mathrm{\&Sigma;}}}({\stackrel{\&OverBar;}{s}}_i-{\stackrel{\&OverBar;}{s}}_{i-1})u(k-i)$

Then the forecast model based on CONTROLLER DESIGN can be expressed as

$y_m\left(z\right)=G_m\left(z\right)u\left(z\right)=\frac{G_{m_1}\left(z\right)}{1-z^{-1}}u\left(z\right)$

In the formula

Represent non-steady component from the object model that weighs, and s ₀=0.Then the model future anticipation is output as

$y_m\left(k\right)=y_m(k-1)+s_{1}u(k-1)+\underset{i=2}{\overset{N}{\mathrm{\&Sigma;}}}(s_i-s_{i-1})u(k-i)$

Confirm that system in future expected performance index is following:

$\min J_P=\underset{i=H_1}{\overset{H_2}{\mathrm{\&Sigma;}}}{[y_{\mathrm{ref}}(k+i)-(r+1)y_m(k+i)-E(k+i)]}^2$

[H in the formula ₁T _s, H ₂T _s] be to optimize time domain, y _Ref(k+i)=w (k+i)-α ⁱ(w (k)-y _P(k)) have for reference locus and stablize similarly definition in the object control, its objective is and hope that system's output installs the reference locus of setting and follow the tracks of setting value,

T _sBe the sampling time, T _RefBe the closed-loop control system Expected Response time, w is a setting value, for normal value setting point tracking w (k+H _i)=w (k); E (k+i) is that predicated error is proofreaied and correct, and its concrete structure, is chosen according to Fig. 1 and answered E (k+i)=i [e (k)-e (k-1)]+e (k) (i>=1) for eliminating the future anticipation output error referring to Fig. 1; R is the twiddle factor of introducing, and after system receives the perturbation of external interference generation parameter, can change twiddle factor and guarantee model prediction output and met in practice, helps to improve the robust performance of system, and its effect sees that Fig. 2 describes.

The following expectation prediction of deriving is exported, and the control system parameter adjusting method is obtained in controlled input, and is specific as follows:

(1) current k controls input u (k)=μ constantly ₁(k)

(2) following H _iStep prediction output

y _m(k+H _i)＝y _fr(k+H _i)+y _fo(k+H _i)，

$y_{\mathrm{fo}}(k+H_i)=U_{H_i}{S_{H_i}}^T,$

$y_{\mathrm{fr}}(k+H_i)=U_{{1H}_i}{S_{{1H}_i}}^T+U_{{2H}_i}{S_{{2H}_i}}^T+y_m(k-1).$

Wherein

$S_{H_i}=\left[\begin{array}{cccc}{s}_1& {\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000477552500021.png,HSA00000477552500022.png"\; state="\{\{state\}\}">s</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& s_{H_i}\end{array}\right],$

$U_{H_i}=\left[\begin{array}{cc}u(k+H_i-1)& u(k+H_i-2)\&CenterDot;\&CenterDot;\&CenterDot;u\left(k\right)\end{array}\right],$

$S_{{1H}_i}=\left[\begin{array}{cc}{s}_{H_i+1}-s_0& s_{H_i+2}-{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000477552500011.png,HSA00000477552500012.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\&CenterDot;\&CenterDot;\&CenterDot;s_N-s_{N-H_i-1}\end{array}\right],$

$U_{{1H}_i}=\left[\begin{array}{cc}u(k-1)& u(k-2)\&CenterDot;\&CenterDot;\&CenterDot;u(k-N+H_i)\end{array}\right],$

$S_{{2H}_i}=\left[\begin{array}{cc}{s}_N-s_{N-H_i}& s_N-s_{N-H_i+1}\&CenterDot;\&CenterDot;\&CenterDot;s_N\end{array}-s_{N-1}\right],$

$U_{{2H}_i}=\left[\begin{array}{cc}u(k-N-1+H_i)& u(k-N-2+H_i)\&CenterDot;\&CenterDot;\&CenterDot;u(k-N)\end{array}\right]$

(3) make H ₁=H ₂=H is by y _Ref(k+H)=y _m(k+H)+E (k+H) must control input

$u\left(k\right)={\mathrm{\&mu;}}_1\left(k\right)=\frac{y_{\mathrm{ref}}(k+H)-(r+1)S_{1H}{U_{1H}}^T-(r+1)S_{2H}{U_{2H}}^T-E\left(k\right)-(r+1)y_m(k-1)}{(r+1){{\mathrm{IS}}_H}^T}$

Wherein I is the capable vector of H dimension unit, E (k)=H [e (k)-e (k-1)]+e (k).

