CN104111605B - The controller and control method of single-input single-output integrator plant production process - Google Patents
The controller and control method of single-input single-output integrator plant production process Download PDFInfo
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Abstract
The present invention relates to a kind of controller of single-input single-output integrator plant production process and control method, mainly solve the presence of integrator plant production process modeling difficulty in the prior art, gained stability of control system is difficult to analyze, the problem of controller regulation parameter is more.The present invention need to only implement the forecast model that impulse response test obtains production process to controlled device, by building the control input of single-degree-of-freedom, using novel error feedback correction method, build algorithm of predictive functional control by using single controller:(1) single-degree-of-freedom control input is set up:Selection system in future control input is made up of a basic function weighting;(2) implement pulse signal excitation to controlled device and obtain process model;(3) system in future expected performance index is set up;(4) derivation of future anticipation output;(5) the error feedback compensation of particularization is built;(6) the stability guarantee of control system and the technical scheme of tracking fixed valure zero-deviation, preferably solve the problem, and the operation optimization available for integrator plant production process is controlled.
Description
Technical field
The present invention relates to a kind of controller of single-input single-output integrator plant production process and its control method.
Background technology
In actual industrial process control application, the situation of input signal excitation occurs in system for a common class object
Under, controlled system oneself can not reach new balance, and its output of process value will be increasedd or decreased down always, and such system is called
Non-self-regulating system.Common Nonself-regulating plant includes the liquid level of the devices such as rectifying column, destilling tower, stripper, in practical operation
Can the influence that these devices be controlled well to reduce to downstream unit very crucial.
Control method currently for such system is mainly to the correct application of Traditional PID adjuster, but this kind of method
Shortcoming still show for Non-self-regulating system need by the adjuster of more than 2 just can ensure that system stably, result in
Regulation parameter is excessive in control method, and the transfer function model of most of these regulation parameters based on gained, limitation compared with
Greatly, and control effect is bad.In addition, PID regulator belongs to passive regulation strategy, it is typically to occur interference or system in the external world
Parameter just adjusts control input after perturbing, so that corresponding control system robust performance is bad, it is difficult to provide very well
Control effect.
The advantage of predictive functional control algorithm is that rapid object can be adapted to, and slow process object is can be suitably used for again,
Existing many applications in actual industrial, and Predictive function control does not have excessive requirement for process model, as long as can be convenient
The feature of reproducing processes, then relevant information can be adopted to represent process model.In view of in actual control operation, can be very convenient
Process model is obtained with method of testing, additionally due to integrator plant production process is after additional pulse signal, its response will be not
The characteristics of carrying out the period for constant, it is possible to convenient that process model is obtained by additional test signal.So, by research
The algorithm of predictive functional control of pulsed test signal method design integrator plant production process has realistic meaning.
Hou Z.S. are taught in document《The model-free learning adaptive control of a
class of SISO nonlinear systems》(Proc.of American Control Conf.,New Mexico,
1997:In 343-344), by the concept for introducing partial differential, it is to avoid the modeling problem of non-linear process, be it is a kind of preferably
The control method of non-linear process, but it does not provide specific systematic parameter adjusting method, more not using system not
Carry out information of forecasting.In practice because predictive control algorithm can utilize forecast model very well, the concept such as feedback compensation has been waited until more
Good engineer applied, wherein predictive functional control algorithm have obtained the pass of more people due to the control input form of its structuring
Note.For this, exploitation combines without identification model and realizes that simple Nonlinear Prediction Models method is very necessary.
Currently for the correct application controlled mainly to Traditional PID adjuster of such system, Majhi is taught in document
《Modified smith predictor and controller for processes with time delay》(IEE
Proc.-Control Theory Appl.1999,140 (5), 359-366) propose for such system PID control newly side
Method, it is follow-up to there are other similar methods to occur again, but the shortcoming of this kind of method still shows and needs to borrow for Non-self-regulating system
The adjuster of more than 2 is helped just to can ensure that system is stable, it is excessive to result in regulation parameter in control method, and these regulation ginsengs
The most of transfer function models based on gained of number, limitation is larger.In addition, PID regulator belongs to passive regulation strategy, generally
It is just to adjust control input after interference occurs for the external world or systematic parameter perturbs, so that corresponding control system Shandong
Rod performance is bad, it is difficult to provide good control effect, for specific tower Liquid level in the presence of external interference, no
Ectocine can be eliminated in time, cause tower level fluctuation, the production of influence downstream.
