Automatic Control of Continuous Autogenous Grinding

T2B2 AUTOMATIC CONTROL OF CONTINUOUS AUTOGENEOUS GRINDING

T.O. Olsen Research Fellow, SINTEF, Automatic Control Division H. Berstad Research Engineer, SINTEF, Automatic Control Division S. Danielsen Mill Superintendent, fosdalens Bergverk A/S

In this paper characteristics of a very simple mathematical model of the autogeneous grinding process is used to determine the state of operation and the optimal value of the feed rate. Two

ABSTRACT A very important problem in autogeneous grinding control is the determination of the mill charge x O, which represents maximal energy consumption of fines. This optimal mill charge depends upon the ore quality, and is subject to variations over time. In this paper a control system which maintains stable mill operation at maximal mill power consumption in spite of ore quality variations is described. Results from full scale test in an industrial mineral dressing plant are included. 1.

measurements are used, mill power consumption and

mill weight as represented by the oil pressure of the mill bearings. Any other available measurement of the mill hold-up weight may of course be substituted. The problem considered is: To control the feed rate so as to run the autogeneous mill at maximum power consumption ylO, in spite of the unknown time dependence of both ylO and optimal mill filling x O. This aim is weighted against the risk for mill fill-up if mill filling x is larger than x O.

INTRODUCTION

The autogeneous grinding process is usually more sensitive to variations in the feed material, i.e. variations in grindability or feed size distribution, than more conventional grinding processes. The need for automatic control of the autogeneous grinding process is therefore even larger than for other grinding processes.

The method of solution applied classifies the state of mill operation as belonging to one of two sets A and B defined as

The mill hold-up weight may easily be controlled by varying the feed rate, and for autogeneous grinding the mill electric power consumption is a sensitive measure of variations in mill hold-up weight. To obtain maximum throughput, the mill should be controlled to yield maximum power consumption. This point, however, is on the boundary of an unstable operating region, and measures must be taken to prevent mill fill-up, which may occur when the hold-up weig~t exceeds the one corresponding to maximum power consumption. (Cfr. Figure 1).

A

{xix < xO}

(1)

B

{xix> xO}

(2)

Depending on x E A or x E B, the feed rate u is set to the corresponding optimal value iteratively. This gives a solution which is easily implemented in hardware. The controller has been installed at Fosdalen Bergverk A/S, Norway, for full scale testing. 2.

Because of the fact that the optimal hold-up weight (or percent filling of the mill) x O varies with varying ore quality, and that the corresponding maximal power consumption ylO also varies, control systems aiming at maintaining a constant power consumption, must have a set-point well below ylO in order to avoid the unstable region. The most important problem when trying to control the autogeneous mill at maximum throughput is the determination of the mill hold-up weight x O which represents maximal energy consumption.

PROCESS MODEL

The mathematical model used is very simple, and the synthesis is based more on the qualitative characteristics of the model than on the quantitative, since the latter are to a large extent unknown. The process is first order, given by x(t) = u(t - ,) - q(t),

x(O) = x

o

(3)

q is the mill outlet flow of solids (volume), and u is the solids feed rate (volume). , represents the time delay caused by the transport of the ore from the feeders to the mill inlet.

Earlier this problem has been overcome(2) by controlling the feed rate based on computation of dYl/dt. The value of dYI/dt is obtained by uSlng a feed rate higher than the mills capacity for time intervals of varying length, and observing the variation in Yl' This on/off control may cause considerable oscillations in the throughput.

(4) The measurements are YI = mill power consumption

225

Y2 = mill bearing oil pressure

tegy, the following procedure is chosen:

The relations between state and measurements are

Let ~T,

(5)

hI (x,a,v)

(6)

x(t) E A

(11)

the decision interval, is chosen so that >

T

u(t)

=

~T

(12)

a is the density of the ore, and v a grindability parameter (the larger v, the easier to grind).

