CN113625556B - Self-adaptive control method of complex industrial system of circulating fluidized bed - Google Patents
Self-adaptive control method of complex industrial system of circulating fluidized bed Download PDFInfo
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Abstract
The invention discloses a self-adaptive control method of a complex industrial system of a circulating fluidized bed, which relates to an industrial control method. The algorithm is based on a CARIMA model, adopts long-period optimization performance indexes, combines identification and self-correction mechanisms, has the characteristics of stronger robustness, low model requirement and the like, and has a wide application range. The algorithm can overcome the defects of the self-adaptive algorithm such as generalized minimum variance, pole allocation and the like. The implicit algorithm does not identify the parameters of the object model, but directly identifies and obtains the parameters in the optimal control law according to the input/output data, so that a large amount of intermediate operations caused by on-line solution of the Diophantine equation are avoided, the calculation workload is reduced, and the time is saved. The system identification technology is suitable for complex industrial systems, and has practical significance in improving the automation level of the complex industrial systems by using a multivariable implicit generalized predictive control algorithm.
Description
Technical Field
The invention relates to an industrial system control method, in particular to a self-adaptive control method of a circulating fluidized bed complex industrial system.
Background
The 21 st century coal industry is rapidly developing, and pollution and combustion efficiency are problems that need to be solved in industrial production. The circulating fluidized bed boiler is the preferred boiler for coal burning because of excellent combustion efficiency and less pollution. The circulating fluidized bed boiler has the characteristics of time varying, multiple parameters, strong coupling, nonlinearity and the like, the mathematical model of the circulating fluidized bed boiler is difficult to build, and the problem of the complex industrial system cannot reach the expected effect by using the conventional control theory.
In response to this problem, in circulating fluidized bed boiler combustion systems, fluidized bed temperature is a critical control parameter that affects production efficiency and efficiency in industrial sites. The circulating fluidized bed boiler is different from the traditional pulverized coal furnace in the past, and because the circulating fluidized bed boiler temperature bed control system has the characteristics of large disturbance, multiple parameters, nonlinearity, strong coupling, large hysteresis and the like, the combustion heat transfer characteristic is extremely complex, the ideal adjusting effect is difficult to obtain by the conventional control means, and the technical difficulty exists in optimizing control. However, most circulating fluidized bed boiler systems have low automation level, and the control mode needs to be improved. Therefore, the improvement of the circulating fluidized bed boiler hearth temperature control algorithm is of great significance to the actual operation of the boiler.
Expert scholars at home and abroad use PID control algorithm to explore circulating fluidized bed boiler in a large amount. Such as "fuzzy adaptive PID control of circulating fluidized bed boiler combustion system based on dynamic domain" (Li Fengze, ma Suxia, dynamic engineering theory, 2021,41 (03): 195-200) [ 1 ], application of fuzzy adaptive PID control in circulating fluidized bed boiler main steam pressure "(Chen Mingshu, mian, industrial control computer, 2013,26 (08): 44-46) [ 2 ]. PID is the most traditional and most routine control algorithm in distributed control systems, and PID control is mostly adopted in actual production and operation processes of factories. However, because the accuracy requirement of the control object model is higher, when the working condition changes, the PID algorithm is difficult to meet the system control.
The generalized predictive control is a predictive control algorithm for realizing self-adaptive control through on-line parameter identification. In the control strategy, firstly, an online identification and estimation model is combined according to past control input, present input and output data and predicted output data. And then rolling and optimizing the predicted output and the expected output according to a certain performance index, and correcting the predicted output to correct and obtain the optimal control law.
The implicit generalized predictive control is used as an implicit improved algorithm of the generalized predictive control, so that the problems of long calculation time and large calculation amount of a generalized predictive control algorithm, which are caused by solving a lost figure equation and inverting a matrix, can be avoided. The implicit generalized predictive control directly estimates the parameters of the controller and can overcome the influence of system disturbance and model mismatch on the system performance to a certain extent. Accordingly, there is presented herein an application of multivariable-based implicit generalized predictive control in a circulating fluidized bed boiler control system.
The rapid development of the coal industry, pollution and combustion efficiency are problems that need to be solved in industrial production. Many complex industrial systems have the characteristics of time varying, multiple parameters, strong coupling, nonlinearity and the like, and the mathematical model is difficult to build, so that the problem of the complex industrial system cannot achieve the expected effect by using the conventional control theory.
Disclosure of Invention
The invention aims to provide a self-adaptive control method of a complex industrial system of a circulating fluidized bed, which combines an implicit generalized predictive control algorithm with on-line identification self-adaptive control to optimize the system and aims to realize the self-adaptive control of the complex industrial system of the circulating fluidized bed and the like; the method is suitable for the control of the circulating fluidized bed system by adopting a system identification technology, and the simulation effect of the method is obviously superior to that of a classical control system.