Predictive function control (PFC) is the third generation model prediction that Richalet and Kuntze are proposed in 1980s
Control algolithm, regards the structure of control input as key, other Model Predictive Controls can be overcome to be likely to occur the not clear control of rule
Input problem processed.Because control input influence control output relation is more complicated in ethylbenzene dehydrogenation production, so being studied using PFC
The PREDICTIVE CONTROL of ethylbenzene catalytic dehydrogenation system is very necessary, and the input for causing control system by the selection of basic function in PFC is advised
Definitely, control performance is higher for rule.Therefore, the present invention designs multiple-input and multiple-output ethylbenzene dehydrogenation by Predictive function control
The advanced control method of production process has realistic meaning.
The content of the invention
The technical problems to be solved by the invention are that have single-input single-output integrator plant production process in the prior art to build
Mould is difficult, and gained stability of control system is difficult to analyze, the problem of controller regulation parameter is more.This method, which has, ensures control system
System robust stability and tracking fixed valure zero deflection, controller parameter advantage easy to adjust.
In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:A kind of single-input single-output integrator plant life
The controller of production process, described controller is implemented according to the characteristics of integrator plant production process using to integrator plant production process
Pulse signal is encouraged, and collection actual test data set up impulse response model, by building single-degree-of-freedom control input, using by mistake
Poor feedback correction method and algorithm of predictive functional control, the single input of control signal or single output.
In above-mentioned technical proposal, the control method of the controller of described single-input single-output integrator plant production process is led to
Cross and build single-degree-of-freedom control input, using error feedback correction method and algorithm of predictive functional control, the list of control signal is defeated
Enter or single output, build algorithm of predictive functional control, comprise the following steps:
(1) single-degree-of-freedom control input is set up:Selection future course control input is made up of a basic function weighting,
U (k)=u (k+j)=μ1(k), j=1,2 ..., Hi-1;
(2) excitation for implementing pulse signal to controll plant obtains procedural test model;
(3) system in future expected performance index is set up;
(4) derivation of future anticipation output;
(5) the error feedback compensation of particularization is built;
(6) stability analysis of control system and the guarantee of tracking fixed valure zero-deviation;
Wherein u (k) is the current control input of system, and u (k+j) is to expect input, μ in system future1(k) add for control input
Weight coefficient.
In above-mentioned technical proposal, technical scheme preferably is, the control of described single-input single-output integrator plant production process
The control method of device processed, it is characterised in that integrator plant production process feature is as follows:
Single-input single-output integrator plant production process can be described as:
WhereinIt is the impulse response coefficient of integrator plant production process, u (k) is process input, yP(k) it is the output of process;By
In the particularity of the impulse response of integrator plant production process, its impulse response coefficient as shown in Figure 1Kept after a certain step-length N
Constant valueUsing this feature, formula (1) is reduced to
Formula (2) is transformed into Z domains, had
In formulaThe steady component of integrator plant production process transmission function is represented, and
Equivalence transformation is done to above formula, the impulse response model of integrator plant production process is obtained
Forecast model then based on design controller is represented by
In formulaRepresent the steady component of integrator plant production process model, and s0=0.Then mould
Type future anticipation is output as
To provide the stability analysis result of system, following three definition is provided:
Define 4.1.Comprising impulse response coefficient in minimum valueAnd maximumBetween all objects, be designated as
And have
Wherein
In the case where as above giving the uncertain description of object,Impulse response coefficient is contained to existWithBetween all objects.
Define 4.2. is for impulse response coefficientControll plant, the sum of the deviations M between object and model is expressed as
Know that the deviation between object and model impulse response coefficient is met by formula (9)
The maximum mismatch between model and object can so be obtained.