Then

The mill outlet flow of solids is, considering a grate outlet mill:

In this way the system is self-adjusting in the sense that as long as x(t) E A, it increases the feed rate until the optimal feed rate u O is obtained. When the ore quality changes so that u O changes, the system tracks this new uO.

q = f(Yl,a,v)

(7)

u(t -

~T)

+ ~u\l tE [t + ~T,tO+ nT]

o

(13)

Assumption 1: h2 (.) and

increases monotonically with boLI

To avoid excessive cycling between uO and Umin the procedure is modified to accept a working point x which is a little lower than x O: Define

x

a.

Assumption 2:

A' f ( .)

and sing

increases .monotoni<..:ally with Y 1 ""d v f(·) decreasesmonotonic~lly with increa-

A"

An A'

a. Let k indicate sample number, the sampling period being ~T, and we get the control procedure:

Assumption 1 is justified by referring to Y2 being a measure of mill weight. No. 2 implies that the mill outlet through the grate always increases when the power consumption increases or when the grindability increases, both of which should increase the production of fines per time unit. At

x x x

the same power consumption, an increasing ore den-

sity is believed to reduce the production of fines and thus the mill outlet flowrate, because more energy is needed to move the charge.

k k

4.

(8)

x(t) E B,

u (t) = u .

(10)

mln

E B

=>

u

k

uk - l u

k

(16)

min

CLASSIFICATION OF THE STATE OF OPERATION

x = hl-l(Yl)

is not unique.

The form of hl(x,a,v) as shown in Figure 2a allows the following alternative definition of the sets A and B: A

B

°

u

ul'u ma )

is the physical upper limit for the feed

This simple strategy is then optimal: (9 )

=>

min(u _ + k l

To estimate the state of operation measurements Yl and Y2 are utilized. Using Yl only, as often done, it is not possible to separate between x E A and x E B because the relation

Thus, if x E A, the feed rate u(t) is too small or optimal (?: u(t) ~ u o) while x E B indicates a too large feed rate. Because u o varies with time, perturbation of the control variable is necessary to determine whether the feed rate is optimal or not when x E A. To the contrary x E B indicates that u(t) > u o and the feed rate must be decreased. To bring the mill back into the stable operating region, this is best done by minimizing the feed rate, if there are no restrictions on feed rate variations.

u

E A"

k

To apply the state control scheme to the autogeneous grinding process it is necessary to know if x(t) belongs to A or B, as shown in the previous section. Failing to classify the state of operation correctly will either lead to too low production rate or to plugging of the mill. Once x is correctly classified as belonging to A or B, however, optimal control is applied according to Eqs. (9), (10).

The optimal operating point is taken to be a mill charge corres~onding to maximal mill power consumption(l),( ), and the optimal state of operation x O is then defined by

u(t)

u

To detect transitions from A" to A' due to parameter variations, the control variable is perturbed if the state x belongs to A" for more than a specified time interval.

With the meager information we have in the process model used, and with a time varying optimal operating point, the approach chosen for the control strategy is an experimenting self-adjusting control scheme.

x(t) E A,

E A'

rate.

CONTROL STRATEGY

°

k

umax

Typical qualitative relations are shown in Figures 2a, 2b and 2c.

3.

(14)

\xIx ~ xO} , aYl \x:sgn(ax)

°

{xix> x}

1}

aYl {xl ax

(17) < O}

aYl {xlsgn(ax) = -l}

(18)

Eqs. (17) and (18) enables the classification of the state of operation without knowledge of either aYl x or x, but only using the sign of ax

In a practical application of the system another difficulty is that the value u o is not known, and it depends on the ore quality. To estimate u o simultaneously with applying the above stra-

°

The latter is not directly available for

226

measurement, and is computed as follows, using the second measurement Y2:

PREVIOUS DATA, are available as stored numbers in the RANOOM ACCESS MEMORY.

