A Comparison of Different Control Strategies of a Rotary Drier

Copyright R! IFAC Automation in Mining. Mineral and Metal Processing. Helsinki. Finland. 1983

A COMPARISON OF DIFFERENT CONTROL STRATEGIES OF A ROTARY DRIER L. Yliniemi and P. U ronen University of Oulu, Department of Process Engineering, Linnanmaa, Oulu, Finland

Abstract. This paper presents control results for a rotary drier given by a conventional feedback control, control based on material and energy balances and by a state control . The results are presented separately and a comparison of these different control strategies is made. The comparison is based on the simulations with an Eclipse S/140 computer and on the experiments carried out with a pilot-plant rotary drier.

INTRODUCTION

feed moisture can be seen as oscillation in the output moisture of material as the figure 2 shows. When the product moisture is at the desired value (0 m-%) , the material begins to overdry, because the product temperature is increased. This means that the energy is used more than is needed.

Much attention has been given in recent years to the reduction of energy used in drying processes. One means of doing this could be to use advanced control systems. In this paper the results of various control s trategies for a rotar y drier are presented. Also the comparison of these strategies based on the simulations and on the experimental work with a pilot-plant rotary drier is done.

Also the behaviour of the feedback PIcontrol based on measuring the product moisture and controlling the fuel flow has been examined. The responses have been presented in Fig. 3, when the feed moisture is increased stepwise from 3.6 m-% to 4.2 m-%. The disturbance can be seen also in the product moisture as the figure 3 shows .

PROCESS EQUIPMENT The experimental work has been carried out with a pilot-plant rotary drier shown in Fig . 1.

Feedforward and feedback control

A detailed description of the drier and its in s trumentation can be found in the references /1,2/.

The basic principle of this strategy is to keep the product moisture constant by calculating in a feedforward manner enthalpy needed in drying utilizing material and energy balances. Fuel flow and combustion air flow are determined based on this. The feedback correction to the fuel flow is based on the direct product moisture measurement. This means in practice that the feedforward control compensates variations in the product moisture affected by slow disturbances and the feedback control compensates faster disturbances. Therefore, the calculation interval of enthalpy balance in the feedforward control is l onger than the interval us ed in the feedback control . The control strategy includes also the opportunity to use as a control variable the delay time of material in the drum. The schematic diagram of this control strategy is presented in Fig. 4.

STRUCTURES OF DIFFERENT CONTROL STRATEGIES Feedback control A most conventional feedback control of a rotary drier is based on measuring the output temperature of the drying gas and control ling the fuel flow utilizing a PIcontroller . This control strategy is a common approach for examp l e in the Finnish mining and mineral industry /3/. The practical control experiments using the feedback control have been carried out with the pilot-plant rotary drier shown in Fig. 1. The drier has been operated in a co-current way and calcite has been used as drying material. The behaviour of thi s feedback PIcontrol is presented in Fig. 2, when the feed moisture i s decreased stepwise from 4 . 2 m- % to 3 .6 m- %. The disturbance in the

The following material and energy flows have been taken into consideration in the balances:

435

436

L. Yliniemi and P. Uronen

The input and output flows of the material balance:

equation: aXi(l,t) aXi(l,t) at + vi(t) al

The input flows: l.

2. 3.

4. 5.

Feed Fuel Primary air Secondary air Leakage alr

solids and moisture flow and composition flow flow flow

(1)

where

Xi is the moisture or temperature of the product or the temperature of drying gas V·l is the corresponding velocity 1 is the drum length f·l is a function of Xi, 1 and t t is time.

The output flows: l.

2.

Product Flue gases

solids and moisture flow and composition

The input and output flows of the energy balance: The input flows: 1. 2. 3.

Feed enthalpy Combustion reactions Other energy as heat, electrical or mechanical

The output flows: 1.

2. 3.