Define 4.3. maximum mismatch
Known by formula (9)Following relation is met with M
It is assumed that sNIt is not zero, i.e.,
Wherein sNRepresent the forecast model impulse response coefficient s of integrator plant production processiThe constant value kept after step-length N,
AndFor the impulse response coefficient of integrator plant production processThe constant value kept after step-length N.
Determine that system in future expected performance index is as follows:
[H in formula1,Hp] it is optimization time domain, i is ith sample moment, JPIt is performance Index Calculation result, yref(k+i)=
w(k+i)-αi(w(k)-yP(k) reference locus) is represented, to cause system output according to the reference locus tracking fixed valure,TsFor sampling time, TrefFor the closed-loop control system expected response time, w is setting value, for constant value set point
Track w (k+Hi)=w (k);E (k+i) is predicated error correction, and E (k+i)=(1-a) E (k-1)+(1+ai) [e (k- are taken herein
1)-e (k-2)]+ae (k-1), a is the parameter introduced, is favorably improved the robust performance of production system.
In above-mentioned technical proposal, technical scheme preferably is, the control of described single-input single-output integrator plant production process
The control method of device processed, it is characterised in that the following desired prediction output of derivation, obtains control input, obtains control system
Parameter adjusting method, it is specific as follows:
(1) current k moment control input u (k)=μ1(k)
(2) following HiStep prediction output
ym(k+Hi)=yfr(k+Hi)+yfo(k+Hi) (14)
In formula:
Wherein,To be row matrix that the impulse response coefficient of integrator plant production process is constituted
Row matrix [u (the k+H being made up of future anticipation control inputi-1)u(k+Hi- 2) ... u (k)],
The matrix constituted for the impulse response coefficient difference of integrator plant production process,
Row matrix [u (k-1) u (k-2) ... u (k-N+ being made up of the first last time system control input
Hi)],
ForSubtract each other the matrix of composition with its impulse response coefficient previous,
The row matrix being made up of the second last time system control input:
[u(k-N-1+Hi) u(k-N-2+Hi)…u(k-N)];
(3) H is made1=Hp=H, by yref(k+H)=ym(k+H)+E (k+H), and make current k moment error correction E (k)=E
(k+H1), system control input can be obtained
I is unit row vector in formula, and
E (k)=(1-a) E (k-1)+(1+aH1)[e(k-1)-e(k-2)]+ae(k-1)。
In above-mentioned technical proposal, technical scheme preferably is, the anticipation function of single-input single-output integrator plant production process
Control method, according to the characteristics of integrator plant production process, utilizes the excitation for implementing pulse signal to integrator plant production process, collection
Actual production data set up impulse response model, by building single-degree-of-freedom control input, introduce novel error feedback compensation
Method, builds algorithm of predictive functional control, comprises the following steps:
(1) single-degree-of-freedom control input is set up:Selection system in future control input is made up of a basic function weighting;
U (k)=u (k+j)=μ1(k) (j=1,2 ..., Hi-1)
(2) implement pulse signal excitation to controll plant and obtain process model;
(3) system in future expected performance index is set up;
(4) derivation of future anticipation output;
(5) the error feedback compensation of particularization is built;
(6) stability of control system ensures and tracking fixed valure zero-deviation;
Wherein u (k) is current system control input, and u (k+i) is to expect input, μ in system future1(k) add for control input
Weight coefficient.