We have

Now, PREVIOUS and PRESENT DATA for each process variable are compared in the ARITHMETIC LOGIC UNIT setting or resetting four PRIMARY FLAGS according to the results of the comparisons carried out. The PRIMARY FLAGS are later on decoded giving the desired control function. The comparison period is closed by replacing the PREVIOUS DATA values with the PRESENT DATA values transferred from the TENP. 11£:-10. This operation also clears the TEMP. MEMO. enabling it to accumulate the average values over the next decision period. Note that the old PREVIOUS DATA values are lost during this operation.

aYl

aYl

a;z-

at

aY2

Y2 x

a;z-

Yl

at ax

(19)

x

(20)

Considering assumption 1 valid, we have aY2 dx

-- > 0

V x EAU B

(21)

and thus from Eq. (20) : sgn(x) = sgn
The decoding of the the four PRIMARY fLAGS is carried out in the LOGIC ~~TRIX working with truth table derived from the characteristics of the process model and control strategy described above. The OUTPUT UNIT interfaces the ore material feeders to the LOGIC ~~TRIX giving ore material feeding control. Three legal control parameters are available in this case.

(22)

Eqs. (19) and (22) now give sgn(yl)sgn(x) sgn(y l )sgn(Y2) = sgn(YI Y2 )

(23) The momentary trend in grinding process is given on behalf of only two time-equidistant data sets. Normally this shall be sufficient to bring the process to an optimal state given with point (xO,yO) in Figure la. Because of changes in density and grindability of the ore, the qualitative relations between the variables may change from

Using Eq. (23) combined with Eqs. (17) and (l8), it is possible to decide if the mill is operating in an unstable region. (x E B). by measuring. ~l and Y2' computing Yl and Y2 and determining the sign of the product YIY2' Because of the derivation of the measurement, the decision will be very sensitive to measurement noise. To decrease the influence of measurement noise, the measurements are filtered by taking m measurements with sampling 6t during une decision sampling period 6T = m6t:

time to time, giving some time worst case condi-

tions. To handle these special conditions, an extra set of control flags is included in the controller. These flags, named SECONDARY FLAGS, are set and reset accordingly to the constellation of the PRIMARY FLAGS. The SECONDARY FLAGS may change the control strategy by modifying the truth table of the LOGIC MATRIX. This is easily done by counting up certain control conditions following each other in sequence. When the numbers of certain events overrange preseable values, the control strategy is changed dependent on the SECONDARY FLAGS. Today, three control functions of this kind are implemented in the controller.

m

L 6y . .

j =1

1,

m6t

J

1,2

(24)

where 6 Yi ,j = Yi (t + jM) - Yi (t + (j - I)M) (25) Both the measurement of mill power and mill bearing oil pressure were subject to large variations due to the rotation of the mill. The period of these variations were much shorter than the expected response time to feed rate perturbations, and where eliminated using analogue low pass filters with suitable cut-off frequencies. 6.

SYSTEM

Besides giving time reference to the INPUT and OUTPUT UNITS, the 100 Hz MASTER CLOCK also increments the SEQUENCE ?ROGRAMMER which is hardwarecoded according to the control algorithm choosen. The controller in use is built up with ordinary TTL-components giving a rather small, rugged, and cheap system solution. The major disadvantage, however, is the hardware-coded programming allowing only small changes in control strategy to be done. A far better solution may be the use of a software programable micro-processor equipment with suitable input/output devices, semiconductor storages, and necessary man/machine communication facilities. This will probably be the next generation of automatic control devices used in autogeneous grinding processes.

REALI~ATION

The controller used during the full scale testing period is in fact a special designed, hardware programable digital con.puting device, a~le to make a lot of logical decisions upon the input variables. A simplified block diagram is shown in Figure 3. The process variables, POWER CONSUMPTION and OIL PRESSURE, available as current signals, are multiplexed in a reed-relay multiplexer, analog to digital converted and finally stored as 8 bits digital words in an accumulating memory, in block diagram named TEMPORARILY MEMORY. In order to reduce the influence of measurement noise, m measurements with sampling period 6t are taken over a decision period of total length 6T. At the end of a decision period the 8 most significant bits of the words stored in the TEMP. MEMO. are equal to the average value of the two variables taken over m samples. These values are in the following named PRESENT DATA. At this time the average values taken over the previous sampling period, named

7.