The invention aims at realizing the following technical scheme:
a method for adaptive control of a circulating fluidized bed complex industrial system, the method comprising the steps of:
generalized Predictive Control (GPC), which is a predictive control algorithm that implements adaptive control through online parameter identification; in the control strategy, firstly, an online identification and estimation model is combined according to past control input, present input and output data and predicted output data; rolling and optimizing the predicted output and the expected output according to a certain performance index, and correcting the predicted output to correct and obtain an optimal control law;
in addition, because GPC introduces a Diophantin equation to perform intermediate operation, calculation amount is large, IGPC algorithm utilizes RLS identification, is not limited to model establishment, identifies parameters according to input and output data, does not need to identify model parameters of a controlled object, and besides the robustness is improved by using feedback correction, IGPC self-correction control identification obtains control parameters, so that the robustness is further improved, and calculation of an inverse matrix when the Diophantin equation is solved can be avoided, calculation amount of the algorithm is reduced, and influence of system disturbance and model errors on the system can be overcome to a certain extent; the algorithm is easier to realize on-line identification and self-adaptive control, and has wider application range;
the circulating fluidized bed system model of the implicit generalized predictive control structure is provided with a CARIMA model of MIMO as follows:
can be broken down into two subsystems:
y 1 (k)＝B 11 (z -1 )u 1 (k-1)+B 12 (z -1 )u 2 (k)+ζ 1 (k)/Δ
A 2 (z -1 )y 2 (k)＝B 21 (z -1 )u 1 (k-1)+B 22 (z -1 )u 2 (k)+ζ 2 (k)/Δ
wherein A is 1 (z -1 )，A 2 (z -1 )，B 11 (z -1 )，B 12 (z -1 )，B 21 (z -1 )，B 22 (z -1 ) Are all z -1 Is a polynomial of (2); y is 1 (k) And y 2 (k) Is output by the system; u (u) 1 (k) And u 2 (k) Is a system input; zeta type 1 (k) And zeta 2 (k) White noise; delta = 1-z -1 。
The adaptive control method of the complex industrial system of the circulating fluidized bed comprises the following two subsystems of the CARIMA model of the multi-input multi-output implicit generalized predictive control:
1) Subsystem 1 model and Dipsilon map equation
1＝E 1j (z -1 )A(z -1 )Δ+z -j F 1j (z -1 )
The predictive equation can be obtained:
y 1 (k+j)＝E 1j (z -1 )B 11 (z -1 )Δu 1 (k+j-1)+E 1j (z -1 )B 12 (z -1 )Δu 2 (k+j-1)+
F 1j (z -1 )y 1 (k)+E 1j (z -1 )ζ 1 (k+j)
(j＝1,2,...,n)
the optimal output prediction is:
obtaining:
polynomial G 11j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 1 (k) Is a unit step response g of (2) 110 ,g 111 ,…,g 11j-1 ,g 11j The first j terms of …, polynomial G 12j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 2 (k) Is a unit step response g of (2) 120 ,g 121 ,…,g 12j-1 ,g 12j The first j items of … are
G 11j (z -1 )＝g 110 +g 111 z -1 +...+g 11j-1 z -j+1 +g 11j z -j +...
G 12j (z -1 )＝g 120 +g 121 z -1 +...+g 12j-1 z -j+1 +g 12j z -j +... (28)
Will beThe decomposition is divided into a known quantity and an unknown quantity at the moment k, and f is used 1 (k+j) represents a known amount:
thenCan be written as
Writing the above into a matrix form:
i.e.
In the method, in the process of the invention,
ΔU 1 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
ΔU 2 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
f 1 ＝[f 1 (k+1),f 1 (k+2),...,f 1 (k+n)] T
2) Subsystem 2 model and Dipsilon map equation
1＝E 2j (z -1 )A 2 (z -1 )Δ+z -j F 2j (z -1 )
Is available in the same way
In the method, in the process of the invention,
ΔU 1 ＝[Δu 1 (k),Δu 1 (k+1),...,Δu 1 (k+n-1)] T
ΔU 2 ＝[Δu 2 (k),Δu 2 (k+1),...,Δu 2 (k+n-1)] T
f 2 ＝[f 2 (k+1),f 2 (k+2),...,f 2 (k+n)] T
for the represented MIMO model, the objective function is employed:
in the method, in the process of the invention,
for a given MIMO system, the system can be decomposed into two independent two-input single-output subsystems, and the performance index of the MIMO is decomposed into the performance indexes of the two subsystems;
J＝J 1 +J 2
in the method, in the process of the invention,
let W 1 ＝[w 1 (k+1),w 2 (k+2),...,w 1 (k+n)] T
Then there are:
J 1 ＝(Y 1 -W 1 ) T (Y 1 -W 1 )+λΔU 1 T ΔU 1
by Y 1 Optimal predicted value of (2)Instead of Y 1 Regarding G12ΔU2+f1 as +.>
And order
Is available in the form of
I.e. DeltaU 1 ＝(G 11 T G 11 +λI) -1 G 11 T (W 1 -G 12 ΔU 2 -f 1 )
Similarly, ΔU can be obtained 2 ＝(G 22 T G 22 +λI) -1 G 22 T (W 2 -G 21 ΔU 1 -f 2 )
When the system is known, G can be calculated in advance 11 ,G 12 ,G 21 ,G 22 ,f 1 ,f 2 U can then be obtained according to the above formula 1 And U 2 。
According to the self-adaptive control method of the circulating fluidized bed complex industrial system, the parameter identification of two subsystems generated by the multi-input multi-output implicit generalized predictive control CARIMA model can be known, when the system parameter is unknown or has slow time variation, the system identification and the control strategy are combined as in the single-input single-output system described above, so that a corresponding self-correction control algorithm is formed;
n parallel predictors are available:
the last equation is written in matrix form:
y 1 (k+n)＝X 1 (k)θ 1 (k)+E 1n ζ 1 (k+n)
wherein X is 1 (k)＝[Δu 1 (k),...,Δu 1 (k+n-1),Δu 2 (k),...,Δu 2 (k+n-1),1]
θ 1 (k)＝[g 11n-1 ,g 11n-2 ,...,g 110 ,g 12n-1 ,g 12n-2 ,...,g 120 ,f 1 (k+n)] T
Output predicted value y 1 (k+n/k)＝X 1 (k)θ 1 (k) Or y 1 (k/k-n)＝X 1 (k-n)θ 1 (k)
Based on least squares method, matrix G can be identified 11 ，G 12 Parameters of (1) and the same thing can obtain G 21 ，G 22 Is a parameter of (a).