For further specifying problem, carry out the theoretical analysis system design as follows so that method for designing why is described and to separate by no means control problem, and the control method of the design system that makes can zero-deviation tracing preset value and the stability of the system of assurance from balance system.

Control law (12) is done equivalence transformation,

(r+1)C ^-1(z)u(z)＝G _r(z)w(z)-G _F(z)e(z) (13)

G wherein _r(z) be the input reference model, G _F(z)=H (1-z ^-1)+1,

$C^{-1}\left(z\right)=\frac{G_c\left(z\right)(1-z^{-1})+z^{-1}{G}_{m_1}\left(z\right)}{(1-z^{-1})}---\left(14\right)$

$G_c\left(z\right)=\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i+\underset{i=1}{\overset{N-H}{\mathrm{\&Sigma;}}}(s_{H+i}-s_{i-1})z^{-i}+\underset{i=N-H+1}{\overset{N}{\mathrm{\&Sigma;}}}(s_N-s_{i-1})z^{-i}---\left(15\right)$

The available structure like Fig. 3 of formula (13) representes that wherein v (z) is the external interference of introducing, and d (z) is that load is disturbed.By Fig. 3, the control system closed loop transfer function, can be expressed as:

$y_P\left(z\right)=\frac{C\left(z\right)G_P\left(z\right)G_r\left(z\right)/(r+1)}{1+C\left(z\right)G_F\left(z\right)[G_P\left(z\right)-(r+1)G_m\left(z\right)]/(r+1)}w\left(z\right)+$

$\frac{[1-C\left(z\right)G_F\left(z\right)G_m\left(z\right)]G_P\left(z\right)}{1+C\left(z\right)G_F\left(z\right)[G_P\left(z\right)-(r+1)G_m\left(z\right)]/(r+1)}d\left(z\right)+$

$\frac{1-C\left(z\right)G_F\left(z\right)G_m\left(z\right)}{1+C\left(z\right)G_F\left(z\right)[G_P\left(z\right)-(r+1)G_m\left(z\right)]/(r+1)}v\left(z\right)---\left(20\right)$

Suppose G _r(z)=1, utilize formula (4), (5), (14) and (15), then formula (16) can be converted into

$y_P\left(z\right)=\frac{G_{P_1}\left(z\right)}{P\left(z\right)}w\left(z\right)+\frac{(r+1)[G_c\left(z\right)-G_{m_1}\left(z\right)-{\mathrm{HG}}_{m_1}\left(z\right)]}{P\left(z\right)}{G}_{P_1}\left(z\right)d\left(z\right)+$

$\frac{(r+1)(1-z^{-1})[G_c\left(z\right)-G_{m_1}\left(z\right)-{\mathrm{HG}}_{m_1}\left(z\right)]}{P\left(z\right)}v\left(z\right)---\left(17\right)$

The proper polynomial of P (z) closed-loop system wherein, and be expressed as

$P\left(z\right)=[G_c\left(z\right)(1-z^{-1})+z^{-1}{G}_{m_1}\left(z\right)](r+1)+[H(1-z^{-1})+1][G_{P_1}\left(z\right)-(r+1)G_{m_1}\left(z\right)]$

$=z^{-N-1}\left[\begin{array}{c}(r+1)\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i{z}^{N+1}+[(r+1)(s_{H+1}-\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i)+(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_1-(r+1)\mathrm{\&Delta;}{s}_1)]z^N+\\ \underset{i=2}{\overset{N-H}{\&Sum;}}[(r+1)(s_{H+i}-s_{H+i-1})+(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-\mathrm{\&Delta;}{s}_i(r+1))-H\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}(r+1)\mathrm{\&Delta;}{s}_{i-1}\right)]z^{N-\mathrm{<figure-callout\; id="1"\; label="i\; +"\; filenames="HSA00000477552500011.png,HSA00000477552500012.png"\; state="\{\{state\}\}">i</figure-callout>}+1}+\\ \underset{i=N-H+1}{\overset{N}{\mathrm{\&Sigma;}}}[(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-\mathrm{\&Delta;}{s}_i(r+1))-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1)\mathrm{\&Delta;}{s}_{i-1}))]z^{N-i+1}-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_N-(r+1)\mathrm{\&Delta;}{s}_N)\end{array}\right]---\left(18\right)$

Wherein

Δ s _i=s _i-s _I-1(s ₀=0).