Product enthalpy Vaporizing reactions Heat losses

The behaviour of this control strategy has been examined experimentally when the step changes in the feed moisture and the feed flow occur. From figure 5 it can be seen that this control strategy eliminates well these disturbances, because the responses, the product moisture and temperature, are stable. The product has not, however, overdried, because the product temperature is constant during the experiment. Fuel flow is controlled exactly according to the actual energy need in all situations. Because the output temperatures of material and drying gas can be kept as low as possible with this kind of control, the risk of explosion and fire decreases which increases the safety of the process. Also dust losses decrease because the overdrying of material does not occur. The control strategy improves the runnability of the process, because the output variables of the process can be better controlled. This makes better also to control successive processes and to decrease disturbances in operation.

or ax

at

+ v

-R

aT

et V ~(T -T )-AR Gm g m v

a(C T ) a CC T ) I!i I!i + v I!i I!i g dl at G m A R m G v g

et V - ~CT -T ) G g m g

(3)

(4)

Notations are defined In the Appendix. The following assumptions have been used in the derivation of the above model: - heat and mass transfer coefficients are constant, - heat transfer by conduction in material and in drying gas is negligible, - diffusion of water vapor in the axial direction is negligible, - heat transfer by radiation is negligible, - flow rate of drying gas in the axial direction is constant, - granular size distribution is constant, - chemical reactions in material do not take place during drying, and - temperature of material and drying gas and moisture of material are functions of time and axial coordinate alone. The dynamic linearized model for the pilotplant rotary drier derived from the equations (2) ••• (4) is the following:

State control

_(Xout:Xin) . v'- vm(X' -X~) m Lout In

- k . T'

l'm,out

(5)

m,out

1

leT -T.) L m,out m,ln et V

V V

_I_eT (C)2

C

m Cl

V

v v

+ -C-

A rotary drier is a typical distributed parameter system, where the temperatures and moistures of the product and drying gas are functions of time and place. The dynamic model developed from the material and energy balances can be presented by the following

(2)

v

a(C T ) acc T ) mm mm + v at m dl

x'out The designing of the state control of a rotary drier is based on a dynamic model developed from material and energy balances. The material and energy flows have been presented above. The different variables of the model of the drier have been presented in Fig. 6.

ax m

m

m

g,out

-T

m,out

) .G'

m

m

~(T'

C

g,out

m

Akl

-cm

v' -

T'

m,out

-T'

m,out

v - ~(T'

L

m,out

) -T'

. )

m,ln (6)

437

Different Control Strategies of a Rotary Drier is minimized. T

Amkl

T'

g,out

m,out

C

g Cl. V v v - -C- g v ~(T'

L

A linear state controller form:

G'

m

G g

~(k)

l-(T' -T' ) g,out m,out g

G

Gm

-Cg

G

(7)

T'

m,out

m

I'm,out .

(G ) 2

G'

g'

g

where the rate of drying is expressed by the equation

R

v

k

=

(8)

T

1

m

The lumped parameter approximation and the substitution of 6 £ by the total length of the drum have been used because the temperatures and moistures inside the drum are very difficult to measure. Mean values of the specific heats Cm,C g in the model have been used because of the~r low temperature dependence. The discrete-time state equations are of the following form: ~(k+l)

=

y(k)

~(k).

=

(15 )

G(k)

_p- l BT S(k),

(16 )

S(k)

(AT)-l (R(k)-Q),

(17)

R(k)

Q+ATR(k+l) [I+BP-lBTR(k+l)]-lA (18)

The optimal ~(k) is determined from the equations 16 ... 18 by the backward calculation.

g

G

C g

-G(k) ~(k),

g,~n

Amkl

~(k) + B~(k) + Cv(k)

of the following

where

-T'.)

g,out

~s

(9)

(10)

The different state, control and disturbance variables of the drier are the following:

The numerical values of the weighting matrices P and Q have been determined experimentally and they have been presented in Appendix. The behaviour of the state controller of the drier has been examined by simulations with an Eclipse S/140 computer for the step changes in the feed moisture and the feed flow. The responses have been presented in the figures 7 and 8. The figures show that the control operates in the both cases in the same way. The product moisture and the product temperature reach the reference state stably, while a little oscillation can be seen in the output temperature of drying gas. A little offsett which can be seen in the response of the product moisture, can be eliminated by using the I-term in the control. The effect of the I-term on the control will be examined in the next phase in the research work. CONCLUSION

x'out x

T'