The working flow of the circulating fluidized bed boiler comprises that coal in a coal bin is processed and conveyed to a coal feeder through a lifter; the coal feeder conveys the coal into a hearth of the circulating fluidized bed boiler through the crawler belt; the limestone system is characterized in that limestone is subjected to primary crushing and secondary crushing, and large limestone is changed into limestone powder and conveyed into a hearth; introducing primary air to quickly raise the temperature in the hearth; introducing secondary air to fully perform the reaction of the hearth and improve the thermal efficiency; the flue gas generated by the circulating fluidized bed boiler reaction is separated into large particles and small particles by a cyclone separator; the large-particle flue gas is sent back to the hearth through the material returning mechanism; the small-particle flue gas passes through a superheater, an economizer and an air preheater; the high temperature flue gas temperature is reduced. Entering a dust remover to separate dust from steam; finally, the flue gas is discharged to the atmosphere from a chimney; a self-adaptive control method for circulating fluidized bed boiler system features that a function is chosen to generate a series of data, and then the function is used as model. Firstly, identifying necessary calculation parameters through parameter identification, and establishing a multi-input multi-output model of the circulating fluidized bed boiler system:
wherein: the coal feeding rate B, the primary air supply rate Q1 and the secondary air supply rate Q2 of the coal conveying system are control variables; bed temperature T of circulating fluidized bed b And main steam pressure p 0 Is a controlled variable; d, d 1 、d 2 Outputting the existing disturbance to the system; the combustion process of the circulating fluidized bed boiler has multivariable coupling characteristics, and in addition, the control problem is solved by adopting advanced control strategies such as generalized predictive control and the like in addition to the requirement of multi-target control.
The self-adaptive control method of the circulating fluidized bed complex industrial system comprises the following algorithm ideas and steps: according to the algorithm of the generalized predictive controller, the change of the curve is predicted, so that the difference between the predicted curve and the ideal curve is analyzed, and the influence of the parameters on the prediction precision of the system is analyzed, so that the main influence parameters and control rules are found.
6. The method for adaptively controlling a complex industrial system of a circulating fluidized bed according to claim 4, wherein the implementation steps of the GPC adaptive control algorithm based on the CARIMA model can be summarized as follows:
step1 set initial valueAnd P (0), inputting initial data, selecting control parameters N, controlling a weighting matrix lambda, outputting a softening coefficient alpha, forgetting factors mu and the like;
step2 adopts the current actual output y (k) and the reference track output yr (k+j);
step3 is controlled by adopting forgetting factor recursion augmentation least square method on-line real-time estimationParameters (parameters)I.e.
Step4, calculating a control matrix G;
step5 calculates and constructs vector Y r 、Y m ；
Step6, calculating and implementing u (k);
step7 returns to Step2 (k→k+1) and continues the cycle.
The self-adaptive control method of the circulating fluidized bed complex industrial system comprises an implicit generalized predictive control algorithm; programming a multivariable implicit generalized prediction self-adaptive control algorithm C language program by utilizing Matlab; setting parameters such as a time domain length p, a predicted length n, a control length m, a control weighting coefficient lambda, a softening coefficient alpha and the like; and obtaining a simulation image.
The invention has the advantages and effects that:
1. the invention provides an application of an implicit generalized predictive self-correction control algorithm based on a multivariable system. The predictive control self-corrector is based on a CARIMA model, adopts long-period optimization performance indexes, combines identification and self-correction mechanisms, has the characteristics of stronger robustness, low model requirement and the like, and has wide application range. The algorithm can overcome the defects of the self-adaptive algorithm such as generalized minimum variance, pole allocation and the like.
2. The implicit algorithm does not identify the parameters of the object model, but directly identifies and obtains the parameters in the optimal control law according to the input/output data, thereby avoiding a large amount of intermediate operations caused by solving the Diophantine equation on line, reducing the calculation workload and saving the time.
