A Multi-Input-single-output Smith Predictor for Feeders Control in SAG Grinding Plants

8/11/2019 A Multi-Input-single-output Smith Predictor for Feeders Control in SAG Grinding Plants

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1070 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 13, NO. 6, NOVEMBER 2005

Fig. 1. Block diagram of a MISO Smith predictor.

[5][7]. Nevertheless, the design of the main controller, unlike

the SISO case, is based on a transfer function matrix with time

delays, which complicate the design. For MISO systems, how-

ever, the design can be simplified, as is illustrated in this work.

This work proposes the use of a Smith predictor for control-

ling the amount of ore and at the same time, maintaining the

right percentages of ore coarseness.

The brief is organized as follows. In Section II, we describe

the structure of the proposed Smith predictor for a class of

MISO systems, representing the feeder system of a SAG mill.

Section III describes a SAG grinding plant and some imple-

mentation issues. Section IV illustrates by an example the

integrated methodology to design the controller for a specificSAG grinding plant. Real-time experiments are considered

in Section V, to illustrate the proposed methodology and the

flexibility of the controller.

II. SMITHPREDICTORS FOR A CLASS OFMISO SYSTEMS

A general MISO system can be described by the following

equation:

(2.1)

where is the number of inputs. Each transfer function modelcan be factorized as

(2.2)

is the factor containing all the time delays and nonmin-

imum phase dynamics. The control objective is to design a con-

troller, so that the output of the system can be driven to a ref-

erence value, in spite of the disturbances, by manipulating each

control signal to satisfy the proportions given by the constants

. Fig. 1 illustrates the structure of the system.

Each control signal is calculated as

(2.3)

Fig. 2. Simplified diagram.

where is the transfer function of afilter, is the con-

troller associated to the input th and represents the contribu-

tion of input th to the total output signal. The values of these

constants are in many applications set by the operators, consid-

ering the coarseness of the transported material. They must sat-

isfy as well the following conditions:

(2.4)

This structure can be simplified by defining the transfer func-

tion :

(2.5)

Thus, the general block diagram is reduced to Fig. 2. The

nominal closed-loop response is

(2.6)

if all the transfer functions and are stable, then the

nominal closed-loop transfer function will be stable.

The closed-loop system, considering the mismatch between

the model and plant is given by

(2.7)

where the model error is defined as

(2.8)

Notice that (2.7) can be reduced to (2.6) only if the model erroris zero.


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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 13, NO. 6, NOVEMBER 2005 1071

Fig. 3. Conveyor belts CT-09 feeding a SAG mill.

The small gain theorem [8] guarantees stability of the closed-

loop system if

where is the sampling time. In order to consider the fact that

in a normal operating condition any controller can be switched

to manual, the following condition:

(2.9)

must be satisfied in order to maintain the stability of the closed-

loop system. The inequality (2.9) can also be expressed as

(2.10)

Hence, and must be chosen to guarantee thiscondition in spite of modeling errors. The fact that can

be independently tuned for each input gives an extra degree of

freedom for meeting the stability constraint. Since a rational

z-transform is periodic in with , (2.10) holds for

all , if [8].

III. FEEDERSCONTROL INSAG GRINDINGCIRCUITS

The SAG grinding plant of the A-2 Codelco-Norte concen-

trator has two SAG lines, where each one consists of a SAG

mill of , and two ball mills of in closed

inverse circuit configuration with hydrocyclones. The plant re-

ceives product of a crushing plant with through threefeeders, as shown in Fig. 3.

Feeders are normally commanded by advanced control strate-

gies, which control the total fresh feed tonnage, mill water ad-

dition and mill speed while monitoring bearing pressure (an in-direct measure of the weight of the mill) and mill power. The

main objective of these supervisory strategies is to maintain a

stable operation and maximize the fresh feed tonnage.

The distributed control system is a TDC-3000 with a Local

Control Network. The control algorithms run on a VAX 3100

connected to a Ethernet network. There is a plant network inter-

face (PLNN) that allows the communication between the equip-

ments connected to the Ethernet network and those connected to

the Local Control Network (LCN). At present the control system

of the SAG plant is being replaced by a modern hybrid platform,

based on Rockwell Automation technology and the application

considered here will be migrated to this platform.

A. Description of the Feeder System

The mineral is transported from the stock piles to the SAG

mill by a set of conveyor belts as shown in Fig. 1.

A weight meter measures tonnage on the belt at the end of it.

Continuous random variations in the size, density and flow of

ore into the feeder will always cause variations in the tonnage

measured at the weight meter. The feeder system has three

feeders, three variables speed conveyor belts and a constant

speed conveyor belt. In addition, there are cameras monitoring

the ore in each feeder. A controller regulates the speed of each

feeder that pulls ore from a stockpile up to the constant speed

conveyor belt. The amount of mineral is determined by thespeed of each feeder. The operator, in manual mode, can change


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1074 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 13, NO. 6, NOVEMBER 2005

Fig. 7. Speed of feeders 1 (- - - ) and 2 ( ).