=

T'

:

g,out i

IV'

u =

I m

I

i

i T'

!_ g, in i-x! -

v

~n

I

I

G'

(11)

m,out -

Lm

G'

=

0

Po

(12)

-;

I

I

T' _ = 0 rn, ~n

(13)

The matrices A, B, C and D for the drier have been determined in the Appendix. All three state variables are measurable. Tr£variable v~ is a function of the rotation speed of the drum and the variable T' . a function of the fuel flow. g,~n Now a state controller has to be designed which generates a control variable ~(k) from the state variables ~(k) so that the system is controlled into the desired state and the quadratic performance criterion N-1 J

L

k=o

[~T(k) ~(k) + ~T(k) p~(k)l,

(14)

The target of the different control strategies is to save energy and to improve product quality. Based on practical control experiments and on simulations the results show that the feedforward together with feedback control based on material and energy balances seems to give the best control result. This control is able to better compensation for the variations in the feed flow and the feed moisture together with the considerable decrease in overdrying than the two feedback control strategies examined in this work. The simulation results given by the state control show that this also is applicable to the control of a rotary drier. The experimental results carried out in the next stage of the research work will show the benefit of a state controller compared with the feedforward and feedback control strategy.

REFERENCES Yliniemi, L., E.A.A. Jutila, and P. Uronen (1981). Modelling and Control of a pilot-Plant Rotary Drier used for Drying of Industrial Concentrates. Pre-

L. Yliniemi and P. Uronen

438

prints of the IFAC 8th Triennial World Congress, Kyoto, pp XXII 198-203. Yliniemi, L., P. Uronen, and K. Leiviska (1982). Control and Economical Examination of a Rotary Drier. Proceedings of the Third International Drying Symposium, Birmingham, pp. 230-237. Yliniemi, L., A. Arola, and E. Jutila (1980). Rotary Driers in the Finnish Mining and Mineral Industry. Report 51. Department of Process Engineering, University of Oulu, Oulu, 7 p. APPENDIX

v

T

.

input

g,l.n

g,out

.

feed temperature

m,l.n

T

product temperature

V

drier volyme

m,out v

X.

feed moisture

l.n

product moisture

X

out kl

drying constant

v

flow rate of drying gas

g

flow rate of material

m

a

volymetric heat transfer coefficient

v

specific heat of drying gas

C g C m G g G m L

specific heat o f material

A

vaporization heat of water

drying gas mass flow, kg/m

A

vaporization heat of water at material temperature

m

material mass flow drum length rotation speed of drum

N

The different matrices of the model are the following:

-v /L m

-k

-a V A

v v

0

-X

eg

out

G m 1 G g

C m

- v /L m

A ·k m 1

--eg

l.n

1 (r -T.) m,out m,l.n L

-a V v v -C-m

G m

-a V

Gg

eg

+ X.

L

0

0

l

kkl

1

v v C m

0

a v

B

temperature of drying gas

output temperature of drying gas

T

T

v

Nomenclature

rate of drying

R

0

0 v /L g

v v

1 G m 1 G g

- v /L g

Different Control Strategies of a Rotary Drier

v

o

/L

m

V v v

- (1,

o

C

-C-

(1 g,ou t -1m,out ) (G ) 2

m

m

T

rn, out

o

G

g

The numerical values of the weighting mat rices P and Q used in the simulations:

l: ~J 0

P

7

0

Q

~

0 1 0

:J

The numerical values of the parameter s of the model used in the simulations: C m C g

0.89 kJ/kg 1.1 kJ /kg

L

3 m

V

0.2 m3/ m

v kl (1,

v

0.0001 l/oC·min 3 17 kJ/min·m °c

A=Am

2260 kJ/kg

G

0.2 kg/m

G

21.6 kg/m

N

1 l/min

-g m -

T _g, in T _g,out T

240

T m,out X.