Drawings
FIG. 1 is a block diagram of a circulating fluidized bed boiler system of the present invention;
FIG. 2 is a flowchart of the steps for implementing the generalized predictive control adaptive algorithm of the present invention;
FIG. 3 is a closed loop block diagram of a generalized predictive control system of the present invention;
FIG. 4 is a generalized predictive control architecture of the present invention;
FIGS. 5-7 are the derivation of the generalized predictive control internal mold structure of the present invention;
FIG. 8 is a diagram of the internal model of the generalized predictive control system of the present invention;
fig. 9 is an illustration of the effect of the softening process of the present invention on generalized predictive control.
Detailed Description
The present invention will be described in detail with reference to the embodiments shown in the drawings.
The invention relates to an application of an implicit generalized prediction self-correction control algorithm based on a multivariable circulating fluidized bed system. The predictive control self-corrector is based on a CARIMA model, adopts long-period optimization performance indexes, combines identification and self-correction mechanisms, has the characteristics of stronger robustness, low model requirement and the like, and has wide application range. The algorithm can overcome the defects of the self-adaptive algorithm such as generalized minimum variance, pole allocation and the like. In recent years, it has attracted a great deal of attention in the world of control theory, and GPC is considered to be the most robust of the self-correcting control methods known so far.
In predictive control theory, a basic model describing the dynamic behavior of the system is required to be a predictive model. It should have predictive functionality, i.e. the ability to predict future output values of the system based on historical data and future inputs of the system.
1. The system adopts a CARIMA model as a prediction model, wherein the model CARIMA is an abbreviation of 'Controller Auto-Regressive Integrated Moving-Average' and can be translated into a 'controlled autoregressive integral sliding Average model'. This model can be written as:
A(z -1 )y(k)＝B(z -1 )u(k-1)+C(z -1 )ξ(k)/Δ (1)
wherein z is -1 Is a backward operator; y (k) and u (k) represent the output and input at time k, respectively; ζ (k) represents a white noise sequence with zero mean; delta = 1-z -1 Is a differential operator.
In the above, n a 、n b 、n c Respectively polynomial a (z -1 )、B(z -1 )、C(z -1 ) Is a function of the order of (2). If the system time lag is greater than zero, B (z -1 ) The coefficient or coefficients of the polynomial head are equal to zero. Clarke et al, when pushing to generalized predictive control, let C (z -1 )＝1。
2. For system robustness enhancement, consider the effect of the current time input u (k) on future time, using the following objective function:
wherein n is the maximum predicted length; m represents the control length, and m is less than or equal to n in total; y (k+j) is the j-th output of the system prediction; w is an expected value output by an object, and a signal w (k+j) is an output reference sequence; λ (j) is a control weighting coefficient, taking a constant value greater than zero, if λ (j) =0 means that the control increment is not constrained.
For the purpose of softening control, the control is to track the reference trajectory instead of directly tracking the output to the set point, as follows:
w(k+j)＝α j y(k)+(1-α j )y r (j＝1,2,…,n) (4)
wherein: y is r Y (k) and w (k) are respectively the set value of the system, the actually measured output value of the system and the reference track, alpha is the softening coefficient, 0<α<1。
To predict the output y (k+j) of step j by rolling optimization, a self-correction algorithm is used for Generalized Minimum Variance Control (GMVC) to obtain an optimal prediction. The Diophantine equation is introduced herein:
1＝A(z -1 )ΔE j (z -1 )+z -j F j (z -1 ) (5)
wherein, the liquid crystal display device comprises a liquid crystal display device,
multiplying both sides of (1) by E j (z -1 )z j And (3) combining the method with the method (4), and finishing a forward generalized forecast equation of the controlled object:
y(k+j)＝G j (z -1 )Δu(k+j-1)+F j (z -1 )y(k)+E j (z -1 )ξ(k+j) (7)
in the method, in the process of the invention,
G j (z -1 )＝B(z -1 )E j (z -1 )＝g 0 +g 1 z -1 +…+g j-1 z -j+1 (8)
neglecting the noise effect, the output predicted value at the k moment can be obtained:
the optimal output predicted value obtainable according to the above equation is represented by a vector:
in the middle of
3. Optimal control rate
If order
W＝[w(k+1),w(k+2),…,w(k+n)] T (13)
Then equation (3) can be represented as a matrix vector:
J＝(Y-W) T (Y-W)+λΔU T ΔU (14)
will optimize the predicted valueInstead of Y, formula (9) is substituted into (13) and +.>The method can obtain:
ΔU＝(G T G+λI) -1 G T (W-F) (15)
Δ U, W, F is the control increment, tracking the reference trajectory, and predicting the vector, respectively. The control amount input at the next time is:
u(k)＝u(k-1)+g T (W-F) (16)
in the formula g T Is (G) T G+λI) -1 G T Is a first row of (c). To solve the optimal control rate deltau, the matrix G and the prediction vector F need to be identified through input and output by using an implicit self-correction method according to a prediction equation.
The m parallel predictors available according to equation (9) are:
y(k+1)＝g 0 Δu(k)+f(k+1)+E 1 ξ(k+1)
y(k+2)＝g 1 Δu(k)+g 0 Δu(k+1)+f(k+2)+E 2 ξ(k+2)
…
y(k+m)＝g m-1 Δu(k)+…+g 0 Δu(k+m-1)+f(k+m)+E m ξ(k+m) (17)
from the above equation, all elements in the matrix G appear in the mth equation, and thus the matrix G can be found by identifying them.
