CN104850679A - Static pressure control method of variable air volume (VAV) air-conditioning system fan on basis of iterative learning - Google Patents

Abstract

The invention discloses a static pressure control method of a variable air volume (VAV) air-conditioning system fan on the basis of iterative learning and proposes that an iterative learning control algorithm is applied to the static pressure control of the VAV air-conditioning system fan. The static pressure control method comprises the following steps: firstly, establishing a state-space model of the VAV air-conditioning system fan, furthermore, converting the continuous state-space model into a discrete state-space model of a system, and verifying the astringency of the control method on the basis of the model to obtain a system astringency condition; and secondarily, according to the obtained system astringency condition, designing a specific iterative learning algorithm, and proving the effectiveness of the algorithm through a simulation experiment. Proved theoretically, the static pressure control method has the characteristics that the steady-state performance and the dynamic performance of the system are greatly improved than a traditional PID (Proportion Integration Differentiation) algorithm, and the static pressure control method has important theoretical guiding significance and practical value.

Description

Based on the method that the air conditioning system with variable fan static pressure of iterative learning controls

Technical field

The present invention relates to a kind of new method controlled for air conditioning system with variable fan static pressure, specifically a kind of method that controls of air conditioning system with variable fan static pressure based on iterative learning

Background technology

Along with expanding economy, the raising of economic level, the application of air-conditioning system is more and more extensive, at field volumes such as commercial field, industrial circle, ordinary residences, can see the figure of air-conditioning system.Thing followed problem is: the energy consumption problem of air-conditioning system is more and more outstanding.Building energy consumption (BEC) Two decades years in the past of China, the speed with annual 10% is increasing, and the proportion shared by BEC in 2004 is in all energy consumptions reaches 20.7%, and is constantly increasing.Survey report show, in the Shelter in South China Cities of China, the energy consumption that the use due to air-conditioning system causes, account for whole building energy consumption 40% on.Meanwhile, the energy consumption caused is used to account for about 31% of family's power consumption at US Air adjusting system.Come to building energy consumption at the 40%-50% of the overall energy consumption of European Union, having in building energy consumption is that the use of air-conditioning system causes greatly.Therefore it is most important that the energy consumption reducing air-conditioning becomes.

In the use of air-conditioning system, due to variable air rate (Variable Air Volume, VAV) air-conditioning system at low load its energy-saving effect be greatly better than determining air quantity (Constant Air Volume, CAV) air-conditioning system, the application of VAV air-conditioning system is increasingly extensive.VAV air-conditioning system generally has refrigeration host computer, chilled water feed system, air conditioner unit, supply air system, the part such as end equipment composition.The energy consumption of corresponding VAV air-conditioning system also depends on the energy consumption of each component units.

As the important component part-supply air system blower fan of VAV air-conditioning system, if can desirably run by track, overshoot very less or do not have, will reduce the duration of runs of system medium power equipment, reduce energy ezpenditure.Therefore, if supply air system can be made to run according to the desired trajectory of specifying, will the energy consumption of supply air system be reduced, and then reduce the overall energy consumption of VAV air-conditioning system.But under CPC control pattern, adopt traditional PID control method, for ensureing that air-supply static pressure is constant in setting static pressure, the ratio control action of system is stronger, thus cause the rotating speed of blower fan to change greatly in adjustment process, cause supply air system to occur stronger overshoot.Characteristic from blower fan: the energy consumption of blower fan depends on compressor flow, fan outlet pressure, working time, therefore will increase the energy consumption of supply air system when system occurs that hyperharmonic is fluctuated, increases the energy consumption of air conditioning system with variable.Simultaneously conventional PID control method can not be eliminated completely and repeat to disturb the impact on system, bad to the tracking effect of static pressure.Therefore for the problems referred to above that conventional PID control method exists, a kind of control method based on iterative learning is proposed.

