Jiang-Jian Wang - Research of Cascade Control With an Application to Central Air-conditioning System

8/13/2019 Jiang-Jian Wang - Research of Cascade Control With an Application to Central Air-conditioning System

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Proceedings of Sixth International Conference on Machine Learning Cybernetics, Hong Kong, 19-22 August 2007

RESEARCH OF CASCADE CONTROL WITH AN APPLICATION TOCENTRAL AIR-CONDITIONING SYSTEM

JIANG-JIANG WANG, CHUN-FA ZHANG, YOU-YIN JING

School of Energy and Power Engineering, North China Electric Power University, Baoding 071003, ChinaE-MAIL: [email protected]

Abstract:

The heat exchanger and air-conditioning space in thecentral air-conditioning system are modeled in mathematic.

Based on the models, we propose a cascade control strategy

for temperature control of air-conditioning system. The

setpoint response controller in the cascade control system is

designed in terms of the robust control H2 optimal

performance specification. According to the system operation

requirement for disturbance rejection, a closed-loop for

rejecting disturbance signals is configured and the controller

in internal loop is figured out by proposing the desired

closed-loop complementary function. Finally, the three

controllers, the designed cascade control, traditional cascade

PID control and single PID control are simulated in central

air-conditioning system. It is found that the setpoint response,

the disturbance rejection, the robust and the performance of

the designed cascade control system are better.

Keywords:Cascade control; Robust; H2 optimal performance

specification; Air-conditioning system

1. Introduction

In the central air-conditioning systems, the function ofair handling units (AHU) is to transfer cooling load from airloop to chilled water loop by forcing airflow over the heatexchanger and into the space to the conditioned. Theperformance of AHU directly influences the performance of

air-conditioning system. Traditionally, AHU is controlledby single loop PID type controller [1] due to their relativelysimple structure. However, in cases where the environmentof process equipment must be controlled to extremely highspecifications, such as cleanrooms (in class one cleanrooms,tolerances of 0.50and 2% RH, respectively), it would bedesirable to integrated PID controllers into complex control

structures to achieve better performance.To obtain better performance, cascade control in

central air-conditioning system has been attracting interestin both academic and application areas. Cascade control has

the characteristics such as faster response and stronger

disturbance rejection and the cascade control is appropriate

to the air-conditioning system that has larger inertia andpure time delay as in [2]. A chip controller combined fuzzycontrol and cascade control is designed to apply centralair-conditioning system as in [3]. An online cascade controlstrategy is proposed and validated, which optimizes thesetpoints of head of secondary pump and chiller watertemperature in series based on the positions of air handling

unit (AHU) as in [4].A novel cascade control system has been implemented

to improve supply air temperature control performance ofAHU in a pilot HVAC system, whose outer loop is used aneural network in [5]. The multiplayer neural network is

trained online by a special training algorithm

simultaneous perturbation stochastic approximation (SPSA)based training algorithm.

Additionally the cascade control system is used to saveenergy. Some researchers used the cascade controlalgorithm to evaluate the data from the sensor network and

manipulate supply air temperature and flow rate fromindividual computer room air conditionings to ensurethermal management while reducing operational expense[6]. The constructed control system was tested in a smartdata center and results show 50% reduction energyconsumption by cooling resources in addition to

improvement in use of critical data center space.In this paper a cascade control system is designed

based on the central air-conditioning system. Finally, thethree controllers, the designed cascade control, traditionalcascade PID control and single PID control are simulated.

2. Math model of central air-conditioning system

The control of humidity and temperature in theair-conditioning space are concerned here. The considered

system has two main parts in a cascade structure, the firstpart is the air-processing unit (heating/cooling system) andthe second part is the air-conditioning room. These towparts are connected by air shaft. In the air processing unit

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recycled and injected air are mixed by means of a flapallowing to take into account the air flows with respect tothe speed. The mixed air is processed by the heat exchanger

and humidifier. The air processed is injected into theair-conditioning room by the means of a fan. Theair-conditioning system is shown in Figure 1.

Figure 1. Control theory of central air-conditioning system

Based on the law conservation of energy [7], the

transfer function of heat exchanger can be expressed:

111

1

( )

1

sKG s e

T s

=

+

(1)

where K1 is the coefficient of amplify, ( s /kg); T1 is

time constant, (s); 1 is the pure time delay of the

controlled object, (s).The thermal balance equation of air-conditioning space

is similar to the heat exchanger, which is shown in (4).