Wherein the model parameters can be vector-codedAnd data parameters->The representation is:
all output expressions can be expressed in matrix form as follows:
or (b)
Adopting a Recursive Least Squares (RLS) parameter identification algorithm with forgetting factors:
where λ is a forgetting factor, with 0.95< λ <1.K (K) is a weight and P (K) is a positive covariance matrix.
In general, for recursive operations, it is necessary to giveInitial value of P (k). According to the recursive least square method, the element G in the matrix G and the vector F can be obtained 0 ，g 1 … and f (k+m).
4. In the generalized predictive control algorithm derivation process, although feedback or closed-loop representation is not explicitly given, when it performs rolling optimization, the base point of optimization is emphasized to be consistent with the actual system. This means that at each step of the control the actual output is detected and compared with the predicted value and the uncertainty of the prediction is corrected in this way. When the actual system has nonlinear, time-varying, model mismatch, interference and other factors, the feedback correction can correct the predicted value in time, so that the optimization is established on the basis of more accurate prediction. Therefore, the method can reduce the requirement on a basic model, improve the control robustness and has very practical significance in practical industrial application. The system model is used for setting a CARIMA model of MIMO as follows:
wherein A is 1 (z -1 )，A 2 (z -1 )，B 11 (z -1 )，B 12 (z -1 )，B 21 (z -1 )，B 22 (z -1 ) Are all z -1 Is a polynomial of (2); y is 1 (k) And y 2 (k) Is output by the system; u (u) 1 (k) And u 2 (k) Is a system input; zeta type 1 (k) And zeta 2 (k) White noise; delta = 1-z -1 。、
Equation (22) can be broken down into two subsystems:
y 1 (k)＝B 11 (z -1 )u 1 (k-1)+B 12 (z -1 )u 2 (k)+ζ 1 (k)/Δ (23)
A 2 (z -1 )y 2 (k)＝B 21 (z -1 )u 1 (k-1)+B 22 (z -1 )u 2 (k)+ζ 2 (k)/Δ (24)
1) Subsystem
From subsystem 1 model of (23) and Dipsilon diagram equation
1＝E 1j (z -1 )A(z -1 )Δ+z -j F 1j (z -1 ) (25)
The predictive equation can be obtained:
y 1 (k+j)＝E 1j (z -1 )B 11 (z -1 )Δu 1 (k+j-1)+E 1j (z -1 )B 12 (z -1 )Δu 2 (k+j-1)+
F 1j (z -1 )y 1 (k)+E 1j (z -1 )ζ 1 (k+j)
(j＝1,2,...,n) (26)
the optimal output prediction is:
wherein G is 11j ＝E 1j B 11 ＝g 11j0 +g 11j1 z -1 +...+g 11jj z -j+1 +...
G 12j ＝E 1j B 12 ＝g 12j0 +g 12j1 z -1 +...+g 12jj z -j+1 +...
Obtained from (25)
From this, it can be seen that polynomial G 11j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 1 (k) Is a unit step response g of (2) 110 ,g 111 ,…,g 11j-1 ,g 11j The first j terms of …, polynomial G 12j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 2 (k) Is a unit step response g of (2) 120 ,g 121 ,…,g 12j-1 ,g 12j The first j items of …. Then there is
G 11j (z -1 )＝g 110 +g 111 z -1 +...+g 11j-1 z -j+1 +g 11j z -j +...
G 12j (z -1 )＝g 120 +g 121 z -1 +...+g 12j-1 z -j+1 +g 12j z -j +... (28)
As in the case of the monovariate method, the compound of formula (27)The decomposition is divided into a known quantity and an unknown quantity at the moment k, and f is used 1 (k+j) represents a known quantity.
Then formula (27) can be written as
Writing the above into a matrix form:
i.e.
In the method, in the process of the invention,ΔU 1 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
ΔU 2 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
f 1 ＝[f 1 (k+1),f 1 (k+2),...,f 1 (k+n)] T
2) Subsystem 2
From subsystem 2 model of (24) and the Dipsilon diagram equation
1＝E 2j (z -1 )A 2 (z -1 )Δ+z -j F 2j (z -1 )
Is available in the same way
In the method, in the process of the invention,ΔU 1 ＝[Δu 1 (k),Δu 1 (k+1),...,Δu 1 (k+n-1)] T
ΔU 2 ＝[Δu 2 (k),Δu 2 (k+1),...,Δu 2 (k+n-1)] T
f 2 ＝[f 2 (k+1),f 2 (k+2),...,f 2 (k+n)] T
5. objective function and optimal control rate
For the MIMO model represented by equation (22), an objective function is used:
/>
in the method, in the process of the invention,
for a given MIMO system equation (22), two independent two-input single-output subsystems (23) and (24) can be decomposed, and their corresponding output predicted values are obtained by equations (30) and (31), respectively, and the performance index of MIMO is decomposed into the performance indexes of the two subsystems.