If the controlled variable H of system and r select to satisfy like lower inequality, then proper polynomial is stable, and can guarantee control system bias free tracing preset value.

$\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}\left|(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1)\mathrm{\&Delta;}{s}_{i-1})\right|+(r+1)|s_{H+1}-\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i|$ (19)

$+\underset{i=2}{\overset{N-H}{\mathrm{\&Sigma;}}}(r+1)|s_{H+i}-s_{H+i-1}|<(r+1)\left|\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i\right|$

Consider the establishment of (19) formula, then can be like lower inequality

$(H+1)|\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_1-(r+1)\mathrm{\&Delta;}{s}_1|+$

$\underset{i=2}{\overset{N-H}{\mathrm{\&Sigma;}}}|(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i)-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1)\mathrm{\&Delta;}{s}_{i-1})|-H_1(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_N-(r+1)\mathrm{\&Delta;}{s}_N)+$

$\underset{i=N-H+1}{\overset{N}{\mathrm{\&Sigma;}}}|(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i)-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1)\mathrm{\&Delta;}{s}_{i-1})|+$

$(r+1)|s_{H+1}-\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i|+\underset{i=2}{\overset{N-H}{\mathrm{\&Sigma;}}}(r+1)|s_{H+i}-s_{H+i-1}|<(r+1)\left|\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i\right|$

Utilize the absolute value triangle inequality,

$(r+1)|s_{H+1}-\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;s})|$

$+\underset{i=2}{\overset{N-H}{\mathrm{\&Sigma;}}}|(r+1)(s_{H+i}-s_{H+i-1})+(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i)-H(\mathrm{\&Delta;}{s}_i-(r+1)\mathrm{\&Delta;}{s}_{i-1})|+H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_N-(r+1)\mathrm{\&Delta;}{s}_N)$

$+\underset{i=N-H+1}{\overset{N}{\mathrm{\&Sigma;}}}\left|(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i)-\mathrm{H\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1)\mathrm{\&Delta;}{s}_{i-1})\right|-H|\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_N-(r+1)\mathrm{\&Delta;}{s}_N|<(r+1)\left|\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i\right|---\left(20\right)$

And following formula is the result that closed-loop control system polynomial expression (18) is used Jury important coefficient cor-responding identified theorems, can know that according to this theorem P (z) stablizes polynomial expression, and the closed-loop control system that is therefore designed is stable.

Further investigate institute's control system designed tracing preset value situation under the situation that external interference exists, because control system is stable, then from importing w to output y _PSteady-state gain do

$K_{{\mathrm{wy}}_P}={\frac{G_{P_1}\left(z\right)z^{-1}}{P\left(z\right)}|}_{z=1}=\frac{{\stackrel{\&OverBar;}{s}}_N}{{\stackrel{\&OverBar;}{s}}_N}=1---\left(21\right)$

Load disturbs d to the steady-state gain that system exports to do

$K_{{\mathrm{dy}}_P}={\frac{(r+1)[G_c\left(z\right)-G_{m_1}\left(z\right)-{\mathrm{HG}}_{m_1}\left(z\right)]G_{P_1}\left(z\right)}{P\left(z\right)}|}_{z=1}=\frac{(r+1)[(H+1)s_N-(H+1)s_N]{\stackrel{\&OverBar;}{s}}_N}{{\stackrel{\&OverBar;}{s}}_N}=0---\left(22\right)$

Output disturbs v to output y _PSteady-state gain do

$K_{{\mathrm{vy}}_P}={\frac{(r+1)(1-z^{-1})[G_c\left(z\right)-G_{m_1}\left(z\right)-H{G}_{m_1}\left(z\right)]}{P\left(z\right)}|}_{z=1}=0---\left(23\right)$

Therefore by (21)-(23) but know control system bias free tracing preset value.

In fact; Condition (19) requirement forecast time domain H should be enough big; And twiddle factor r should select according to model mismatch situation

, so that guarantee the control system robust stability.In practical application, the model mismatch situation can solve through effective selection twiddle factor.