Summary of the invention

Invention will overcome the shortcoming of prior art, solve conventional PID control method and control air conditioning system with variable fan static pressure value, cause the rotating speed of blower fan to change greatly in adjustment process, cause supply air system to occur stronger overshoot, increase the energy consumption of air conditioning system with variable; When there is repeatability interference, bad to the tracking effect of static pressure; A kind of method that air conditioning system with variable fan static pressure based on iterative learning controls is proposed.

Fan Control Method by Static Pressure in VAV System based on iterative learning of the present invention, its job step is:

Step 1. sets up the model of air quantity variable air conditioner supply air system.From the principle that air conditioning system with variable runs, the process setting up the model of air quantity variable air conditioner supply air system is as follows:

The direct current motor of blower fan is analyzed:

Armature circuit voltage equation:

$u_a\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{dt}+R_a{i}_a\left(t\right)+E_a\left(t\right)---\left(1\right)$

U _a(t)=armature voltage

I _a(t)=armature supply

L _a=armature circuit inductance

R _a=armature circuit resistance

E _a(t)=back electromotive force

Electromagnetic torque equation:

M _m(t)＝C _mi _a(t) (2)

M _m(t)=electromagnetic torque

C _m=motor torque coefficient

I _a(t)=armature supply

Torque balance equation on motor reel:

$J_m\frac{{\mathrm{d\ω}}_m\left(t\right)}{dt}+f_m{\mathrm{\ω}}_m\left(t\right)=M_m\left(t\right)-M_c\left(t\right)---\left(3\right)$

M _m(t)=electromagnetic torque

M _c(t)=open circuit loss

F _mviscosity friction coefficient on=motor reel

J _mmoment of inertia on=motor reel

Back electromotive force equation:

E _a(t)＝C _eω _m(t) (4)

C _e=back emf coefficient

Ignore open circuit loss obtain by equation above

$u_a\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{dt}+R_a{i}_a\left(t\right)+C_e{\mathrm{\ω}}_m\left(t\right)---\left(5\right)$

$J_m\frac{{\mathrm{d\ω}}_m\left(t\right)}{dt}+f_m{\mathrm{\ω}}_m\left(t\right)=C_m{i}_a\left(t\right)---\left(6\right)$

Can obtain according to fan operation characteristic First Law, the relation of fan pressure head under fan pressure head and standard design rotating speed under different actual speed

$\frac{P_r}{P_s}={\left(\frac{N_r}{N_s}\right)}^2---\left(7\right)$

P _rfan pressure head under=actual speed

P _sfan pressure head under=standard design rotating speed

N _r=actual speed

N _s=standard design rotating speed

The relation of rotation speed of fan and angular velocity:

ω _m(t)＝2πN _r(8)

Arrange

$P_r=P_s{\left(\frac{N_r}{N_s}\right)}^2=P_s{\left(\frac{{\mathrm{\ω}}_m\left(t\right)}{2{\mathrm{\πN}}_s}\right)}^2---\left(9\right)$

Diagonal angle speed linearity the higher order term neglected wherein obtain

$P_r=P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{{\mathrm{\πN}}_s}{\mathrm{\ω}}_m\left(t\right)---\left(10\right)$

Pipe system is analyzed

${\mathrm{gz}}_1+\frac{u_1^2}{2}+\frac{p_1}{\mathrm{\ρ}}+w_e={\mathrm{gz}}_2+\frac{u_2^2}{2}+\frac{p_2}{\mathrm{\ρ}}+w_f---\left(11\right)$

The height in z=relative datum face

U=mean flow rate

P=gauge pressure

W _e=blower fan work

W _f=pipeline mechanical power loss

Because the height in the relative datum face of fan outlet and pipe system static pressure measuring point is basically identical, the wind speed of fan outlet and pipe system static pressure measuring point is basically identical, then above formula changes into

P ₂＝P ₁-ρw _f(12)

Then get i _a(t), ω _mt () is state variable, P ₂for output variable obtains following state equation:

$\stackrel{\·}{X}=\left[\begin{array}{cc}-\frac{R_a}{L_a}& -\frac{C_e}{L_a}\\ \frac{C_m}{J_m}& \frac{f_m}{J_m}\end{array}\right]X+\left[\begin{array}{c}\frac{1}{L_a}\\ 0\end{array}\right]u_a---\left(13\right)$

$y=\left[\begin{array}{cc}0& P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{{\mathrm{\πN}}_s}\end{array}\right]X+{\mathrm{\ρw}}_f$

For air conditioning system with variable, because the air quantity flowing through supply air system is change, reflects to enable the model of supply air system and the impact that this change exports model add interference at output terminal, and joined in the impact that pipeline mechanical energy causes.

Continuous state space model conversation is become separate manufacturing firms model by step 2..On the basis of linear continuous system state-space expression, be used in the separate manufacturing firms expression formula that method that input end adds a sampling switch and zero-order holder obtains system:

X[(k+1)T]＝AX(kT)+Bu(kT)

y＝CX(kT)+d(kT) (14)

Wherein T is the sampling period, and K is the integer of 0 to N.Add a batch axle parameter, and add the interference of repeatability, obtain the two-dimensional state spatial expression of system

$\left\{\begin{array}{c}X(t+1,k)=AX(t,k)+Bu(t,k)\\ y(t,k)=CX(t,k)+d(t,k)\end{array}\right.---\left(15\right)$

K represents batch coordinate, and t represents time coordinate, and the value of t is between 0 to N, and N represents the number in sampling period.

The design of step 3. iterative learning control law and convergence checking.

The design of 3.1 iterative learning rates:

For the air conditioning system with variable to use CPC control pattern, controlling object is that the static pressure of air supply duct is controlled to setting value, reduces the concussion process of system responses simultaneously.Namely one group of list entries is found

U _k＝[u _k(0),u _k(1),u _k(2),...,u _k(N-1)]

Make output sequence can follow the tracks of object output sequence

Y _d＝[y _d(1),y _d(2),...,y _d(N)]

That is:

$\left\{\begin{array}{c}e(t,k)=y_d\left(t\right)-y(t,k)\\ \underset{k\→\mathrm{\∞}}{\lim }\left|\right|e(t,k)\left|\right|\→0\end{array}\right.---\left(16\right)$

Definition:

Δu(t-1,k)＝u(t-1,k+1)-u(t-1,k)

Δd(t,k)＝d(t,k+1)-d(t,k)

In conjunction with above definition, then the two-dimensional discrete state-space expression of blower fan and air-supply pipeline static-pressure system, can change into two-dimentional Roesser model:

Therefore control object and also just change into searching

Δu(t-1,k)

E (t, k) is restrained.

Design control law:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)(18)

Wherein L is iterative learning control law.

3.2 convergence checkings:

Because interference is repeatability interference, then can obtain:

The state-transition matrix of definition two-dimentional system is as follows:

$T=\left[\begin{array}{cc}A& BL\\ -CA& I-CBL\end{array}\right]$

$T^{1,0}=\left[\begin{array}{cc}A& BL\\ 0& 0\end{array}\right]$

$T^{0,1}=\left[\begin{array}{cc}0& 0\\ -CA& I-CBL\end{array}\right]$

Obtain according to two-dimentional system is theoretical:

T ^i,j＝T ^1,0·T ^i-1,j+T ^0,1·T ^i,j-1

T ^i,j＝0(i＜0 or j＜0)

Suppose x (0, k)=x0 all sets up then to arbitrary k>0:

The adequate condition of system convergence is: T ^0,1asymptotically stability, namely the eigenwert of matrix I-CBL is all positioned at unit circle.The span of law of learning L can be determined thus, as long as the value of L is suitable, just can ensures that output valve must be followed the tracks of setting value, and obtain desirable dynamic process

Step 4. iterative learning control method realizes:

4.1 starting condition: (0, k)=x0 sets up arbitrary k>0 setting starting condition x, and goes to get u (t, 1)=0

U (t, k) is applied on the separate manufacturing firms model of system by 4.2, and the response obtaining model exports y (t, k) and then obtains e (t, k)=y _d(t)-y (t, k)

4.3 scopes judging e (t, k), are applied on real system when its coincidence loss requires by control sequence, when not meeting error requirements, the control sequence of kth+1 time:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)

And turn back to 4.2

4.4 when the control sequence that coincidence loss requires is applied on real system, the output of measuring system, and compared with reference locus, obtains error amount, and when coincidence loss requires, retentive control sequence is constant, otherwise returns 4.2.