Writing formula (32) as:
J＝J 1 +J 2 (33)
in the method, in the process of the invention,
for the subsystem equation (23), the corresponding subsystem objective function is equation (34), and the output prediction value is equation (30). In the formula (30), ΔU at the previous time is used 2 Value replaces deltau at time k 2 Value, i.e. G 12 ΔU 2 Seen as a known quantity.
Then equation (30) can be written as:
then as in the univariate system, another
W 1 ＝[w 1 (k+1),w 2 (k+2),...,w 1 (k+n)] T
Then formula (34) may be expressed as
J 1 ＝(Y 1 -W 1 ) T (Y 1 -W 1 )+λΔU 1 T ΔU 1 (36)
By Y 1 Optimal predicted value of (2)Instead of Y 1 Handle G 12 ΔU 2 +f 1 Is regarded as->
And order
Is available in the form of
I.e. DeltaU 1 ＝(G 11 T G 11 +λI) -1 G 11 T (W 1 -G 12 ΔU 2 -f 1 ) (37)
Similarly, ΔU can be obtained 2 ＝(G 22 T G 22 +λI) -1 G 22 T (W 2 -G 21 ΔU 1 -f 2 ) (38)
When the system is known, G can be calculated in advance 11 ,G 12 ,G 21 ,G 22 ,f 1 ,f 2 U can then be obtained according to formulas (37) and (38) 1 And U 2 。
6. Identification of parameters
When the system parameters are unknown or have slow time variation, the system identification is combined with the control strategy to form a corresponding self-correction control algorithm.
From equation (9), n parallel predictors can be obtained:
the last equation is written in matrix form:
y 1 (k+n)＝X 1 (k)θ 1 (k)+E 1n ζ 1 (k+n) (39)
wherein X is 1 (k)＝[Δu 1 (k),...,Δu 1 (k+n-1),Δu 2 (k),...,Δu 2 (k+n-1),1]
θ 1 (k)＝[g 11n-1 ,g 11n-2 ,...,g 110 ,g 12n-1 ,g 12n-2 ,...,g 120 ,f 1 (k+n)] T
Output predicted value y 1 (k+n/k)＝X 1 (k)θ 1 (k) Or y 1 (k/k-n)＝X 1 (k-n)θ 1 (k)
As with the single-input single-output system, the matrix G can be identified by the least square method 11 ，G 12 Parameters of (1) and the same thing can obtain G 21 ，G 22 Is a parameter of (a).
A specific embodiment of the present invention will be given below by taking a circulating fluidized bed boiler control system in a thermal power plant as an example.
The circulating fluidized bed boiler had a capacity of 135MW and a thermal efficiency of about 91.28%. The working flow is as follows: the coal in the coal bunker is transported to a coal feeder by a lifter through a series of processes. The coal feeder conveys coal into the circulating fluidized bed boiler furnace through the crawler belt. For the limestone system, the limestone is subjected to primary crushing and secondary crushing, and large limestone is changed into limestone powder and is conveyed into a hearth. And primary air is introduced to rapidly raise the temperature in the hearth. And secondary air is introduced to fully perform the reaction of the hearth and improve the thermal efficiency. The flue gas generated by the circulating fluidized bed boiler reaction is separated into large particles and small particles by a cyclone separator. And the large-particle flue gas is returned to the hearth through the material returning mechanism. The small-particle flue gas passes through a superheater, an economizer and an air preheater. The high temperature flue gas temperature is reduced. Enters a dust remover to separate dust from steam. And finally, the flue gas is discharged to the atmosphere from the chimney. The structure of the circulating fluidized bed boiler system is shown in fig. 1.
First, a function is selected to generate a series of data, and then the function is used as a model. Firstly, identifying necessary calculation parameters through parameter identification, and establishing a multi-input multi-output model of the circulating fluidized bed boiler system:
wherein: coal feeding rate B and primary air supply rate Q of coal conveying system 1 And the air supply rate Q of the secondary air 2 Is a control variable; bed temperature T of circulating fluidized bed b And main steam pressure p 0 Is a controlled variable; d, d 1 、d 2 The existing disturbances are output for the system. The combustion process of the circulating fluidized bed boiler has multivariable coupling characteristics, and in addition, the control problem is solved by adopting advanced control strategies such as generalized predictive control and the like in addition to the requirement of multi-target control.
The method comprises the following steps: according to the algorithm of the generalized predictive controller, the change of the curve is predicted, so that the difference between the predicted curve and the ideal curve is analyzed, and the influence of the parameters on the prediction precision of the system is analyzed, so that the main influence parameters and control rules are found.
The implementation steps of the GPC adaptive control algorithm based on the CARIMA model can be summarized as follows:
step1 set initial valueAnd P (0), inputting initial data, selecting control parameters N, controlling a weighting matrix lambda, outputting a softening coefficient alpha, forgetting factors mu and the like;
step2 uses the current actual output y (k) and the reference trajectory output y r (k+j)；
Step3 adopts forgetting factor recursion augmentation least square method to estimate controlled parameters in real time on lineI.e.
Step4, calculating a control matrix G;
step5 calculates and constructs vector Y r 、Y m ；
Step6, calculating and implementing u (k);
step7 returns to Step2 (k→k+1) and continues the cycle.
Fig. 2 is a flow chart of an implicit generalized predictive control algorithm.