As above proof procedure explanation; Owing to adopt step signal test procurement process model among the present invention; Make and be very easy to realize in practical engineering application; The deviation of control system tracing preset value can be effectively eliminated in the new Error Feedback bearing calibration of introducing, and the twiddle factor of introducing in the performance index simultaneously can effectively improve the robust performance of control system, under the situation that external interference exists; Regulate the tracking performance that twiddle factor can improve control system, more than three characteristics guaranteed that institute's summary of the invention is applied to non-ly when balance system, can obtain better technical effect.

Description of drawings

The error calibration method that Fig. 1 introduces for the present invention.

Fig. 2 is the action diagram of twiddle factor among the present invention.

Fig. 3 is the closed-loop control system block diagram.

Fig. 4 is embodiment 1 a butadiene extraction rectification column flow process.

Fig. 5 is embodiment 1 a butadiene extraction rectification column B liquid level control curve.

Fig. 6 is the control curve of output to comparative example 1.

Fig. 7 is the control curve of output to perturbed system θ=6 of comparative example 1.

Fig. 8 is the perturbed system K=1.4 to comparative example 1, θ=7, the control curve of output of T=2.

Fig. 9 is the perturbed system K=1.4 to comparative example 1, θ=7, the control curve of output of T=2 after regulating twiddle factor r=0.15.

E among Fig. 1 (k-1) is k-1 system's output error constantly, and e (k) is current k system's output error constantly.

Y among Fig. 2 _P(k) be non-from the current output of balance system, y _m(k+i) be system's future anticipation output, r is a twiddle factor, and E (k+i) is the future anticipation error.

W among Fig. 3 (z) is the given input of system, G _r(z) be input reference model, y _Ref(z) be that C (z) is a controller, G with reference to input _P(z) be controlled device, G _m(z) be forecast model, G _F(z) be the feedback compensation model, u (z) is the input of current system, y _P(z) be the actual output of system, d (z) disturbs for system's input, and v (z) disturbs for system's output, and e (z) is a feedback error.

1 is the extraction solvent charging among Fig. 4, and 2 is C ₄The raw material charging, L ₁, L ₂Be respectively the liquid level of extraction distillation column A, B, F flows to the flow of tower B for tower A.

Through embodiment the present invention is done further elaboration below.

Embodiment

[embodiment 1]

To 100,000 tons of butadiene production devices of certain factory, consider extractive distillation column as shown in Figure 4, the liquid level L of its extractive distillation column B ₂The flow F process step signal test that gets into tower B with the A tower obtains following process prescription

$G\left(s\right)=\frac{K}{s}{e}^{-\mathrm{\&theta;s}}$

K=0.2273 wherein, θ=10.

Embodiment:

(1), confirms system model parameter N=30 and sampling time T according to process feature _s=1s.

(2) choose suitable match point H=24, r=0, closed loop response time T _Ref=1s verifies following formula

$\underset{i=1}{\overset{N+1}{\mathrm{\&Sigma;}}}|(H+1)(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_i-(r+1)\mathrm{\&Delta;}{s}_i-H(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{s}}_{i-1}-(r+1){\mathrm{\&Delta;s}}_{i-1})|+(r+1)|s_{H+1}-\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i|+$

$\underset{i=2}{\overset{N-H}{\mathrm{\&Sigma;}}}(r+1)|s_{H+i}-s_{H+i-1}|<(r+1)\left|\underset{i=1}{\overset{H}{\mathrm{\&Sigma;}}}{s}_i\right|$

Whether set up, then do not reselect suitable match point H if do not satisfy.If controlled device is an Object with Time Delay, the match point H that then selects is greater than retardation time.

(3) ask Optimum solution, make H ₁=H ₂=H, then y _Ref(k+H)=y _m(k+H)+and E (k+H), get current moment control law

$u\left(k\right)={\mathrm{\&mu;}}_1\left(k\right)=\frac{y_{\mathrm{ref}}(k+H)-(r+1)S_{1H}{U_{1H}}^T-(r+1)S_{2H}{U_{2H}}^T-E\left(k\right)-(r+1)y_m(k-1)}{(r+1){{\mathrm{IS}}_H}^T}$

And with the control input action of current time to object.

(4) k → k+1, repeating step 2-3.