222

2

( )1

sKG s eT s

=

+

. (2)

whereK2is the amplify coefficient of room, ( s /kg); T 2

is time constant, (s); 2 is the pure time delay of the

controlled object, (s).

3. Control System Design

The controlled object has two segments that are oneorder inertia process with time delays so that the cascadecontrol system can be used to obtain better performance.

When the fresh air has disturbance, the internal loop canreject the disturbance and keep the supply air temperatureconstant. The cascade control system has some advantagesof disturbance rejection and stable output, but the tuning ofcontroller parameters is very difficult. There are some

researches to study simple controller design and tuning ruleof traditional cascade control system [8, 9 and 10].Here we designed the cascade control system for the

air-conditioning system, which is shown in Figure 2.G1andG2are respectively the controlled process of heat exchangerand air-conditioning room; G1m and G2m are respectivelyidentification models, C is the setpoint response controllerandFis the internal loop controller .

Figure 2. Cascade control system of air temperature in theair-conditioning space

3.1. Setpoint response controller

When identification models G1mand G2mare matchedwith the controlled process G1and G2, the transfer functionof setpoint response in the cascade control system can be

simplified the below form:

1 2( ) ( ) ( ) ( )

cH s C s G s G s= . (7)

The controller C is solved in terms of the robust

control H2 optimal performance specification min||e||

and here it satisfies the performance specification

min||W(s)(1-H(s))|| ,in which W(s)is the input function of

setpoint. To the central air-conditioning system, the step

signal is often used and W(s) is correspondingly equal to1/s.

22

22

The pure time segments in the controlled object can be

approximately replaced to (8) and (9) in n/norders all-passpade.

1 1

1

( )

( )

s nn

nn

Q se

Q s

= . (8)

2 2

2

( )

( )

s nn

nn

Q se

Q s

= . (9)

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where,

0

(2 )! !( ) ( )

(2 )! !( )!

ni

nn j j

i

n i nQ s s

n i n i

=

=

. (10)

j=1,2; i=1,2,,n

Here the integer n is enough large, which makes thatthe error due to the approximation is quite less than theerror of identification model and actual process, so that the

controller C can be shoveled. Put (8) and (9) into theperformance specification and the below form can begotten:

2

2( )(1 ( ))cW s H s 2

1 2 1 2

1 2 1 2 2

( ) ( )1(1 )

( 1)( 1) ( ) ( )

nn nn

nn nn

K K Q s Q s

s T s T s Q s Q s

=

+ +

2

1 2 1 2

1 2 1 2 2

( ) ( ) ( ))

( ) ( ) ( 1)( 1)

nn nn

nn nn

Q s Q s K K C s

sQ s Q s s T s T s

=

+ +

(11)

Then using the orthogonal property of H2norms, (11)

can be transferred to the form as following:

2

2( )(1 ( ))

cW s H s

2

1 2 1 2

1 2 2

( 1)( 1) ( ))

( 1)( 1)

T s T s K K C s

s T s T s

+ + =

+ +

+

2

1 2 1 2

1 2 2

( ) ( ) ( ) ( )

( ) ( )

nn nn nn nn

nn nn

Q s Q s Q s Q s

sQ s Q s

(12)

The above equation is minimized and the first item in

the right should be equal to zero, thus the ideal controllercan be gotten and C is shown in (13)

1 2

1 2

( 1)( 1( )

T s T sC s

K K

+ +=

) (13)

However, it is non-regular and it is not to implementpsychically and so a low-pass filter is added in the

controller, which is shown as following:

2

1( )

( 1)c

c

J ss

=

+

(14)

So the regular controller C can be got as following:

1 2

2

1 2

( 1)( 1( )( 1)

c

T s T sC sK K s

+ +=

+

) (15)

where cis a control parameter.

cis needed to tuning in control system. Whencis

relatively little, the response of setpoint is quick, but theneeded energy of controller is relatively large. When

enlargingc,the response of setpoint will be slow, but the

needed energy of controller is relatively little. So both

should be considered to the tuning ofc. In practical

application, c can be initialized to (1+2) and then be

tuned monotonically on-line to obtain better control

performance.

