CN110069015A - A kind of method of Distributed Predictive function control under non-minimumization state-space model - Google Patents

Abstract

The invention discloses a distributed prediction function control method under a non-minimization state space model, comprising the following steps: Step 1, establishing a distributed prediction function control non-minimization state space model; A distributed predictive function control controller under the model. The invention establishes a distributed prediction function control method under the non-minimization state space model by means of data acquisition, model establishment, prediction mechanism, optimization, etc., and uses this method under the premise of ensuring higher control accuracy and stability. , which can effectively make up for the deficiencies of traditional distributed predictive function control methods in multivariable process control with non-self-balancing objects, and meet the needs of actual industrial processes.

Description

A Method of Distributed Predictive Function Control Based on Non-minimizing State Space Model

technical field

The invention belongs to the technical field of automation, and relates to a design method of distributed predictive function control under a non-minimization state space model.

Background technique

Although the distributed predictive function control (DPFC) has a good control effect, the rapidity of the system is still not good enough. Especially in the case of introducing interference, it takes too long to restore stability again, and some industrial processes may not meet the requirements. At the same time, when interference is introduced and the set value is small, the output cannot track the set value perfectly, and there is a slight deviation. Although the deviation is small, it does exist. In the actual industrial production process, as the requirements for the control accuracy and safe operation of the product are getting higher and higher, it is necessary to eliminate some small deviations. Therefore, it is necessary to make some improvements to the distributed predictive function control.

SUMMARY OF THE INVENTION

Model predictive control based on non-minimum state space (NMSS) offers the advantages of state space methods, such as easy analysis and simple structural design. In response to this fact, the present invention proposes a new extended non-minimum state space model (EMSMS), which takes into account the influence of output errors, measured outputs and inputs on the design of model predictive control controllers. The extended non-minimum state space model Predictive control maintains the good advantages of the state-space model and prevents the further increase of the tracking error, which can control the error well. The extended non-minimum state space model and the distributed predictive function control are combined here, which not only maintains the better control effect of the distributed predictive function control, but also improves the rapidity of the system to a certain extent.

The technical scheme of the present invention is to establish a distributed prediction function control method under the non-minimization state space model by means of data acquisition, model establishment, prediction mechanism, optimization, etc. Under the premise of stability, it can effectively make up for the deficiencies of the traditional distributed predictive function control method in multivariable process control with non-self-balancing objects, and meet the needs of actual industrial processes.

The steps of the method of the present invention include:

Step 1. The distributed prediction function controls the establishment of a non-minimized state space model. The specific steps are:

1.1. Considering the multi-variable N-input N-output large-scale system in the industrial process as a subsystem composed of N first-order inertia plus pure lag (FOPDT) models, the following form of N-input N-output multi-variable first-order inertia can be obtained Plus pure lag (FOPDT) model system:

Among them, K ₁₁ ,…,K _ij ,…,K _nn is the steady-state gain of the j-th input to the i-th output of the multivariable process object, i=1,…,n; j=1,…,n,T ₁₁ ,…,T _ij ,…,T _nn is the time constant of the jth input to the ith output of the multivariate process object, τ ₁₁ ,…,τ _ij ,…,τ _nn is the jth input of the multivariate process object Lag time for the ith output.

1.2. The transfer function of the input of the j-th object to the output of the i-th object is:

1.3. Under the condition of sampling time T _s , discretize step 1.2, we can get:

Among them, k represents time, d=τ _ij /T _s integer part, α _ij =eT _s /T _ij , _yi (k), _yi (k-1) are the ith subsystem at time k and The output at time k-1, u _i (kd-1) is the input of the ith subsystem at time kd-1, u _j (kd-1) is the input of the jth subsystem at time kd-1, It reflects the influence of other subsystem inputs on the output of the ith subsystem.

1.4. For the first-order difference of the discretized model orientation, we get:

Among them, Δy _i (k), Δy _i (k-1) are the output increments of the ith subsystem at time k and time k-1, respectively, Δu _i (kd-1) is the ith subsystem at kd-1 The input increment at time 1, Δu _j (kd-1) is the input increment of the jth subsystem at time kd-1, Reflects the incremental influence of other subsystem inputs on the output of the ith subsystem.