RESULTS FROM FULL SCALE TESTS

At Fosdalens Bergverk A/S a low grade iron ore is ground in an one-stage, open-circuit autogeneous mill. The 6m4> x 6m mill rotates at 12.2 rpm, on babbit bearings with circulating lubrication. The ore is of a very fluctuating grindability, mainly due to variations in the amount of keratophyres from the hanging wall of the ore bodies mixed with the greenschits, limestone and quartzite of the footwall. The keratophyres is 3.5 times as hard to grind as the ore. Another important disturbance on the process is the varying amount of large ore pieces. These factors prevents efficient ap-

227

tion and bearing oil pressure. This may be overcome by using a cascade controller with the belt weight as measurement and feeder amplitude as control variable, and letting the self-adjusting controller adjust the set-point of the feed rate loop.

plication of i.e. constant mill power control. The manual control of the mill had already been greatly improved by using both mill power and mill bearing oil pressure as measurements.

Because

these measurements were directly available in the control room, the present plant was chosen for the full scale tests of the self-adjusting controller. An important factor in this decision was also the changing ore quality, because we believe that the greatest benefits of the self-adjusting controller as opposed to a constant power consumption control scheme is achieved when the ore quality is changing often and much.

5. There are indications that the control step 6u should be adjusted to suit the different ore qualities. This is partly due to the feeding system as mentioned above, causing in reality a variation in the gain between controller output and feed rate with varying ore consistency, and partly due to the fact that decreasing steepness of h l (·) increases the possibility of entering the unstable region by increasing the feedrate a given step.

The mill has been run by automatic control intermittently since August 1975, and several characteristics of the system have been observed:

One possible modification is to use a control step proportional to the slope of hl(')' On-line adjustments of the control step has not been included in the installed system.

1. Due to the relatively rapid changes in ore quality, it is difficult to obtain comparable quantitative measurements of the possible improvements of the process when run by automatic control. Because of the fact that'there is only one mill, parallel simultaneous runs on manual and automatic control is not possible, and by comparing the performance in periods of successively manual and automatic control, one must bear in mind that the ore quality may not be exactly the same during the automatic and the manual control periods. There

5. It has been easy to select suitable values both for the filtering time interval 6t and the decision time interval 6T. The control step 6u could maybe for some ore qualities have been larger, but a value of about 2.5 % of maximal vibration amplitude has been found to be well suited for this mill. 8.

CONCLUSION

is, however, a distinct increase in production

rate when the self-adjusting controller is operating relative to manual control. As an example, the average production pr. shift is shown on Figure 4, for periods of both manual and automatic control. The increase in production when the selfadjusting controller takes over is apparent.

The described system performs satisfactory, and the control strategy is relatively simple, which enabled a low-cost realization of the system. The self-adjusting controller operates the mill near maximum power consumption at varying ore

qualities, and detects and counteracts successfully indications of unstable operation. The system is very sensitive to deviations from the maximal power consumption, and the optimal operating point is determined without large variations in the feed rate.

The average increase in production rate due to the self-adjusting controller is estimated to ca. 10%. Higher values have been observed, but this conservative estimate is stated allowing for possible well-suited ore during the automatic control periods.

The full-scale tests showed considerable increases in production rate at various ore qualities. A conservative estimate based on these tests is ca. 10 % increase -in production rate, although short time tests with constant ore quality has shown increases of 17.9 % increase. One should bear in mind that the largest increases are expected when the ore is easily ground. In such periods the operator will be satisfied with the production rate, and not strive to increase it, while he in periods of more difficult ore will make greater efforts to keep up the production rate by trying to optimize the grinding conditions by manual control.

2. A short-time experiment, in which the mill was run on manual control for four hours and on automatic control for the following four hours, was done to evaluate the performance of the self-adjusting controller during a period of constant ore quality. The result was an average production rate of 134 t/h during the manual control phase, and 158 t/h during the automatic control phase; which is an 17.9 % increase during the automatic control phase. 3. By switching from manual to automatic control, the feed rate increases and generally stabilizes at a higher niveau, indicating that by manual control the mill is usually run at lower power consumption than the optimal value. Figure 5 illustrates this effect, and also shows that the controller has no difficulty in preventing mill fillup by bringing the system back to the stable region after the feed rate has been too high. The automatic control system is usually faster to detect a transfer into the unstable operating region than the mill operator is when manual control is used, and the time elapsing before stable operation is once more attained is thus decreased by automatic control.