3.2. Internal loop controller

As Figure.2 shows, the disturbance transfer function ofmiddle process is shown as following:

1

1

( )( )

1 ( ) ( )

ad

s

T G sH s

T F s G= =

+ s. (16)

Then the closed-loop complementary sensitivityfunction is obtained as following:

1

1

( ) ( )

( ) 1 ( ) (d

a

F s G sf

T s T F s G= = + )s . (17)

In the ideal condition, Td(s) should be as the form:

Td(s)=1se , which means that when the Ta disturbance

inputs to the middle process, the internal loop controller F

should detect the error of Ts after1 time delay. Then the

controller F outputs a reverse isoparametric signal to reject

the disturbance. Actually it is considered that the output ofcontroller is limited and the error is gradually offset. Herebased on the robust control H2 optimal performanceobjective, the actual desired closed-loop complementary

sensitivity function is designed as the following:

11

( )1

s

d

f

T s es

=

+

(18)

wheref is another control parameter.

TheF(s)can be solved from (17) and is shown in (19).

1

( ) 1( )

1 ( ) (

d

d

T sF s

T s G s=

). (19)

To carry out conveniently, (19) is transferred and F(s)can be is shown as following:

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1

1 1

( )( )1 ( ) (

F sF sF s G s

=

). (20)

whereF1(s)can be expressed as following:

11

1 1

( ) ( 1)( )

( ) ( 1)

d

f

T s T sF s

G s K s

+= =

+

. (21)

So the configuration of observer F can be shown inFigure 3.

Figure 3. Configuration of observerF

fis needed for tuning in control system. Whenf is

relatively large, the robust of control system is relativelystrong, but at the meantime the disturbance rejection will be

weak. When lesseningf, robust of control system is

relatively weak, the disturbance rejection will be relatively

strong. So the robust and disturbance rejection should beboth considered to be the tuning off. In practical

application, f can be initialized near the time delay of

P1,1. If the process P1 has not pure time delay, f can

also be initialized near to the time constant of P1. Thenfis tuned automatically on-line to obtain better controlperformance.

4. Simulation

To certify the validation of the designed cascadecontrol system in central air-conditioning system, wechoose the summer work condition and compare thedesigned cascade control system to the traditional singleclosed-loop PID control and the traditional cascade control

PID control.The parameters of central air-conditioning system: the

volume of air-conditioning room is 10m long, 8m wide and

4.5m high, the air specific heat capacity is Ca=1.0 kJ/kg ,

the air density is 1.2 kg/m3, Based on the criterion in theheating, ventilation and air-conditioning field, the number

of taking a breath in air-conditioning room and thecalculation of the supply air is Ga=1.08kg/s, the heat

resistance of wall is 1/R=0.2kw/ and the temperature

error of supply cold-water and back-water to the heat

exchanger in summer is Twin-Twout=-5.At last the parameters of middle process, heat

exchanger, are calculated as following: K1= -19.35 s

/kg, T

1=30s [12] and1=3s due to the short distance. The

parameters of air-conditioning room are calculated as

following: K2=0.4 s /kg, T 2=338s and2=60s [13].

Additionally, the gains of disturbances, Ta and Qroom, are

k1= -0.05 kg/ s , k2=0.2 kw/and k3=0.93/kw.

The simulation includes the setpoint response anddisturbance rejection. First, the desired step compares thethree controllers and at 1500s the step of disturbance, Ta, is

-1 to compare the disturbance rejection. The simulation

includes four kinds of comparison and certifies thevalidation the designed cascade control system.

4.1. Simulation 1

The PID parameters are tuned in the robust PID tuningmethod [14]. The PID parameters of the traditional single

PID control are tuned as following: Kp=0.199, Ki= 0.0006and Kd= 7.063. In the traditional cascade control system,the parameters of the internal-loop PID controller are firstlytuned toKp=0.227,Ki=0.001 andKd=0.37, the internal-loopforms the closed-loop and the internal PID controller run inthe system and then the parameters of the outer-loop PID

controller are tuned toKp=4.343,Ki=0.012 andKd=138.7.The parameters of the designed cascade control is

initializedc=(1+2)=63 andf =1=3.