Advantage of the present invention and beneficial effect:

The present invention is on the basis of iterative learning, and combine air quantity variable air conditioner supply air system blower fan model, propose the method that the air quantity variable air conditioner supply air system fan static pressure based on iterative learning controls, design two parts of establishment and iterative learning method that the present invention mainly comprises air quantity variable air conditioner supply air system blower fan model are formed, control relative to conventional PID, adopt the control method based on iterative learning, the overshoot produced in air quantity variable air conditioner supply air system fan operation process can be reduced, the dynamic property of enhancing system, the repeatability interference run in the process of system cloud gray model can be overcome simultaneously, realize the tracking to fan static pressure value, the steady-state behaviour of raising system.Therefore location algorithm proposed by the invention has better using value.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the control effects figure adopting conventional PID control method.

Fig. 3 adopts the design sketch based on the control method of iterative learning.

Embodiment

With reference to accompanying drawing:

The method controlled based on iterative learning air quantity variable air conditioner supply air system fan static pressure of the present invention, its job step is:

Step 1. sets up the model of air quantity variable air conditioner supply air system.From the principle that air conditioning system with variable runs, the process setting up the model of air quantity variable air conditioner supply air system is as follows:

The direct current motor of blower fan is analyzed:

Armature circuit voltage equation:

$u_a\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{dt}+R_a{i}_a\left(t\right)+E_a\left(t\right)---\left(1\right)$

U _a(t)=armature voltage

I _a(t)=armature supply

L _a=armature circuit inductance

R _a=armature circuit resistance

E _a(t)=back electromotive force

Electromagnetic torque equation:

M _m(t)＝C _mi _a(t) (2)

M _m(t)=electromagnetic torque

C _m=motor torque coefficient

I _a(t)=armature supply

Torque balance equation on motor reel:

$J_m\frac{{\mathrm{d\ω}}_m\left(t\right)}{dt}+f_m{\mathrm{\ω}}_m\left(t\right)=M_m\left(t\right)-M_c\left(t\right)---\left(3\right)$

M _m(t)=electromagnetic torque

M _c(t)=open circuit loss

F _mviscosity friction coefficient on=motor reel

J _mmoment of inertia on=motor reel

Back electromotive force equation:

E _a(t)＝C _eω _m(t) (4)

C _e=back emf coefficient

Ignore open circuit loss obtain by equation above

$u_a\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{dt}+R_a{i}_a\left(t\right)+C_e{\mathrm{\ω}}_m\left(t\right)---\left(5\right)$

$J_m\frac{{\mathrm{d\ω}}_m\left(t\right)}{dt}+f_m{\mathrm{\ω}}_m\left(t\right)=C_m{i}_a\left(t\right)---\left(6\right)$

Can obtain according to fan operation characteristic First Law, the relation of fan pressure head under fan pressure head and standard design rotating speed under different actual speed

$\frac{P_r}{P_s}={\left(\frac{N_r}{N_s}\right)}^2---\left(7\right)$

P _rfan pressure head under=actual speed

P _sfan pressure head under=standard design rotating speed

N _r=actual speed

N _s=standard design rotating speed

The relation of rotation speed of fan and angular velocity:

ω _m(t)＝2πN _r(8)

Arrange

$P_r=P_s{\left(\frac{N_r}{N_s}\right)}^2=P_s{\left(\frac{{\mathrm{\ω}}_m\left(t\right)}{2{\mathrm{\πN}}_s}\right)}^2---\left(9\right)$