In practical operation; Operating personnel hope the liquid level of tower B be controlled at total tower liquid level 60% and the fluctuation more little good more; The liquid level of utilizing the method control tower B that is invented is shown in Fig. 5 solid line; Can find to disturb under the situation about existing in extraneous load from the control curve, can guarantee that bias free makes the liquid level of system control 60% place of total tower liquid level, its control effect is very good.Investigate systematic parameter serious parameter perturbation K=0.3227 takes place; θ=14; Control the result this moment shown in dotted line among Fig. 5, even can find system's generation parameter perturbation, institute's inventive method still can be kept the stability of control system; And can guarantee that control system still remains on 60% of total tower liquid level, explain that the design inventive method has very strong robust performance.Further investigate in system and take place to adjust controller parameter twiddle factor r=0.1 respectively after the serious parameter perturbation; The effect of control system behind the r=0.2; This moment, dotted line and the dotted line among Fig. 5 seen in control system output; Can find out that by curve the adjusting twiddle factor is very crucial for improving the control system performance, have very important physical property, in practical application, suitably adjust the robustness that twiddle factor helps to improve control system.

[embodiment 2]

Consider non-ly to be from the balance system structrual description:

$G\left(s\right)=\frac{K}{s(\mathrm{Ts}+1)}{e}^{-\mathrm{\&theta;s}}$

In the formula: K=1, T=4, θ=5.

Utilize and embodiment 1 similar operation step selection control Parameter H=14 under nominal case, T _s=1, T _Ref=1, r=0.

Use the inventive method, t=100 add constantly amplitude be 0.1 load control should be non-from balance system when disturbing, control curve of output of its tracking unit step signal is seen shown in Fig. 6 solid line.As can beappreciated from fig. 6, the present invention follows the tracks of the setting value requirement for this non-can reaching in the short period of time from balance system, and tracking error is zero.

Use the inventive method, consider controlled system outside the bound pair process back systematic parameter that makes a difference drift about, become θ=6 retardation time.The same amplitude that when t=100, adds is that 0.1 load is disturbed, and keeps simulation parameter identical with Fig. 6, and system controlled curve of output and saw shown in Fig. 7 solid line this moment.Can find that from Fig. 7 even parameter drift takes place, under the situation of not regulating controller parameter, the present invention still can bias free tracing preset value, and interference free performance is very outstanding.

Use the inventive method, cause systematic parameter that serious drift takes place after further considering controlled system the bound pair process making a difference outside, i.e. K=1.4, θ=7, T=2 keeps simulation parameter identical with Fig. 6, and system controlled curve of output and saw shown in Figure 8 this moment.It is thus clear that even the perturbation of serious parameter takes place control system, the present invention still can bias free tracing preset value, and can eliminate the interference of outer bound pair system, shows that institute's inventive method has very superior performance.

Use the inventive method; As shown in Figure 9 to Fig. 8 system control curve of situation behind adjustment control parameter twiddle factor r=0.15 that perturb; Can find that from Fig. 9 through the adjustment twiddle factor, institute's inventive method makes the control system performance obviously improve; So for guaranteeing to obtain best control effect, twiddle factor is a very crucial adjusting parameter in practical application.

Comparative example

Consider that embodiment 2 is non-from the balance system structrual description:

$G\left(s\right)=\frac{K}{s(\mathrm{Ts}+1)}{e}^{-\mathrm{\&theta;s}}$

In the formula: K=1, T=4, θ=5.Use Majhi method (IEE Proc.-Control Theory Appl.1999; 140 (5), 359-366) control this system, relevant controlled variable is referring to its bibliographical information; Under nominal case, its control of application Majhi method curve of output is as a result seen shown in Fig. 6 dotted line.Can find that by Fig. 6 though the Majhi method also can be controlled this object, even when initial tracing preset value, be better than the inventive method, it obviously is worse than the inventive method aspect interference free performance.

Perturbation takes place the taking into account system parameter is to become θ=6 retardation time; Under the situation of retentive control parameter constant; Using Majhi method system control curve of output sees among Fig. 7 shown in the dotted line; Can find by Fig. 7, no matter the tracing preset value still be anti-interference aspect, the inventive method obviously is superior to the control result that the Majhi method obtains.

Further investigating the serious perturbation of systematic parameter generation is K=1.4, θ=7, and T=2 under the situation of retentive control device parameter constant, uses the Majhi method and can't guarantee that control system is stable, can't show in Fig. 8 so it controls the result.And can find out that from the curve of Fig. 8 using the inventive method still can provide extraordinary tracking and interference free performance, has further shown the superiority of the inventive method.