The comparison curves of three controllers are shownin Figure 4, where N PID, T PID and S PID respectively

denotes the designed cascade control system, the traditionalcascade PID control system and the single PID controlsystem.

Temperatu

re()

Time (s)

Figure 4. The simulation results of three controllers

It is seen that the setpoint response of the designedcontrol system has not overshoot while the others have bothovershoot and the cascade PID control responses quicker

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than single PID control. Although the setpoint response ofthe designed cascade control system is slower than the PIDcontrol system, the governing time of designed control

system is shorter than the PID control system.Additionally it is also found that the disturbance

rejection of the designed control and the traditional cascadePID control are similar and is better than the single PIDcontrol system, but the adjusting time of the designedcontrol is relatively long.

4.2. Simulation 2

To certify the robust of three controllers, some control

process parameters are changed to simulate. In G1andG2the gain both increase 10% and becomes 21.3 s /kg

and 0.924 s /kg. The other parameters still keep

constant in simulation 1, which include controllers andprocess. The comparison curves of three controllers areshown in Figure.5. It is seen that the setpoint response andthe disturbance rejection are similar to the simulation 1.However, the overshoot of single PID control is bigger thanthe simulation 1. The simulation 2 can prove the robust of

the designed cascade control system.

Time (s)

Figure 5. The robust simulation results of three controllers

4.3. Simulation 3

To fasten the response of the designed cascade control

system, the parameters, candf , are only tuned to half

andc =(1+2)/2=32 andf =1/2=1.5. The other

controllers and the parameters in simulation 1 are kept

constant. The simulation results are shown in Figure 6.As Figure 6 shows, it is seen that the setpoint response

of the designed control system becomes quicker than theother controllers and the performance is better than thetraditional cascade PID control and single PID control.

From this point, it can be seen that the tuning of thedesigned cascade control is easier than the PID controls.

As long ascandf are monotonically tuned, the controlsystem can obtain better performance.

Temperature()

Time (s)


4.4. Simulation 4

The identification models G1mandG2mare absolutelymatched with the process G1and G2in simulation 1, 2 and

3. The simulation 4 certifies the validation of the designedcascade control system when the identification models arenot matched with the process. In G1m and G2m the T1

decease 30% and becomes 21s and2also deceases 30% to

become 42s. The other parameters still keep constant. Thetuning method of the PID parameters in simulation 4 is the

same in simulation 1. Based on these parameters, theparameters of controllers are tuned.

The PID parameters of the traditional single PIDcontrol are tuned as following: Kp= 0.239, Ki= 0.0007 andKd= 6.214. The parameters of the internal-loop PIDcontroller are firstly tuned to Kp=0.185, Ki=0.011 and

Kd=0.278 and the parameters of the outer-loop PIDcontroller are tuned toKp=4.343,Ki= 0.015 andKd= 114.98.

Based on the identification models G1m and G2m, the

parameters of the designed cascade control is initializedc

=(1+2)=45 andf =1=3. The simulation results of

three controllers are shown in Figure 7.

Temperature()

Temperature()

Time (s)


(identification model is not matched with the process)

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It is seen that the overshoot of the setpoint response ofthe designed control system is less than the cascade PIDcontrol and single PID control. It is also found that the

disturbance rejection of the designed control and thetraditional cascade PID control are similar and is better thanthe single PID control system. Although the adjusting timeof the designed control is relatively longer, the parameter

c is tuned simply and the performance of system will be

better than PID control.

5. Conclusion

In this paper a designed cascade control system was

applied to central air-conditioning system. The designedcascade control system has only two tuned parameters, c

andf, which is less than the parameters of PID control

system. Additionally,c andf are easily tuned, which

dont effects each other. Through the three controllers weresimulated, it is found that the setpoint response and thedisturbance rejection of cascade control system are both

better than single PID control system. The governing timeof the designed cascade control system is shorter than thePID control system, although sometimes the setpointresponse of the designed cascade control system is slowerthan the PID control system. On the whole, the performanceof the designed cascade control system is better than the

traditional cascade PID control system and single PIDcontrol system.

Acknowledgements

The authors would like to acknowledge the financialand technical support of the school of Energy and PowerEngineering and the major lab of power station in NorthChina Electric Power University during the course of thisresearch.

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Jiang-Jian Wang - Research of Cascade Control With an Application to Central Air-conditioning System