63

_m,in

~n

68 20

°c °c °c °c

0.035

X -out v -g v m

0 60 m/min

Ut

150 kg/hr

m

AM-O'

°c °c

0.116 m/min

439

440

L. Yliniemi a nd P . Uronen

Flue gas fan Primary

1~PROCESS COMPUTER

Fig. 1.

!N!

!N!

I

I

8

~

0

U

.r:

0

'-

8 w :>

A pilot-plant drier with auxiliary devices and in s trumentation .

w :>

0::

..:.:: >::

.,..< ~

0

.88 E-I S

T m,out

72

6

40 64

5

30

2

4

20

1

3

mm

56

x.

~n

x 0

10

Fig. 2.

20

30

40

50

out

60 t (min)

The responses given by the feedback PI - control based on measuring the ou tput temperature of drying gas.

.

.'Tj. . ()Q

:""

r

..,..

-

~

>-3

::r

:::=

rt>

Ul

,-

~

r>

::r rt>

m f ue l

El

III

.. .

j

I"t

r>

(:l.

.. . III CO

"~ o ...,

T

m, out m fu e l

.....-

N

....t

X. l.n

I"t

m m m g T .

"....o

T

III

r>

o

;:l

Ul

I"t

" III

I"t

rt>

g ,l.n

g , out Tcombu s X

out

CO

'<

-

....

...

oL

U·m fu e l PI- I

.

r

...

...'"

---

... ... ......

.....

.-

.tlc -

•

-A.~ +...

N

....""'-

...,

~

chambe r

en en

w

UN PI-2

~o+-

,1/

I"t

19

::r rt>

"o '< " ".rt>. . I"t

III

.........

L.. J

-&.+

-

rt>

"rt> ;:l

I"t

C"l

o

;:l I"t

"....o en

r-

I"t

" I"t

rt>

.. .

()Q

rt>

P -1

U. m g

u

Ul

+.,0+-_[

;-

~

T combu s ti on chamber

r-

+-

0

U. m m

-

r-

PI-4

(:l.

"

PI - S

Ndes ir ed l

PI-3

X-I drum

Mode l 2

des ired

III

p..

P

t:!

..... ..., ...,

X out

,\ 1 ~~

o

"

X ,des ire d out

Mode l 1

m m

-

r-

~ ...

Tcombus ti on chambe r, se tpo i n t va lue

-

III

g' I"t

III '1

'<

Pdrum , s etpo int va lue

~

+

o ...,

IDrn , desl.re . d

t:!

".rt>. .

"

~

i .p.p....

442

L . Yliniemi and P . Uronen X

mf uel

X.

ou t 1n

T m,out

°c

X. In

m- %m- kg/h 70

4

3

2

50 2

0

30

3 1 1

10

o

o Fig. 3.

50

100

150 tCmin)

The r es ponses given by the feedback PI-control based on measuring the product moisture .

mm Tm,out

X X.

kg h

In

3

ID m

150 00

2

1

100

T m,out

50

X

out

0

50

o

0

o Fig. 5.

100

200

300 tCmin)

The responses in the product moisture control for s tep changes in feed moisture and feed flow. DISTURBANCE VARIABLES

X. 1n m

m

INPUT VARIABLES T . g,1n

OUTPUT Vi\P.IABLES X

out

T

T=f Cv ) m

Fig. 6 .

The different variables of the rotary drier .

m,out

T

g ,out

Different Control Strategies of a Rotary Drier

X

out

m-I:

T

m,out

443

T

g,out

°c

°c T

m,out

3

60

2

0

1

20

T

g,out

X

out

o o Fig. 7.

4

2

6

8

10

Simulated responses for a state controller in step change in the feed moisture; x. : 3.5+4.2 m-% ~n

0.2

0

X

out

o

o Fig. 8.

2

4

6

Simulated responses for a state controller the feed flow; ~ : 150+165 kg/hr m

8 ~n

k

10

step change

~n