1.5. From step 1.3 and step 1.4; obtain:

Δx _i,j (k+1)=A _i,j,m Δx _i,j (k)+B _i,j,m Δu _i (k)+D _i,j,m Δu _j (k)

Δy _i (k+1)=C _i,j,m Δx _i,j (k+1)

where Δx _i,j (k)=[Δy _i (k),Δu _i (k-1),…,Δu _i (kd),Δu _j (k-1),…,Δu _j (kd)] ^T , Δu _i (k-1),,Δu _i (kd), Δu _j (k-1),…,Δu _j (kd) represent k-1,…,kd respectively, the input increment and output increment at time ;Δx _i,j (k+1)=[Δy _i (k+1),Δu _i (k),…,Δu _i (k-d+1),Δu _j (k),…,Δu _j (k -d+1)] ^T , Δy _i (k+1), Δu _i (k-d+1), Δu _j (k-d+1) represent the output increase of the ith subsystem at time k+1, respectively Quantity, the input increment of the ith subsystem at the time k-d+1, the input increment of the jth subsystem at the time k-d+1, and T represents the transpose symbol of the matrix.

B _i,j,m = [0 1 0 0 0 ... 0] ^T ;

C _i,j,m = [1 0 0 ... 0 0 0 0];

D _i,j,m = [0 ... 0 0 1 0 ... 0] ^T ;

1.6. According to step 1.5, the non-minimum state space model can be obtained:

_zi (k+1)=Azi (k)+BΔu _i (k)+DΔu _j (k)+CΔr _{i (} k+1)

in: e _i (k)=y _i (k)-r _i (k)

e _i (k+1)=e _i (k)+C _i,j,m A _i,j,m Δx _i,j (k)+C _i,j,m B _i,j,m Δu _i (k )+D _i,j,m B _i,j,m Δu _j (k)-Δr _i (k+1)

ri (k) is the reference trajectory at time _{k, Δr i (} k+1) is the reference trajectory increment at time k+1, e _i (k), e _i (k+1) are k, k+1 respectively The error between the system output and the reference trajectory at time.

Step 2, the design of the distributed predictive function control controller under the non-minimized state space model, the specific steps are:

2.1. According to step 1.6, we can get:

Z _i =Gz _i (k)+SΔU _i,j +ΨΔR _i

Among them, P represents the optimization time domain, M represents the control time domain

ΔU _i,j = [Δu _i (k) Δu _i (k+1) … Δu _i (k+M-1),Δu _j (k) Δu _j (k+1) … Δu _j (k+M-1) )] ^T

ΔR _i =[Δr _i (k+1) Δr _i (k+2) … Δr _i (k+P)] ^T

r _i (k+ii)=λ ⁱⁱ y _i (k)+(1-λ ⁱⁱ )c _i (k),ii=1,2,...,P

λ represents the softening factor, c _i (k) represents the set value of the i-th subsystem at time k, Δr _i (k+1), Δr _i (k+2), ..., Δr _i (k+P) represent respectively The reference trajectory increments at time k+1,...,k+P.

2.2. Take the i-th subsystem objective function:

J _i =Z _i ^T Q _i,m Z _i +ΔU _i,j ^T R _i,j,m ΔU _i,j

Wherein, Q _i,m =block diag(Q _i,1 ,Q _i,2 ,...,Q _i,P-1 ,Q _i,P )

r _i,1 ,…,r _i,M ,r _j,1 ,…,r _j,M respectively represent the values of the reference trajectories of the ith and jth subsystems from time 1,…,k time.

2.3. From step 2.2, we can get:

ΔU _i,j =-(S ^T Q _i,m S+R _i,j,m ) ^-1 S ^T Q _i,m (Gz _i (k)+ΨΔR _i )

u _i (k)=[1 0 … 0]ΔU _i,j +u _i (k-1)

Among them, u _i (k) and u _i (k-1) represent the control quantities of the i-th subsystem k and k-1, respectively.

2.4. Use the control increment ΔU _i,j of the ith subsystem to obtain the actual control variable u _i (k)=[1 0 … 0]ΔU _i,j +u _i (k-1) of the ith subsystem in the i-th subsystem; then similarly, the control quantities of the 1st,...,n subsystems can be obtained respectively.

Detailed ways

The present invention will be further described below.