As above institute's set forth is that the present invention is applied to non-outstanding control effect from balance system.In actual industrial process; The control effect is not good enough after existing its non-characteristic from weighing apparatus of many production runes to make the PID regulator be difficult to use or use; So the present invention can effectively solve the non-control from balance system of the single output of single input; Owing to adopted the Error Feedback bearing calibration and the twiddle factor notion of predictive control theory, particularization, made to have very strong interference free performance and robust performance after this inventive method of system applies.Though as above example has simply non-ly been done simulation study from balance system to two, other are non-ly controlled from balance system but can be widely used in oil refining, chemical industry, pharmacy, machinery, aviation etc. equally by its control thought knowledge capital invention.

Claims (3)

1. non-forecast Control Algorithm from balance system; According to non-characteristics from balance system, utilize and implement the step signal excitation from balance system non-, gather the actual production data and set up step response model; Through making up single-degree-of-freedom control input; Introduce the Error Feedback bearing calibration of becoming privileged, build algorithm of predictive functional control, may further comprise the steps:

(1) sets up single-degree-of-freedom control input: select system in future control input to form by a basis function weighting;

u(k)＝u(k+j)＝μ ₁(k)?(j＝1，2，…，H _i-1)

(2) controlled device is implemented the excitation procurement process model of step signal;

(3) set up system in future expected performance index, in performance index function, introduce the notion of twiddle factor;

(4) derivation of future anticipation output;

The Error Feedback of (5) building particularization is proofreaied and correct;

(6) stability of control system guarantees and follows the tracks of the setting value zero-deviation;

Wherein u (k) is the current control input of system, and u (k+j) is the following expectation input of system, μ ₁(k) be control input weighting coefficient.

2. non-forecast Control Algorithm from balance system according to claim 1 is characterized in that, and is non-following from the balance system characteristic:

The single output of single input is non-to can be described as from balance system:

$y_P\left(k\right)=\underset{i=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}({\stackrel{\&OverBar;}{a}}_i-{\stackrel{\&OverBar;}{a}}_{i-1})u(k-i)---\left(1\right)$

Wherein

Be step-response coefficients, y _P(k) be process output, u (k) is the process input; Note

Then

$y_P\left(k\right)=\underset{i=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{s}}_{i}u(k-i)---\left(2\right)$

Notice that step-response coefficients

will or reduce with fixing speed increase behind a certain step-length N, then

$y_P\left(k\right)={\stackrel{\&OverBar;}{s}}_{1}u(k-1)+\&CenterDot;\&CenterDot;\&CenterDot;{\stackrel{\&OverBar;}{s}}_{i}u(k-i)\&CenterDot;\&CenterDot;\&CenterDot;+{\stackrel{\&OverBar;}{s}}_{N}u(k-N)+{\stackrel{\&OverBar;}{s}}_N\underset{i=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}u(k-N-i)---\left(3\right)$

Wherein ${\stackrel{\&OverBar;}{s}}_N={\stackrel{\&OverBar;}{a}}_N-{\stackrel{\&OverBar;}{a}}_{N-1};$

Following formula is transformed to the Z territory, have

$y_P\left(z\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{s}}_i{z}^{-i}u\left(z\right)+{\stackrel{\&OverBar;}{s}}_N{z}^{-1-N}\frac{1}{1-z^{-1}}u\left(z\right)=G_P\left(z\right)u\left(z\right)=\frac{G_{P_1}\left(z\right)}{1-z^{-1}}u\left(z\right)---\left(4\right)$

The non-steady component of

expression in the formula, and

from the balance system transport function

Following formula is done equivalence transformation, get non-step response model from balance system

$y_P\left(k\right)=y_P(k-1)+{\stackrel{\&OverBar;}{s}}_{1}u(k-1)+\underset{i=2}{\overset{N}{\mathrm{\&Sigma;}}}({\stackrel{\&OverBar;}{s}}_i-{\stackrel{\&OverBar;}{s}}_{i-1})u(k-i)---\left(5\right)$

Then the forecast model based on CONTROLLER DESIGN can be expressed as

$y_m\left(z\right)=G_m\left(z\right)u\left(z\right)=\frac{G_{m_1}\left(z\right)}{1-z^{-1}}u\left(z\right)---\left(6\right)$

