DESIGN, SIMULATION AND IMPLEMENTATION OF DECENTRALIZED PI CONTROLLERS FOR A MULTIVARIABLE FEED BLENDING SYSTEM AT THE FALCONBRIDGE SUDBURY SMELTER

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1 DESIGN, SIMULATION AND IMPLEMENTATION OF DECENTRALIZED PI CONTROLLERS FOR A MULTIVARIABLE FEED BLENDING SYSTEM AT THE FALCONBRIDGE SUDBURY SMELTER B. Boulet McGill University Departent of Electrical and Coputer Engineering, Centre for Intelligent Machines 3480 University Street, Montréal, Québec H3A 2A7 Telephone: (54) Fax: (54) E-ail: benoit@ece.cgill.ca L. Ryan Falconbridge Liited Falconbridge Technology Centre, Falconbridge, Ontario, Canada P0M S0 Telephone: (705) Fax: (705) E-ail: lionel_ryan@sudbury.falconbridge.co C. Graves, B. MacKay Hatch 28 Pine Street, Sudbury, Ontario, Canada P3C X3 Telephone: (705) Fax: (705) E-ails: cgraves@hatch.ca, backay@hatch.ca ABSTRACT Falconbridge's new Raglan ine started to ship nickel ore concentrate to Sudbury for selting in the spring of 998. The selter's new continuous feed blending process allows for the blending of concentrate slurry fro the Strathcona ill with a dry Raglan concentrate before it is roasted and fed into the electric selting furnace. Accurate control of the concentrate ratio and density of the blended slurry was deeed critical to achieve efficient roaster and furnace operation. This paper reports on the nonlinear ultivariable process odeling, decentralized controller design, and siulation studies that led to a successful coissioning of the feed blending control syste.

2 INTRODUCTION Falconbridge Liited's new Raglan ine in Northern Quebec started to ship its nickel ore concentrate to Sudbury for selting in the spring of 998. The new feed blending process at the Sudbury selter allows for the blending of concentrate slurry coing fro the Strathcona ill with a dry Raglan concentrate before it is roasted and fed into the electric selting furnace. Accurate control of the ore concentrate ratio and density of the blended slurry was deeed critical to achieve efficient roaster and furnace operation. A process odeling and siulation study was undertaken to assess the feasibility of using decentralized proportional-integral (PI) controllers for this coupled nonlinear ultivariable process. The PI controllers were ipleented and successfully coissioned in May of 998. This paper discusses the dynaic odeling, siulation, control design and ipleentation aspects of the project. The basic idea behind the process is to ix dry Raglan concentrate with Strathcona slurry and water in a repulper tank to aintain both a concentrate dry ass ratio setpoint, and a density setpoint at the output of the repulper tank. The ost iportant controlled variable is the pulp density, followed by the Raglan to Strathcona dry ass ratio (R:S in short). The repulper tank level ust also be regulated. A siplified flowsheet of the open-loop process is given in the next section. The overall process actually consists of two repulper tanks and two roaster feed tanks. However, since it is syetrical, only one repulper/roaster feed tank pair was analyzed in this work. Note that the roaster feed tanks downstrea of the repulpers are operated in open loop. These tanks are large, so their dynaics are quite slow. An operator keeps an eye on their levels, and siply changes the roaster feed rate when the levels get too close to their liits. FEED BLENDING PROCESS Description of the Feed Blending Process The odel of the feed blending process is essentially coposed of three interconnected subsystes (Figure ): Repulper tank Transfer pup Roaster feed tank

3 Raglan concentrate water filter cakes Strathcona slurry repulper tank transfer pup roaster feed tank to roaster Figure : Feed blending syste There are at least four significant disturbances in this process: the Strathcona filter cakes that are dropped in the repulper tank when one or two filters are switched on, the specific gravity of the incoing slurry, its density, and its pressure. Only the filter cakes are odeled as an external disturbance. In the past, these filters were used to increase the density of the pulp going into the roasters. This is still required, although usually the addition of dry Raglan concentrate is sufficient to increase the density to a point where finer density control using process water becoes possible. The effects of the slurry disturbances are odeled as perturbations to the linearized process dynaics rather than exogenous disturbance inputs. A nonlinear open-loop odel of the feed blending process was developed and prograed as a siulator in Matlab Siulink TM. In order to use a frequency-doain loopshaping ethod for the PI controllers, the full nonlinear odel was linearized around the desired operating point (see, e.g., [Kuo] on linearization). The R:S ratio r is not easurable, and the dry ass flow rate of Strathcona S is not easured. However, the latter can be indirectly easured by subtracting the known ass flow rate of Raglan concentrate R into the repulper fro the easured total dry ass flow rate coing out of the repulper. With the tank level well regulated and having fast closed-loop dynaics, the total dry ass flow rate at the output rapidly follows a change of concentrate ass flow rate at the input, and akes the indirect easureent of dry ass flow rate of Strathcona accurate enough for our purposes. Moreover, the dynaics