Non-self-regulating system feature is as follows:Single-input single-output integrator plant production process can be described as:
WhereinIt is the impulse response coefficient of integrator plant production process, u (k) is process input, yP(k) it is the output of process;By
In the particularity of Nonself-regulating plant impulse response, its impulse response coefficient as shown in Figure 1Constant value is kept after a certain step-length NUsing this feature, above formula is reduced to
Above formula is transformed into Z domains, had
In formulaThe steady component of integrator plant production process transmission function is represented, and
Equivalence transformation is done to above formula, the impulse response model of integrator plant production process is obtained
Forecast model then based on design controller is represented by
In formulaRepresent the steady component of integrator plant production process model, and s0=0.Then model
Future anticipation is output as
Determine that system in future expected performance index is as follows:
[H in formula1,Hp] it is optimization time domain, yref(k+i)=w (k+i)-αi(w(k)-yP(k)) for reference locus have and
Similar definition in stable object control, the purpose is to wish that system exports set-mounted reference locus tracking fixed valure,TsFor sampling time, TrefFor the closed-loop control system expected response time, w is setting value, for constant value set point
Track w (k+Hi)=w (k);E (k+i) is predicated error correction, and E (k+i)=(1-a) E (k-1)+(1+ai) [e (k- are taken herein
1)-e (k-2)]+ae (k-1), a is the parameter introduced, is favorably improved the robust performance of production system.
The following desired prediction output of derivation, obtains control input, obtains control system parameter adjusting method, specifically
It is as follows:
(1) current k moment control input u (k)=μ1(k)
(2) following HiStep prediction output
ym(k+Hi)=yfr(k+Hi)+yfo(k+Hi)
In formula:
(3) H is made1=Hp=H, by yref(k+H)=ym(k+H)+E (k+H), and make current k moment error correction E (k)=E
(k+H1), control input can be obtained
I is the unit row vector of an appropriate dimension in formula, and
E (k)=(1-a) E (k-1)+(1+aH1)[e(k-1)-e(k-2)]+ae(k-1)。
Further deeply to describe the problem, it is carried out as follows theory analysis system design to illustrate the method energy why designed
The Predictive function control of single-input single-output integrator plant production process is solved the problems, such as, and the control method of design can energy zero-deviation
Track set-point and ensure the stability of system.
Equivalence transformation is done to control law (16), obtained
C-1(z) u (z)=Gr(z)w(z)-GF(z)e(z) (17)
Wherein
Formula (17) can be described with the control structure shown in Fig. 2, and wherein d represents d (z), and other members have identical definition,
And d (z), v (z) are the load disturbance and output interference introduced, G respectivelyr(z) it is input reference model, C (z) is controller.This
Outside due to GF(z) it is feedback filter, 0 < a < 2 should be had by stabilizing it.
By Fig. 2, control system closed loop transfer function, is represented by:
Assuming that Gr=1, (z) using formula (4), (5), (14) and (15), then formula (21) can be converted into
In formula:
P (z)=(z-1) P2(z)+az-1[H1(1-z-1)(GP1(z)-Gm1(z))+P1(z)+GP1(z)-Gm1(z)],
WhereinΔsi=si-si-1。
The stability for knowing now closed-loop control system by (21) is determined by P (z).
If prediction step H1With there is a > 0, when a → 0 (i.e. when a level off to 0), selection is met such as lower inequality, then special
It is stable to levy multinomial, and can guarantee that control system zero deflection tracks set-point.
Consider that (23) formula is set up, then can obtain such as lower inequality
Using absolute value triangle inequality, obtain
And (23) are exactly multinomial P2(z) result of application Jury important coefficient determination of stability theorems, so P2(z) it is stable.
Lemma (Xi Yugeng, PREDICTIVE CONTROL, 1993) is now utilized, when a → 0, if following formula is set up, P (z) is stable.
P2(z)z-1[H1(1-z-1)(GP1(z)-Gm1(z))+P1(z)+GP1(z)-Gm1(z)]|Z=1> 0 (24)
Formula (24) is equivalent toAnd what it always set up, so P (z) is stable.
Further investigate designed control system and set-point situation is tracked in the presence of external interference, due to control
System processed is stable, then from input w to output yPSteady-state gain be
The steady-state gain that load disturbance d is exported to system is
Output interference v to output yPSteady-state gain be
Therefore know that control system can zero deflection tracking set-point by (25)-(27).
Procedure declaration as indicated above, due to obtaining procedural test model using pulsed test signal in the present invention, these surveys
Try reality of work to be very easy to realize in engineer applied, formula (25)-(27) illustrate that the error feedback correction method introduced can have
Effect eliminates the deviation that control system tracks set-point, above aspects ensures institute's content of the invention non-certainly applied to single-input single-output
During the production process that weighs, preferable technique effect is achieved.