Take boiler drum water level control as an example:

The boiler drum water level control system is a typical multi-variable complex object, and the adjustment method is to control the opening of the feed water valve.

Step 1. The establishment of the boiler drum water level control system model, the specific steps are:

1.1. Considering the multi-variable N-input N-output large-scale system in the boiler drum water level control system as a subsystem composed of N first-order inertia plus pure lag (FOPDT) models, the following forms of N-input and N-output are obtained: Variable first-order inertia plus pure lag (FOPDT) model system:

Among them, K ₁₁ ,…,K _ij ,…,K _nn is the steady-state gain of the j-th input to the i-th output of the boiler drum water level control system, i=1,…,n; j=1,…,n , T ₁₁ ,…,T _ij ,…,T _nn is the time constant of the jth input to the i-th output of the boiler drum water level control system, τ ₁₁ ,…,τ _ij ,…,τ _nn is the boiler drum water level The lag time of the jth input to the ith output of the control system.

1.2. The transfer function of the input of the j-th object to the output of the i-th object in the boiler drum water level control system is:

1.3. Under the condition of sampling time T _s , discretize step 1.2, we can get:

Among them, k represents time, d=τ _ij /T _s integer part, α _ij =eT _s /T _ij , _yi (k), _yi (k-1) are the ith subsystem at time k and Drum water level at time k-1, u _i (kd-1) is the valve opening of the ith subsystem at time kd-1, u _j (kd-1) is the valve of the jth subsystem at time kd-1 opening, It reflects the influence of other subsystem inputs on the drum water level of the ith subsystem.

1.4. For the first-order difference of the discretized model orientation, we get:

Among them, Δy _i (k), Δy _i (k-1) are the drum water level increments of the ith subsystem at time k and time k-1, respectively, and Δu _i (kd-1) is the ith subsystem at time k-1. The valve opening increment at time kd-1, Δu _j (kd-1) is the valve opening increment of the jth subsystem at time kd-1, It reflects the incremental influence of other subsystem inputs on the drum water level of the ith subsystem.

1.5. From step 1.3 and step 1.4; obtain:

Δx _i,j (k+1)=A _i,j,m Δx _i,j (k)+B _i,j,m Δu _i (k)+D _i,j,m Δu _j (k)

Δy _i (k+1)=C _i,j,m Δx _i,j (k+1)

where Δx _i,j (k)=[Δy _i (k),Δu _i (k-1),…,Δu _i (kd),Δu _j (k-1),…,Δu _j (kd)] ^T ,

Δu _i (k-1),…,Δu _i (kd), Δu _j (k-1),…,Δu _j (kd) represent k-1,…,kd, respectively, the valve opening increment at time, the steam Include water level increment; Δx _i,j (k+1)=[Δy _i (k+1),Δu _i (k),…,Δu _i (k-d+1),Δu _j (k),…, Δu _j (k-d+1)] ^T , Δy _i (k+1), Δu _i (k-d+1), Δu _j (k-d+1) respectively represent the ith subsystem at k+1 The water level increment of the steam drum at the moment, the valve opening increment of the ith subsystem at the time k-d+1, the valve opening increment of the jth subsystem at the time k-d+1, T represents the transpose of the matrix symbol.

B _i,j,m = [0 1 0 0 0 ... 0] ^T ;

C _i,j,m = [1 0 0 ... 0 0 0 0];

D _i,j,m = [0 ... 0 0 1 0 ... 0] ^T ;

1.6. According to step 1.5, the non-minimum state space model can be obtained:

_zi (k+1)=Azi (k)+BΔu _i (k)+DΔu _j (k)+CΔr _{i (} k+1)

in: e _i (k)=y _i (k)-r _i (k)

e _i (k+1)=e _i (k)+C _i,j,m A _i,j,m Δx _i,j (k)+C _i,j,m B _i,j,m Δu _i (k )+D _i,j,m B _i,j,m Δu _j (k)-Δr _i (k+1)

ri (k) is the reference trajectory at time _{k, Δr i (} k+1) is the reference trajectory increment at time k+1, e _i (k), e _i (k+1) are k, k+1 respectively The error between the system drum water level and the reference trajectory at time.