Another great benefit of the automatic control system is the opportunity it presents for the mill operator to use more of his time for tasks other than monitoring the mill's state of operation. with the self-adjusting controller operating the mill, the operator on his one-man shift may take more care of maintenance work and give more attention to the rest of the plant, i.e. transport systems, ore bins etc. 9.

ACKNOWLEDGEMENTS

We gratefully acknowledge the financial support for this work from the Royal Norwegian Council for Scientific Research (NTNF) and from the Norwegian Association of Mines (BVLI). We are also indepted to Fosdalens Bergverk A/S for the opportunity to test the controller on a full scale grinding mill.

4. At Fosdalens Bergverk A/S the control variable is not the feed rate of ore directly, but the amplitude of the vibrating feeders. Due to this system the feed rate variation in the vibrating feeders' amplitude is to some extent dependent upon the consistency of the ore. Using up to seven different feeders in a cyclus, this fact may at times cause some oscillations in both power consump-

228

REFERENCES (1) Digre, M., "Wet Autogeneous Grinding in Tumbling Mills", Acta Polytechnica Scandinavica, Chemistry incl. Metallurgy Series No. 88, 1969. (2) BVLI TR-15/l, The Norwegian Association of Mines, Trondheim, 1971. (3)

Williamson, J .E .• "The Automatic Control of Grinding Medium in Pebble Mills. J.S. Afr. I.M. & M. 60 (1963) 333-45.

(4) Oswald, D.J. and Ziegler, J .G., "Inventory Control of Grinding Mills Using Bearing Pressure Measurement. SHE Trans. 254 (1973) 201-205.

229

Quantitative relation between xl' u and Yl' Y ' 2

Maximal power consumption I I I I I

Sfable region

Unstable region

I I I I

L..-

.....

XO

C>

X

a.

x

" b.

230

Figure 2:

Examples of h (·), h (·) and f(.) (qualitative) l 2

x Q.

x b.

c.

231

~ !'(lJ

VI

~~ i'tJ:b:

~

:tJ

@.

~~

b

"'CfI a ,

(',(,0,

~q; b~

",t;1 flJ

~~ !=,.

1

1 ~~

~'1

-ic

~

c:::C\

('>VI

t;~

c:::~

~:;t

b

~~

~~

1»?tJ

r-

~~

~~

~~

.,~

ri>

~~

&

Rf.£D - RELAY MULTIPLEXER

~ UJ \-'.

8

'D I-' \-'. H,

\-'. Cl>

P. eT I-'

o

(J

K

\::IQ)

p. \-'-

0"Ic:::

~~

'"

Iltl

tJ

~C'I

~M flJ

~

'i

'8"

ANAL06-DI61T;4L CONVERTER

o

H,

et-

::Y Cl>

N (J

W

o

N

;:l et-

tJ ~

b

q

I
C)

c:::

~ c:::

If

'1

§ --t

k ~~cs

"';;:D

,L,tl~~

V"'_t»

~~

LOGIC MATRIX

~

PRIMARY

FLAGS

o

TEMPORARILY I--MEMORY (PRESENT DATA)

Z\

b

'i

I

n I
ARIT/{METIC LOGIC UNIT

L)

t7

cr

~

RANDOM ACC£S5 I~ MEMORY ....,.(PRE.VIOUS DATA)

SECONDARY FlAGSPRES£T COUNTERS.

f;.

~~

I'r>, 1:::\1\ Mr>,

<.r.-;

I-' I-' Cl>

'i

Figure 4:

Production rates during manual

a~d

autcffi8tic control periods.

f80

I f60

I

140

Manual con/rol

-

-

Automatic control

120

100 2

J

5

6

233

7

B

9

-

Sh,ff nr.

Figure 5:

Mill bearing oil pressure aDd mill power consumption before aDd after transfer to a~tomatic control.

S.'i!ched 10 our. control

" ..

, il

iJ

14

15

16.

17

234

18

19

21

.,~