Brief description of the drawings
Fig. 1 is the impulse response of single-input single-output integrator plant production process.
Fig. 2 is closed-loop control system block diagram.
Fig. 3 is embodiment butadiene extraction rectifying column flow.
Fig. 4 is embodiment butadiene extraction rectifying column B Liquid level curves.
Fig. 5 is embodiment butadiene extraction rectifying column B Liquid level curves.
Y in Fig. 1PTo produce process pulsation test and excitation result,For pulse value, t is the time.
W is the given input of system, G in Fig. 2rFor input reference model, yrefFor reference input, C is controller, GPTo be controlled
Object, GmFor forecast model, GFFor feedback compensation model, u inputs for current system, yPFor system reality output, d is that system is defeated
Enter interference, v is that system exports interference, and e is feedback error.
1 is extractant charging in Fig. 3, and 2 be C4Feedstock, L1, L2Respectively extraction distillation column A, B liquid level, F is
Tower A flows to tower B flow.
The present invention is expanded on further below by specific embodiment.
Embodiment
【Embodiment】
For 100,000 tons of butadiene production devices of certain factory, it is considered to extractive distillation column as shown in Figure 3, its extractive distillation column B
Liquid level L2The flow F for entering tower B with A towers by pulsed test signal obtains following process description
Wherein K=0.2273, θ=10.
Embodiment:
(1) according to process feature, system model parameter N=80 and sampling time T is determineds=1s.
(2) suitable match point H=24, a=1, closed loop response time T are chosenref=10s verifies following formula
Whether set up, suitable match point H is reselected if being unsatisfactory for.If controll plant is Object with Time Delay, select
Match point H be greater than lag time.
(3) askOptimal solution, make H1=H2=H, then yref
(k+H)=ym(k+H)+E (k+H), obtains current time control law
And the control input at current time is applied to object.
(4) k → k+1, repeat step 2-3.
In practical operation, operating personnel wish tower B Liquid level total tower liquid level 60% and fluctuate it is the smaller the better,
Invented method control tower B liquid level is utilized as shown in figure 4, caning be found that what is existed in extraneous load disturbance from controlling curve
In the case of, it can be ensured that zero deflection make it that at the 60% of the total tower liquid level of the Liquid level of system that its control effect is very good.Examine
Examine systematic parameter and occur serious Parameter Perturbation K=0.1827, θ=12, even if now control result as shown in figure 5, it can be found that
Parameter Perturbation occurs for system, and institute's inventive method still can maintain the stability of control system, and can ensure that control system is still protected
Hold the 60% of total tower liquid level, the control system that thus explanation is designed using the present invention has very strong robust performance.
Claims (3)
1. a kind of controller of single-input single-output integrator plant production process, described controller is according to integrator plant production process
Feature, using pulse signal excitation is implemented to integrator plant production process, collection actual test data are set up impulse response model, led to
Cross and build single-degree-of-freedom control input, using error feedback correction method and algorithm of predictive functional control, the list of control signal is defeated
Enter or single output;
The integrator plant production process feature is as follows:
Single-input single-output integrator plant production process can be described as:
WhereinIt is the impulse response coefficient of integrator plant production process, u (k) is system control input, yP(k) it is that system control is defeated
Go out;The impulse response coefficient of integrator plant production processConstant value is kept after step-length NThus formula (1) is reduced to
Formula (2) is transformed into Z domains, had
In formulaThe steady component of integrator plant production process transmission function is represented, and
Formula (3) is converted, the impulse response model for obtaining integrator plant production process is:
Forecast model then based on design controller is represented by
In formulaRepresent the steady component of integrator plant production process model, wherein siIt is forecast model arteries and veins
Rush response coefficient and s0=0;Then the future anticipation of the forecast model is output as
To provide the stability analysis result of system, following three definition is provided:
Define 4.1.Comprising forecast model impulse response coefficient in minimum valueAnd maximumBetween all objects, be designated as
The minimum value of ith sample moment impulse response coefficient is represented,Represent ith sample moment impulse response coefficient most
Big value, and have
Wherein
The difference of the minimum value of i-th and i-1 sampling instant impulse response coefficient is represented,Represent that i-th and i-1 is adopted
The difference of the maximum of sample moment impulse response coefficient;Given in minimum valueAnd maximumBetween all objects it is not true
Under fixed description,Forecast model impulse response coefficient is contained to existWithBetween all objects;
Define 4.2. is for the impulse response coefficient of integrator plant production processControll plant, controll plant and forecast model
Between sum of the deviations M be expressed as
The controll plant and forecast model impulse response coefficient s are known by formula (9)iBetween deviation meet
The maximum mismatch between forecast model and controll plant can so be obtained;
Define 4.3. maximum mismatch
For the maximum deviation between controll plant and forecast model, known by formula (9)Following relation is met with M
It is assumed thatsNIt is not zero, i.e.,
Wherein sNRepresent the forecast model impulse response coefficient s of integrator plant production processiThe constant value kept after step-length N, it is determined that
System in future expected performance index is as follows:
[H in formula1,Hp] it is optimization time domain, i is ith sample moment, JPIt is performance Index Calculation result, yref(k+i)=w (k+
i)-αi(w(k)-yP(k) reference locus) is represented, to cause system output according to the reference locus tracking fixed valure,TsFor sampling time, TrefFor the closed-loop control system expected response time, w is setting value,It is basis
TsFor sampling time and TrefThe numerical value that closed-loop control system expected response Time Calculation is obtained, w (k are tracked for constant value set point
+Hi)=w (k);E (k+i) is predicated error correction, and E (k+i)=(1-a) E (k-1)+(1+ai) [e (k-1)-e (k- are taken herein
2)]+ae (k-1), a are the parameters introduced;
A > 0 and a level off to 0 when, if when meeting such as lower inequality (22), proof system is stable:
Wherein with H1For prediction step.
2. the control method of the controller of the single-input single-output integrator plant production process described in claim 1, by building list
Free degree control input, utilizes error feedback correction method and algorithm of predictive functional control, the single input of control signal or single defeated
Go out, build algorithm of predictive functional control, comprise the following steps:
(1) single-degree-of-freedom control input is set up:Selection future course control input is made up of the weighting of following basic function
U (k)=u (k+j)=μ1(k), j=1,2 ..., Hi-1;
(2) excitation for implementing pulse signal to controll plant obtains procedural test model;
(3) system in future expected performance index is set up;
(4) derivation of future anticipation output;
(5) error feedback compensation is built;
(6) stability analysis of control system and the guarantee of tracking fixed valure zero-deviation;
Wherein u (k) is system control input, and u (k+j) is to expect input, μ in system future1(k) it is control input weight coefficient.
3. the control method of the controller of single-input single-output integrator plant production process according to claim 2, its feature
It is the following desired prediction output of derivation, obtains control input, obtain control system parameter adjusting method, specifically such as
Under:
(1) system control input u (k)=μ1(k)
(2) following HiStep prediction output
ym(k+Hi)=yfr(k+Hi)+yfo(k+Hi) (14)
In formula:
Wherein,It is the row matrix that the impulse response coefficient of integrator plant production process is constituted:
The row matrix being made up of future anticipation control input:[u(k+Hi-1) u(k+Hi- 2) ... u (k)],
The matrix constituted for the impulse response coefficient difference of integrator plant production process,
The row matrix being made up of the first last time system control input:
[u(k-1) u(k-2)…u(k-N+Hi)],
ForSubtract each other the matrix of composition with its impulse response coefficient previous,
The row matrix being made up of the second last time system control input:
[u(k-N-1+Hi) u(k-N-2+Hi)…u(k-N)];
(3) H is made1=Hp=H, by yref(k+H)=ym(k+H)+E (k+H), and make current k moment error correction E (k)=E (k+
H1), system control input can be obtained
I is unit row vector in formula, and
E (k)=(1-a) E (k-1)+(1+aH1)[e(k-1)-e(k-2)]+ae(k-1)。
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