In the formula

Represent non-steady component from the object model that weighs, and s ₀=0.Then the model future anticipation is output as

$y_m\left(k\right)=y_m(k-1)+s_{1}u(k-1)+\underset{i=2}{\overset{N}{\mathrm{\&Sigma;}}}(s_i-s_{i-1})u(k-i)---\left(7\right)$

Confirm that system in future expected performance index is following:

$\min J_P=\underset{i=H_1}{\overset{H_2}{\mathrm{\&Sigma;}}}{[y_{\mathrm{ref}}(k+i)-(r+1)y_m(k+i)-E(k+i)]}^2---\left(8\right)$

[H in the formula ₁T _s, H ₂T _s] be to optimize time domain, y _Ref(k+i)=w (k+i)-α ⁱ(w (k)-y _P(k)) have for reference locus and stablize similarly definition in the object control, its objective is and hope that system's output installs the reference locus of setting and follow the tracks of setting value,

T _sBe the sampling time, T _RefBe the closed-loop control system Expected Response time, w is a setting value, for normal value setting point tracking w (k+H _i)=w (k); E (k+i) is that predicated error is proofreaied and correct, and its concrete structure, is chosen according to Fig. 1 and answered E (k+i)=i [e (k)-e (k-1)]+e (k) (i>=1) for eliminating the future anticipation output error referring to Fig. 1; R is the twiddle factor of introducing, and after system receives the perturbation of external interference generation parameter, can change twiddle factor and guarantee model prediction output and met in practice, helps to improve the robust performance of system, and its effect sees that Fig. 2 describes.

3. non-forecast Control Algorithm according to claim 1 from balance system, the following expectation prediction output that it is characterized in that deriving, the control system parameter adjusting method is obtained in controlled input, and is specific as follows:

(1) current k controls input u (k)=μ constantly ₁(k)

(2) following H _iStep prediction output

y _m(k+H _i)＝y _fr(k+H _i)+y _fo(k+H _i) (9)

$y_{\mathrm{fo}}(k+H_i)=U_{H_i}{S_{H_i}}^T---\left(10\right)$

$y_{\mathrm{fr}}(k+H_i)=U_{{1H}_i}{S_{{1H}_i}}^T+U_{{2H}_i}{S_{{2H}_i}}^T+y_m(k-1)---\left(11\right)$

Wherein

$S_{H_i}=\left[\begin{array}{cccc}{s}_1& s_2& \&CenterDot;\&CenterDot;\&CenterDot;& s_{H_i}\end{array}\right],$

$U_{H_i}=\left[\begin{array}{cc}u(k+H_i-1)& u(k+H_i-2)\&CenterDot;\&CenterDot;\&CenterDot;u\left(k\right)\end{array}\right],$

$S_{{1H}_i}=\left[\begin{array}{cc}{s}_{H_i+1}-s_0& s_{H_i+2}-s_1\&CenterDot;\&CenterDot;\&CenterDot;s_N-s_{N-H_i-1}\end{array}\right],$

$U_{{1H}_i}=\left[\begin{array}{cc}u(k-1)& u(k-2)\&CenterDot;\&CenterDot;\&CenterDot;u(k-N+H_i)\end{array}\right],$

$S_{{2H}_i}=\left[\begin{array}{cc}{s}_N-s_{N-H_i}& s_N-s_{N-H_i+1}\&CenterDot;\&CenterDot;\&CenterDot;s_N\end{array}-s_{N-1}\right],$

$U_{{2H}_i}=\left[\begin{array}{cc}u(k-N-1+H_i)& u(k-N-2+H_i)\&CenterDot;\&CenterDot;\&CenterDot;u(k-N)\end{array}\right].$

(3) make H ₁=H ₂=H is by y _Ref(k+H)=y _m(k+H)+E (k+H) must control input

$u\left(k\right)={\mathrm{\&mu;}}_1\left(k\right)=\frac{y_{\mathrm{ref}}(k+H)-(r+1)S_{1H}{U_{1H}}^T-(r+1)S_{2H}{U_{2H}}^T-E\left(k\right)-(r+1)y_m(k-1)}{(r+1){{\mathrm{IS}}_H}^T}---\left(12\right)$

Wherein I is the capable vector of H dimension unit, E (k)=H [e (k)-e (k-1)]+e (k).

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