And programming a multivariable implicit generalized predictive adaptive control algorithm C language program by utilizing Matlab. Setting parameters such as a time domain length p, a predicted length n, a control length m, a control weighting coefficient lambda, a softening coefficient alpha and the like. A simulated image may be obtained.
Claims (6)
1. A method for adaptively controlling a complex industrial system of a circulating fluidized bed, the method comprising the steps of:
generalized Predictive Control (GPC), which is a predictive control algorithm that implements adaptive control through online parameter identification; in the control strategy, firstly, an online identification and estimation model is combined according to past control input, present input and output data and predicted output data; rolling and optimizing the predicted output and the expected output according to a certain performance index, and correcting the predicted output to correct and obtain an optimal control law;
in addition, because GPC introduces a Diophantin equation to perform intermediate operation, calculation amount is large, IGPC algorithm utilizes RLS identification, is not limited to model establishment, identifies parameters according to input and output data, does not need to identify model parameters of a controlled object, and besides the robustness is improved by using feedback correction, IGPC self-correction control identification obtains control parameters, so that the robustness is further improved, and calculation of an inverse matrix when the Diophantin equation is solved can be avoided, calculation amount of the algorithm is reduced, and influence of system disturbance and model errors on the system can be overcome to a certain extent; the algorithm is easier to realize on-line identification and self-adaptive control, and has wider application range;
the circulating fluidized bed system model of the implicit generalized predictive control structure is provided with a CARIMA model of MIMO as follows:
can be broken down into two subsystems:
y 1 (k)＝B 11 (z -1 )u 1 (k-1)+B 12 (z -1 )u 2 (k)+ζ 1 (k)/Δ
A 2 (z -1 )y 2 (k)＝B 21 (z -1 )u 1 (k-1)+B 22 (z -1 )u 2 (k)+ζ 2 (k)/Δ
wherein A is 1 (z -1 )，A 2 (z -1 )，B 11 (z -1 )，B 12 (z -1 )，B 21 (z -1 )，B 22 (z -1 ) Are all z -1 Is a polynomial of (2); y is 1 (k) And y 2 (k) Is output by the system; u (u) 1 (k) And u 2 (k) Is a system input; zeta type 1 (k) And zeta 2 (k) White noise; delta = 1-z -1 ；
The CARIMA model of the multi-input multi-output implicit generalized predictive control comprises two subsystems:
1) Subsystem 1 model and Dipsilon map equation
1＝E 1j (z -1 )A(z -1 )Δ+z -j F 1j (z -1 )
The predictive equation can be obtained:
y 1 (k+j)＝E 1j (z -1 )B 11 (z -1 )Δu 1 (k+j-1)+E 1j (z -1 )B 12 (z -1 )Δu 2 (k+j-1)+F 1j (z -1 )y 1 (k)+E 1j (z -1 )ζ 1 (k+j)
(j＝1,2,...,n)
the optimal output prediction is:
obtaining:
polynomial G 11j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 1 (k) Is a unit step response g of (2) 110 ,g 111 ,…,g 11j-1 ,g 11j The first j terms of …, polynomial G 12j (z -1 ) The first j terms are exactly y 1 (k) Concerning u 2 (k) Is a unit step response g of (2) 120 ,g 121 ,…,g 12j-1 ,g 12j The first j items of … are
G 11j (z -1 )＝g 110 +g 111 z -1 +...+g 11j-1 z -j+1 +g 11j z -j +...
G 12j (z -1 )＝g 120 +g 121 z -1 +...+g 12j-1 z -j+1 +g 12j z -j +... (28)
Will beThe decomposition is divided into a known quantity and an unknown quantity at the moment k, and f is used 1 (k+j) represents a known amount:
thenCan be written as
Writing the above into a matrix form:
i.e.