Diagonal angle speed linearity the higher order term neglected wherein obtain

$P_r=P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{{\mathrm{\πN}}_s}{\mathrm{\ω}}_m\left(t\right)---\left(10\right)$

Pipe system is analyzed

${\mathrm{gz}}_1+\frac{u_1^2}{2}+\frac{p_1}{\mathrm{\ρ}}+w_e={\mathrm{gz}}_2+\frac{u_2^2}{2}+\frac{p_2}{\mathrm{\ρ}}+w_f---\left(11\right)$

The height in z=relative datum face

U=mean flow rate

P=gauge pressure

W _e=blower fan work

W _f=pipeline mechanical power loss

Because the height in the relative datum face of fan outlet and pipe system static pressure measuring point is basically identical, the wind speed of fan outlet and pipe system static pressure measuring point is basically identical, then above formula changes into

P ₂＝P ₁-ρw _f(12)

Then get i _a(t), ω _mt () is state variable, P ₂for output variable obtains following state equation:

$\stackrel{\·}{X}=\left[\begin{array}{cc}-\frac{R_a}{L_a}& -\frac{C_e}{L_a}\\ \frac{C_m}{J_m}& \frac{f_m}{J_m}\end{array}\right]X+\left[\begin{array}{c}\frac{1}{L_a}\\ 0\end{array}\right]u_a---\left(13\right)$

$y=\left[\begin{array}{cc}0& P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{{\mathrm{\πN}}_s}\end{array}\right]X+{\mathrm{\ρw}}_f$

For air conditioning system with variable, because the air quantity flowing through supply air system is change, reflects to enable the model of supply air system and the impact that this change exports model add interference at output terminal, and joined in the impact that pipeline mechanical energy causes.

Continuous state space model conversation is become separate manufacturing firms model by step 2..On the basis of linear continuous system state-space expression, be used in the separate manufacturing firms expression formula that method that input end adds a sampling switch and zero-order holder obtains system:

X[(k+1)T]＝AX(kT)+Bu(kT)

y＝CX(kT)+d(kT) (14)

Wherein T is the sampling period, and K is the integer of 0 to N.Add a batch axle parameter, and add the interference of repeatability, obtain the two-dimensional state spatial expression of system

$\left\{\begin{array}{c}X(t+1,k)=AX(t,k)+Bu(t,k)\\ y(t,k)=CX(t,k)+d(t,k)\end{array}\right.---\left(15\right)$

K represents batch coordinate, and t represents time coordinate, and the value of t is between 0 to N, and N represents the number in sampling period.

The design of step 3. iterative learning control law and convergence checking.

The design of 3.1 iterative learning rates:

For the air conditioning system with variable to use CPC control pattern, controlling object is that the static pressure of air supply duct is controlled to setting value, reduces the concussion process of system responses simultaneously.Namely one group of list entries is found

U _k＝[u _k(0),u _k(1),u _k(2),...,u _k(N-1)]

Make output sequence can follow the tracks of object output sequence

Y _d＝[y _d(1),y _d(2),...,y _d(N)]

That is:

$\left\{\begin{array}{c}e(t,k)=y_d\left(t\right)-y(t,k)\\ \underset{k\→\mathrm{\∞}}{\lim }\left|\right|e(t,k)\left|\right|\→0\end{array}\right.---\left(16\right)$

Definition:

Δu(t-1,k)＝u(t-1,k+1)-u(t-1,k)

Δd(t,k)＝d(t,k+1)-d(t,k)

In conjunction with above definition, then the two-dimensional discrete state-space expression of blower fan and air-supply pipeline static-pressure system, can change into two-dimentional Roesser model:

Therefore control object and also just change into searching

Δu(t-1,k)

E (t, k) is restrained.

Design control law:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)(18)

Wherein L is iterative learning control law.