Fig. 8. Percentage of tonnage supplied by feeder 1. (- - - ), calculatedpercentage ( ).

change in the weights does not produce a major upset in the

tonnage response, Fig. 6.

B. Tracking Performance of a PID Based Strategy and a MISO

Smith Predictor Controller

In the following experiments, the set-point is provided by an

advanced control strategy controlling the SAG grinding circuit,

which tries to maximize the throughput, while keeping a stable

operation by monitoring pressure bearing and mill power. These

objectives are accomplished by manipulating the mill water ad-

dition and mill speed.

The strategy used to control the feeders before the implemen-

tation of proposed controller considered two feeders in open

loop and a single PID controller, acting over the third feederto control the total tonnage. This controller was tuned following

the IMC tuning guideline [8]. With this strategy, it was not pos-

sible to maintain the right proportion among the feeders. In ad-

dition, the PID controller has to be detuned in order to cope with

the long time delay. Fig. 9 shows the response of this strategy

to track this time varying tonnage set-point; with this perfor-

mance the advanced control strategy was not able to operate

for long periods of time. On the other hand, the proposed con-

troller, which considers a MISO Smith predictor and PI con-

trollers acting on each feeder, as described in Section II, pro-

vides a better tracking of the time-varying set-point, as seen in

Fig. 10. In addition, the system is flexible since the operators

can set the right proportions associated to each feeder and theycan also take any feeder out of operation, without affecting the

Fig. 9. PID Controller. Total tonnage (), set-point ( 0 0 0 ).

Fig. 10. MISO Smith predictor. Total tonnage (), set-point ( 0 0 0 ).

stability of the system. A year of closed-loop operation has vali-

dated the operation of the controller enabling the advanced con-

trol strategy to operate all this time.

VI. CONCLUSION

The use of multiple Smith predictors has enabled the effi-

cient control of the tonnage, as well as, the right proportion on

the material being feed to the SAG mill. These characteristics

have made the system indispensable for a stable and long-time

operation of advanced control strategies aimed to optimize the

process. The tuning of the controller considers a small amount

of parameters clearly related to the desired performance and ro-

bustness of the algorithm. From the experimental tests can be

seen that under the proposed strategy the total tonnage is not

very sensitive to changes in the percentage assigned to each

feeder. Furthermore the tracking performance has been dramat-ically improved compared to the strategy previously used in

plant. The system has demonstrated, during its one year oper-

ation, itsflexibly and reliability.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for their helpful

comments to improve the presentation of this work.

REFERENCES

[1] S. M. Jones Jr.,Autogenous and semiautogenous mills 2000 update,inProc. Int. Conf. SAG, Vancouver, Canada, Apr. 2001, pp. 362372.

[2] O. A. Bascur,Integrated grinding/flotation controls and management,inProc. Copper 91-Cobre 91 Int. Symp., vol. II, Ottawa, Canada, Aug.1821, pp. 411427.


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[3] O. J. M. Smith,Closed control of loops with dead time, Chem. Eng.Prog., vol. 53, pp. 217219, 1957.

[4] G. Alevisakis and D. E. Seborg,An extension of the Smith predictorof multivariable linear systems containing time delays,Int. J. Control,vol. 3, no. 17, p. 514, 1973.

[5] B. A. Ogunnaike and W. H. Ray, Multivariable controller design forlinear systems having multiple time delays, AIChE J, vol. 25, pp.10431057, 1979.

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[7] Q. Wang, B. Zou, and Y. Zhang, Decoupling Smith predictor design formultivariable systems with multiple time delays,Trans. IChemE, pt. A,vol. 78, pp. 565572, 2000.

[8] M. Morari and E. Zafiriou,Robust Process Control. Englewood Cliffs,NJ: Prentice-Hall, 1998.

[9] L. Ljung, System IdentificationTheory for the User. EnglewoodCliffs, NJ: Prentice-Hall, 1987.

[10] A. Inginundarson and T. Hagglund,Robust automatic tuning of an in-dustrial PI controller for dead-time systems, in Proc. IFAC Workshopon Digital Control, Terrassa, Spain, 2000, pp. 149154.

[11] C. Maffezzoni and P. Rocco,Robust tuning of PID regulators basedon step response identification,in Proc. 3rd Eur. Control Conf., Rome,Italy, 1995, pp. 24772482.

[12] G. C. Goodwin, M. Gevers, and B. Miness,Quantifying the error inestimated transfer functions with application to model order selection,IEEE Trans. Autom. Control, vol. 37, no. 7, pp. 913928, Jul. 1992.

[13] K. Hong, D. Kang, and J. Kim,Robust Smith predictor design via un-certainty quantification: application to a reclaimer,inProc. IFAC Conf.System Identification, Santa Barbara, CA, 2000, pp. 351356.

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A Multi-Input-single-output Smith Predictor for Feeders Control in SAG Grinding Plants