In the method, in the process of the invention,
ΔU 1 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
ΔU 2 ＝[Δu(k),Δu(k+1),...,Δu(k+n-1)] T
f 1 ＝[f 1 (k+1),f 1 (k+2),...,f 1 (k+n)] T
2) Subsystem 2 model and Dipsilon map equation
1＝E 2j (z -1 )A 2 (z -1 )Δ+z -j F 2j (z -1 )
Is available in the same way
In the method, in the process of the invention,
ΔU 1 ＝[Δu 1 (k),Δu 1 (k+1),...,Δu 1 (k+n-1)] T
ΔU 2 ＝[Δu 2 (k),Δu 2 (k+1),...,Δu 2 (k+n-1)] T
f 2 ＝[f 2 (k+1),f 2 (k+2),...,f 2 (k+n)] T
for the represented MIMO model, the objective function is employed:
in the method, in the process of the invention,
for a given MIMO system, the system can be decomposed into two independent two-input single-output subsystems, and the performance index of the MIMO is decomposed into the performance indexes of the two subsystems;
J＝J 1 +J 2
in the method, in the process of the invention,
let W 1 ＝[w 1 (k+1),w 2 (k+2),...,w 1 (k+n)] T
Then there are:
J 1 ＝(Y 1 -W 1 ) T (Y 1 -W 1 )+λΔU 1 T ΔU 1
by Y 1 Optimal predicted value of (2)Instead of Y 1 Handle G 12 ΔU 2 +f1 is regarded as->
And order
Can obtain DeltaU 1 ＝(G 11 T G 11 +λI) -1 G 11 T (W 1 -f 1 )
I.e. DeltaU 1 ＝(G 11 T G 11 +λI) -1 G 11 T (W 1 -G 12 ΔU 2 -f 1 )
Similarly, ΔU can be obtained 2 ＝(G 22 T G 22 +λI) -1 G 22 T (W 2 -G 21 ΔU 1 -f 2 )
When the system is known, G can be calculated in advance 11 ,G 12 ,G 21 ,G 22 ,f 1 ,f 2 U can then be obtained according to the above formula 1 And U 2 。
2. The adaptive control method of a complex industrial system of a circulating fluidized bed according to claim 1, wherein the parameter identification of two subsystems generated by the multi-input multi-output implicit generalized predictive control CARIMA model can be known, when the system parameter is unknown or has slow time variation, the system identification and the control strategy are combined to form a corresponding self-correction control algorithm like the single-input single-output system described above;
n parallel predictors are available:
the last equation is written in matrix form:
y 1 (k+n)＝X 1 (k)θ 1 (k)+E 1n ζ 1 (k+n)
wherein X is 1 (k)＝[Δu 1 (k),...,Δu 1 (k+n-1),Δu 2 (k),...,Δu 2 (k+n-1),1]
θ 1 (k)＝[g 11n-1 ,g 11n-2 ,...,g 110 ,g 12n-1 ,g 12n-2 ,...,g 120 ,f 1 (k+n)] T
Output pre-processingMeasured value of y 1 (k+n/k)＝X 1 (k)θ 1 (k) Or y 1 (k/k-n)＝X 1 (k-n)θ 1 (k)
Based on least squares method, matrix G can be identified 11 ，G 12 Parameters of (1) and the same thing can obtain G 21 ，G 22 Is a parameter of (a).
3. The method for adaptively controlling a complex industrial system of a circulating fluidized bed according to claim 1, wherein the circulating fluidized bed boiler work flow comprises that coal in a coal bunker is processed and transported to a coal feeder through a lifter; the coal feeder conveys the coal into a hearth of the circulating fluidized bed boiler through the crawler belt; the limestone system is characterized in that limestone is subjected to primary crushing and secondary crushing, and large limestone is changed into limestone powder and conveyed into a hearth; introducing primary air to quickly raise the temperature in the hearth; introducing secondary air to fully perform the reaction of the hearth and improve the thermal efficiency; the flue gas generated by the circulating fluidized bed boiler reaction is separated into large particles and small particles by a cyclone separator; the large-particle flue gas is sent back to the hearth through the material returning mechanism; the small-particle flue gas passes through a superheater, an economizer and an air preheater; reducing the temperature of the high-temperature flue gas; entering a dust remover to separate dust from steam; finally, the flue gas is discharged to the atmosphere from a chimney; firstly, selecting a function to generate a series of data, and taking the function as a model; firstly, identifying necessary calculation parameters through parameter identification, and establishing a multi-input multi-output model of the circulating fluidized bed boiler system:
wherein: coal feeding rate B and primary air supply rate Q of coal conveying system 1 And the air supply rate Q of the secondary air 2 Is a control variable; bed temperature T of circulating fluidized bed b And main steam pressure p 0 Is a controlled variable; d, d 1 、d 2 Outputting the existing disturbance to the system; circulation typeThe combustion process of the annular fluidized bed boiler has multivariable coupling characteristics, and in addition, the requirement of multi-target control is met, and an advanced control strategy of generalized predictive control is needed to solve the control problem.
4. A method for adaptively controlling a complex industrial system of a circulating fluidized bed according to claim 3, wherein the algorithm idea and steps are as follows: according to the algorithm of the generalized predictive controller, the change of the curve is predicted, so that the difference between the predicted curve and the ideal curve is analyzed, and the influence of the parameters on the prediction precision of the system is analyzed, so that the main influence parameters and control rules are found.
5. A method for adaptively controlling a complex industrial system of a circulating fluidized bed according to claim 3, wherein the implementation steps of the GPC adaptive control algorithm based on the CARIMA model can be summarized as follows:
step1 set initial valueAnd P (0), inputting initial data, selecting a control parameter N, controlling a weighting matrix lambda, outputting a softening coefficient alpha and forgetting a factor mu;
step2 uses the current actual output y (k) and the reference trajectory output y r (k+j)；
Step3 adopts forgetting factor recursion augmentation least square method to estimate controlled parameters in real time on lineI.e. < ->
Step4, calculating a control matrix G;
step5 calculates and constructs vector Y r 、Y m ；
Step6, calculating and implementing u (k);
step7 returns to Step2, k→k+1, continuing the cycle.
6. A method of adaptive control of a circulating fluidized bed complex industrial system of claim 3, wherein the implicit generalized predictive control algorithm; programming a multivariable implicit generalized prediction self-adaptive control algorithm C language program by utilizing Matlab; setting a time domain length p, a predicted length n, a control length m, a control weighting coefficient lambda and a softening coefficient alpha; and obtaining a simulation image.
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