3.2 convergence checkings:

Because interference is repeatability interference, then can obtain:

The state-transition matrix of definition two-dimentional system is as follows:

$T=\left[\begin{array}{cc}A& BL\\ -CA& I-CBL\end{array}\right]$

$T^{1,0}=\left[\begin{array}{cc}A& BL\\ 0& 0\end{array}\right]$

$T^{0,1}=\left[\begin{array}{cc}0& 0\\ -CA& I-CBL\end{array}\right]$

Obtain according to two-dimentional system is theoretical:

T ^i,j＝T ^1,0·T ^i-1,j+T ^0,1·T ^i,j-1

T ^i,j＝0(i＜0orj＜0)

Suppose x (0, k)=x0 all sets up then to arbitrary k>0:

The adequate condition of system convergence is: T ^0,1asymptotically stability, namely the eigenwert of matrix I-CBL is all positioned at unit circle.The span of law of learning L can be determined thus, as long as the value of L is suitable, just can ensures that output valve must be followed the tracks of setting value, and obtain desirable dynamic process

Step 4. iterative learning control method realizes:

4.1 starting condition: (0, k)=x0 sets up arbitrary k>0 setting starting condition x, and goes to get u (t, 1)=0

U (t, k) is applied on the separate manufacturing firms model of system by 4.2, and the response obtaining model exports y (t, k) and then obtains e (t, k)=y _d(t)-y (t, k)

4.3 scopes judging e (t, k), are applied on real system when its coincidence loss requires by control sequence, when not meeting error requirements, the control sequence of kth+1 time:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)

And turn back to 4.2

4.4 when the control sequence that coincidence loss requires is applied on real system, the output of measuring system, and compared with reference locus, obtains error amount, and when coincidence loss requires, retentive control sequence is constant, otherwise returns 4.2

For example, referring to accompanying drawing 1:

After determining localization method, the technical solution adopted for the present invention to solve the technical problems is proposed:

1. in Experimental Area, build experiment porch, carry out actual experiment test, obtain many groups different known defeated as output data, utilize MATLAB and adopt least square fitting to go out the parameter of system state space equation

$A=\left[\begin{array}{cc}-1& -0.25\\ 1& 0\end{array}\right]$

$B=\left[\begin{array}{c}1\\ 0\end{array}\right]$

C＝[0 1.6057]

And get the sampling period be 1 second by experiment the parameter of separate manufacturing firms expression formula of supply air system is as follows:

$A=\left[\begin{array}{cc}0.3033& -0.1516\\ 0.6065& 0.9098\end{array}\right]$

$B=\left[\begin{array}{c}0.6065\\ 0.3608\end{array}\right]$

C＝[0 1.6057]

Select repeatability interference for 5sin (2 π t) simultaneously

2., according to acquisition system separate manufacturing firms expression formula, calculating iterative learning rate is 1.5

3. on MATLAB, carry out emulation experiment then with reference to Fig. 1, acquisition control sequence is applied on experimental provision.Eventually through the control effects obtained after several iteration as Fig. 3, in order to show that control effects that control effects adopts pid control algorithm to carry out controlling to obtain is as Fig. 2 simultaneously, as seen from the figure, adopt the method that the present invention mentions: reduce regulating time, decrease overshoot, improve the dynamic property of system; Reduce the steady-state error of system, improve steady-state behaviour.Further illustrate using value of the present invention.

Content described in this instructions embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (1)

1., based on the Fan Control Method by Static Pressure in VAV System of iterative learning, its job step is:

Step 1. sets up the model of air quantity variable air conditioner supply air system; From the principle that air conditioning system with variable runs, the process setting up the model of air quantity variable air conditioner supply air system is as follows:

The direct current motor of blower fan is analyzed:

Armature circuit voltage equation:

$u_a=\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{\mathrm{dt}}+R_a{i}_a\left(t\right)+E_a\left(t\right)---\left(1\right)$

U _a(t)=armature voltage

I _a(t)=armature supply

L _a=armature circuit inductance

R _a=armature circuit resistance

E _a(t)=back electromotive force

Electromagnetic torque equation:

M _m(t)＝C _mi _a(t) (2)

M _m(t)=electromagnetic torque

C _m=motor torque coefficient

I _a(t)=armature supply

Torque balance equation on motor reel:

$J_m=\frac{d{\mathrm{\ω}}_m\left(t\right)}{\mathrm{dt}}=f_m{\mathrm{\ω}}_m\left(t\right)=M_m\left(t\right)-M_c\left(t\right)---\left(3\right)$

M _m(t)=electromagnetic torque

M _c(t)=open circuit loss

F _mviscosity friction coefficient on=motor reel

J _mmoment of inertia on=motor reel

Back electromotive force equation:

E _a(t)＝C _eω _m(t) (4)

C _e=back emf coefficient

Ignore open circuit loss obtain by equation above

$u_a\left(t\right)=L_a\frac{{\mathrm{di}}_a\left(t\right)}{\mathrm{dt}}+R_a{i}_a\left(t\right)+C_e{\mathrm{\ω}}_m\left(t\right)---\left(5\right)$

$J_m\frac{d{\mathrm{\ω}}_m\left(t\right)}{\mathrm{dt}}+f_m{\mathrm{\ω}}_m\left(t\right)=C_m{i}_a\left(t\right)---\left(6\right)$

Can obtain according to fan operation characteristic First Law, the relation of fan pressure head under fan pressure head and standard design rotating speed under different actual speed

$\frac{P_r}{P_s}={\left(\frac{N_r}{N_s}\right)}^2---\left(7\right)$

P _rfan pressure head under=actual speed

P _sfan pressure head under=standard design rotating speed

N _r=actual speed

N _s=standard design rotating speed

The relation of rotation speed of fan and angular velocity:

ω _m(t)＝2πN _r(8)

Arrange

$P_r=P_s{\left(\frac{N_r}{N_s}\right)}^2=P_s{\left(\frac{{\mathrm{\ω}}_m\left(t\right)}{2\mathrm{\π}{N}_s}\right)}^2---\left(9\right)$

Diagonal angle speed linearity the higher order term neglected wherein obtain

$P_r=P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{\mathrm{\π}{N}_s}{\mathrm{\ω}}_m\left(t\right)---\left(10\right)$

Pipe system is analyzed

${\mathrm{gz}}_1+\frac{u_1^2}{2}+\frac{p_1}{\mathrm{\ρ}}+w_e={\mathrm{gz}}_2+\frac{u_2^2}{2}+\frac{p_2}{\mathrm{\ρ}}+w_f---\left(11\right)$

The height in z=relative datum face

U=mean flow rate

P=gauge pressure

W _e=blower fan work

W _f=pipeline mechanical power loss

Because the height in the relative datum face of fan outlet and pipe system static pressure measuring point is basically identical, the wind speed of fan outlet and pipe system static pressure measuring point is basically identical, then above formula changes into

P ₂＝P ₁-ρw _f(12)

Then get i _a(t), ω _mt () is state variable, P ₂for output variable obtains following state equation:

$\stackrel{.}{X}=\left[\begin{array}{cc}-\frac{R_a}{L_a}& -\frac{C_e}{L_a}\\ \frac{C_m}{J_m}& \frac{f_m}{J_m}\end{array}\right]X+\left[\begin{array}{c}\frac{1}{L_a}\\ 0\end{array}\right]u_a---\left(13\right)$

$y=\left[\begin{array}{cc}0& P_s\frac{{\mathrm{\ω}}_m\left(t_0\right)}{\mathrm{\π}{N}_s}\end{array}\right]X+\mathrm{\ρ}{w}_f$

For air conditioning system with variable, because the air quantity flowing through supply air system is change, reflects to enable the model of supply air system and the impact that this change exports model add interference at output terminal, and joined in the impact that pipeline mechanical energy causes;

Continuous state space model conversation is become separate manufacturing firms model by step 2.; On the basis of linear continuous system state-space expression, be used in the separate manufacturing firms expression formula that method that input end adds a sampling switch and zero-order holder obtains system:

X[(k+1)T]＝AX(kT)+Bu(kT)

y＝CX(kT)+d(kT) (14)

Wherein T is the sampling period, and K is the integer of 0 to N; Add a batch axle parameter, and add the interference of repeatability, obtain the two-dimensional state spatial expression of system

$\left\{\begin{array}{c}X(t+1,k)=\mathrm{AX}(t,k)+\mathrm{Bu}(t,k)\\ y(t,k)=\mathrm{CX}(t,k)+d(t,k)\end{array}\right.---\left(15\right)$

K represents batch coordinate, and t represents time coordinate, and the value of t is between 0 to N, and N represents the number in sampling period;

The design of step 3. iterative learning control law and convergence checking;

The design of 3.1 iterative learning rates:

For the air conditioning system with variable to use CPC control pattern, controlling object is that the static pressure of air supply duct is controlled to setting value, reduces the concussion process of system responses simultaneously; Namely one group of list entries is found

U _k＝[u _k(0),u _k(1),u _k(2),...,u _k(N-1)]

Make output sequence can follow the tracks of object output sequence

Y _d＝[y _d(1),y _d(2),...,y _d(N)]

That is:

$\left\{\begin{array}{c}e(t,k)=y_d\left(t\right)-y(t,k)\\ \underset{k\→\∞}{\lim }\left|\right|e(t,k)\left|\right|\→0\end{array}\right.---\left(16\right)$

Definition:

Δu(t-1,k)＝u(t-1,k+1)-u(t-1,k)

Δd(t,k)＝d(t,k+1)-d(t,k)

In conjunction with above definition, then the two-dimensional discrete state-space expression of blower fan and air-supply pipeline static-pressure system, can change into two-dimentional Roesser model:

Therefore control object and also just change into searching

Δu(t-1,k)

E (t, k) is restrained;

Design control law:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)(18)

Wherein L is iterative learning control law;

3.2 convergence checkings:

Because interference is repeatability interference, then can obtain:

The state-transition matrix of definition two-dimentional system is as follows:

$T=\left[\begin{array}{cc}A& \mathrm{BL}\\ -\mathrm{CA}& I-\mathrm{CBL}\end{array}\right]$

$T^{\mathrm{1,0}}=\left[\begin{array}{cc}A& \mathrm{BL}\\ 0& 0\end{array}\right]$

$T^{\mathrm{0,1}}=\left[\begin{array}{cc}0& 0\\ -\mathrm{CA}& I-\mathrm{CBL}\end{array}\right]$

Obtain according to two-dimentional system is theoretical:

T ^i,j＝T ^1,0·T ^i-1,j+T ^0,1·T ^i,j-1

T ^i,j＝0(i<0orj<0)

Suppose x (0, k)=x0 all sets up then to arbitrary k>0:

The adequate condition providing system convergence is: T ^0,1asymptotically stability, namely the eigenwert of matrix I-CBL is all positioned at unit circle; The span of law of learning L can be determined thus, as long as the value of L is suitable, just can ensures that output valve must be followed the tracks of setting value, and obtain desirable dynamic process

Step 4. iterative learning control method realizes:

4.1 starting condition: (0, k)=x0 sets up arbitrary k>0 setting starting condition x, and goes to get u (t, 1)=0

U (t, k) is applied on the separate manufacturing firms model of system by 4.2, and the response obtaining model exports y (t, k) and then obtains

e(t,k)＝y _d(t)-y(t,k)

4.3 scopes judging e (t, k), are applied on real system when its coincidence loss requires by control sequence, when not meeting error requirements, the control sequence of kth+1 time:

u(t-1,k+1)＝u(t-1,k)+L·e(t,k)

And turn back to 4.2

4.4 when the control sequence that coincidence loss requires is applied on real system, the output of measuring system, and compared with reference locus, obtains error amount, and when coincidence loss requires, retentive control sequence is constant, otherwise returns 4.2.