Step 2. The design of the boiler drum water level control system controller, the specific steps are:

2.1. According to step 1.6, we can get:

Z _i =Gz _i (k)+SΔU _i,j +ΨΔR _i

Among them, P represents the optimization time domain, M represents the control time domain

ΔU _i,j = [Δu _i (k) Δu _i (k+1) … u _i (k+M-1),Δu _j (k) Δu _j (k+1) … Δu _j (k+M-1) )] ^T

ΔR _i =[Δr _i (k+1) Δr _i (k+2) … Δr _i (k+P)] ^T

r _i (k+ii)=λ ⁱⁱ y _i (k)+(1-λ ⁱⁱ )c _i (k),ii=1,2,...,P

λ represents the softening factor, c _i (k) represents the set value of the i-th subsystem at time k, Δr _i (k+1), Δr _i (k+2), ..., Δr _i (k+P) represent respectively The reference trajectory increments at time k+1,...,k+P.

2.2. Take the i-th subsystem objective function:

J _i =Z _i ^T Q _i,m Z _i +ΔU _i,j ^T R _i,j,m ΔU _i,j

Wherein, Q _i,m =block diag(Q _i,1 ,Q _i,2 ,...,Q _i,P-1 ,Q _i,P )

r _i,1 ,…,r _i,M ,r _j,1 ,…,r _j,M respectively represent the values of the reference trajectories of the ith and jth subsystems from time 1,…,k time.

2.3. From step 2.2, we can get:

ΔU _i,j =-(S ^T Q _i,m S+R _i,j,m ) ^-1 S ^T Q _i,m (Gz _i (k)+ΨΔR _i )

u _i (k)=[1 0 … 0]ΔU _i,j +u _i (k-1)

Among them, u _i (k), u _i (k-1) represent the valve opening of the ith subsystem k, k-1, respectively.

2.4. Use the valve opening increment ΔU _i,j of the ith subsystem to obtain the actual valve opening of the ith subsystem u _i (k)=[1 0 … 0]ΔU _i,j +u _i (k- 1) Acting on the ith subsystem; then similarly, the valve openings of the 1st, . . . , n subsystems can be obtained respectively.

Claims (3)

1. the Distributed Predictive function control method under a kind of non-minimumization state-space model, includes the following steps:

Step 1 establishes Distributed Predictive function control non-minimumization state-space model；

Distributed Predictive function controls controller under step 2, design non-minimumization state-space model.

2. the Distributed Predictive function control method under non-minimumization state-space model as described in claim 1, feature It is:

Step 1 is specific as follows:

1.1, the multivariable N input N output large scale system in industrial process is regarded as and purely retarded is added by N number of one order inertia (FOPDT) the N input N output multivariable one order inertia of the subsystem composition of model, available following form adds purely retarded (FOPDT) model system:

Wherein, K₁₁,…,K_ij,…,K_nnFor the steady-state gain that j-th of multivariable process object input exports i-th, i= 1,…,n；J=1 ..., n, T₁₁,…,T_ij,…,T_nnThe time exported for j-th of multivariable process object input to i-th is normal Number, τ₁₁,…,τ_ij,…,τ_nnThe lag time that i-th is exported for j-th of multivariable process object input；

1.2, transmission function of the input of j-th of object to the output of i-th of object are as follows:

1.3, in sampling time T_sUnder the conditions of, discretization is carried out to step 1.2, available:

Wherein, k indicates moment, d=τ_ij/T_sInteger part,y_i(k),y_iIt (k-1) is respectively i-th of subsystem The output at k moment and k-1 moment, u_iIt (k-d-1) is input of i-th of subsystem at the k-d-1 moment, u_j(k-d-1) it is Input of j-th of subsystem at the k-d-1 moment,The input of other subsystems is reflected to i-th The influence of a subsystem output；

1.4, it to the first-order difference after the model orientation of discretization, obtains:

Wherein, Δ y_i(k),Δy_i(k-1) be respectively i-th of subsystem the output increment at k moment and k-1 moment, Δ u_i It (k-d-1) is input increment of i-th of subsystem at the k-d-1 moment, Δ u_jIt (k-d-1) is j-th of subsystem at the k-d-1 moment Input increment,It reflects other subsystems and inputs the shadow exported to i-th of subsystem Ring increment；

1.5, by step 1.3 and step 1.4；It can obtain:

Δx_i,j(k+1)=A_i,j,mΔx_i,j(k)+B_i,j,mΔu_i(k)+D_i,j,mΔu_j(k)

Δy_i(k+1)=C_i,j,mΔx_i,j(k+1)

Wherein, Δ x_i,j(k)=[Δ y_i(k),Δu_i(k-1),…,Δu_i(k-d), Δ u_j(k-1),…,Δu_j(k-d)]^T, Δ u_i (k-1),…,Δu_i(k-d), Δ u_j(k-1),…,Δu_j(k-d) k-1 is respectively indicated ..., k-d is the input increment at moment, defeated Increment out；Δx_i,j(k+1)=[Δ y_i(k+1),Δu_i(k),…,Δu_i(k-d+1), Δ u_j(k),…,Δu_j(k-d+1)]^T, Δy_i(k+1),Δu_i(k-d+1), Δ u_j(k-d+1) respectively indicate i-th of subsystem the k+1 moment output increment, i-th Input increment, j-th subsystem input increment at k-d+1 moment of a subsystem at the k-d+1 moment, T representing matrix turn Set symbol；

B_i,j,m=[0 1000 ... 0]^T；

C_i,j,m=[1 00 ... 000 0]；

D_i,j,m=[0 ... 0010 ... 0]^T；

1.6, according to step 1.5, non-minimum state-space model can be obtained:

z_i(k+1)=Az_i(k)+BΔu_i(k)+DΔu_j(k)+CΔr_i(k+1)

Wherein:e_i(k)=y_i(k)-r_i(k)e_i(k+1)=e_i(k)+C_{i,j, m}A_i,j,mΔx_i,j(k)+C_i,j,mB_i,j,mΔu_i(k)+D_i,j,mB_i,j,mΔu_j(k)-Δr_i(k+1)r_iIt (k) is the reference locus at k moment, Δ r_i It (k+1) is the reference locus increment at k+1 moment, e_i(k), e_iIt (k+1) is respectively k, etching system output and reference locus when k+1 Error.

3. the Distributed Predictive function control method under non-minimumization state-space model as claimed in claim 2, feature Be: step 2 is specific as follows:

2.1, it according to step 1.6, can obtain:

Z_i=Gz_i(k)+SΔU_i,j+ΨΔR_i

Wherein, P indicates optimization time domain, and M indicates control time domain

ΔU_i,j=[Δ u_i(k) Δu_i(k+1) … Δu_i(k+M-1),Δu_j(k) Δu_j(k+1) … Δu_j(k+M-1)]^T

ΔR_i=[Δ r_i(k+1) Δr_i(k+2) … Δr_i(k+P)]^T

r_i(k+ii)=λⁱⁱy_i(k)+(1-λⁱⁱ)c_i(k), ii=1,2 ..., P

λ indicates the softening factor, c_i(k) setting value at i-th of subsystem k moment, Δ r are indicated_i(k+1), Δ r_i(k+2) ..., Δ r_i (k+P) k+1 is respectively indicated ..., k+P moment reference locus increment；

2.2, i-th of subsystem objectives function is taken:

J_i=Z_i ^TQ_i,mZ_i+ΔU_i,j ^TR_i,j,mΔU_i,j

Wherein, Q_i,m=block diag (Q_i,1,Q_i,2,…,Q_i,P-1,Q_i,P)

r_i,1,…,r_i,M,r_j,1,…,r_j,MRespectively indicate value of i-th, the j subsystem from the reference locus at 1 ..., k moment；

2.3, it can be obtained by step 2.2:

ΔU_i,j=-(S^TQ_i,mS+R_i,j,m)^-1S^TQ_i,m(Gz_i(k)+ΨΔR_i)

u_i(k)=[1 0 ... 0] Δ U_i,j+u_i(k-1)

Wherein, u_i(k), u_i(k-1) control amount at i-th of subsystem k, k-1 moment is respectively indicated；

2.4, the controlling increment Δ U of i-th of subsystem is utilized_i,j, obtain the practical control amount u of i-th of subsystem_i(k)=[1 0 … 0]ΔU_i,j+u_i(k-1) i-th of subsystem is acted on；Then the control of the 1st ..., n subsystem is similarly found out respectively Amount.