4 of R:S becoe alost independent of the repulper tank level dynaics. This is the reason why we chose to design the tank level PI controller first, with fast closed-loop dynaics. Given the desired total ass flow rate in the process and the desired R:S ratio, the Raglan ass flow rate setpoint is coputed for the loss-in-weight controller feeding the repulper tank. The R:S ratio is indirectly controlled by coputing the corresponding setpoint for dry ass flow rate of Strathcona concentrate, and by foring an error signal using the indirect easureent of Strathcona for the ratio PI controller. The density loop, which uses a nuclear density eter, was designed last. Siulated open-loop and closed-loop responses to process disturbances were obtained, together with actual closed-loop responses. It was found that the adopted decentralized PI control strategy perfored well in spite of the nonlinear couplings between variables. This was achieved through careful analysis and design procedures, and by running several siulation experients to test the robustness of the closed-loop syste under various process disturbances and odel perturbations. Modeling Assuptions The following assuptions were ade to obtain the odels and design the controllers. Perfect ixing in the repulper tank Linear transfer pup characteristic Linear slurry valve characteristic The last assuption ay be the least valid as valves are inherently nonlinear, but closedloop robustness against variations in the slurry valve gain was checked in the siulations. This robustness analysis indicated that the actual control syste should perfor as expected. The Raglan concentrate ass flow rate into the repulper is controlled via a fast and accurate loss-in-weight control syste. We chose to ignore its dynaics in the odel. The repulper tank subsyste odel is the ost coplex of the three, because the evolution of three different types of aterials inside the tank (Raglan, Strathcona and water) have to be siulated individually. Our approach to odel this is to keep track of the total ass of each aterial in the repulper tank by using separate integrators. The transfer pup is assued to have a voluetric flow varying linearly with pup otor speed. The roaster feed tank is odeled using integrators for dry ix, water, and ix slurry. The volue of ix varies according to the ass of slurry coing in fro the repulper via the transfer pup, and going out to the roaster. Both the nonlinear and the linearized odels are described in soe details in the next section.

5 CONTROL STRATEGY The objectives of the feed blending control syste are to:. Maintain the pulp density around 70% (or other subsequent setpoints), to within %, at the output of the repulper 2. Maintain the R:S dry ass ratio close to its setpoint 3. Maintain the repulper tank level close to its setpoint 4. Reject disturbances that ay affect the density and the ratio 5. Provide robustness to variations in process dynaics, including slurry valve characteristics Three single-input, single-output decentralized PI controllers, described in the PI Controller Design section, were designed to achieve the above objectives. See the closedloop syste block diagra of Figure 5 for ore details on the architecture. The use of decentralized PI controllers was favored as a first design for ease of ipleentation on the selter's Foxboro DCS, tunability, fault isolation, and also because plant personnel are failiar with this technology. Sensors and Measured Variables The following sensors are used: density eter at the output of the repulper, downstrea of the transfer pup, agnetic floweter at the output of the repulper, downstrea of the transfer pup, ultrasonic level transitter for repulper tank level, agnetic floweter for process water going into repulper, ultrasonic level transitter for roaster feed tank. In addition to the direct easureents provided by these sensors, they are used to copute the dry ass flow rate of ix (or pulp) at the output of the repulper. A easureent of the dry Raglan concentrate feed rate fro the loss-in-weight controller is used for R:S ratio control. The easureents directly used for feedback control are: pulp density at the output of the repulper repulper tank level dry ass flow rate of ix at the output of the repulper ass flow rate of Raglan

6 Actuators and Control Variables The following actuators are used: control valve for Strathcona slurry input to repulper AC otor with variable-frequency drive for transfer pup control valve on the water line going into the repulper These actuators are used to odulate the following variables for feedback control: voluetric flow rate of Strathcona slurry into the repulper voluetric flow rate of ix at the output of the repulper water flow rate into the repulper A low-level water flow rate controller not discussed in this paper allows the density controller to output a water flow rate setpoint to the flow rate controller. For the purpose of this study, the roaster feed rate was considered as an exogenous input, i.e., it is not used for feedback control and its variations are seen as disturbances. NONLINEAR OPEN-LOOP MODEL Nonlinear Open-Loop Evaluation Model of the Repulper Tank Due to space liitations, we only give the equations for the repulper tank. The total asses of Strathcona SR, Raglan RR, and water wr in the repulper tank vary according to the following first-order nonlinear differential equations. The notation used can be found in Appendix A. The dot above a sybol indicates tie derivative. Mass of Strathcona in repulper: = SR SR S f SR RR Mass of Raglan in repulper: RR RR = R SR RR Mass of water in repulper: ( f ) ( f ) s f wr = S w f f s f f wr SR RR () (2) (3)

7 The three ass equations above allow us to copute the ix density at the output of the repulper tank f, and the R:S ratio r. Density at the output of the repulper tank: SR RR f = (4) SR RR wr Raglan to Strathcona ratio: RR r = (5) SR Repulper tank level: h 4 πd SG SG RR SR Rep = Rep 2 R S wr (6) PI CONTROLLER DESIGN Three single-input, single-output proportional-integral (PI) controllers, described in the next subsections, were designed to achieve the objectives listed in the Control Strategy section. The PI controller designs were carried out in the frequency-doain using a odel linearized around the operating point. The classical technique of loopshaping was used to ensure sufficient gain and phase argins for each loop. See the block diagra of the closed-loop syste for ore details on the architecture. Since the feed blending syste is ultivariable and coupled, we proceeded sequentially as follows to design the overall control syste, starting fro the linearized odel.. Design the repulper tank level controller, 2. Close the tank level control loop and recopute the transfer function atrix, 3. Design the ratio controller based on the transfer function atrix of step 2, 4. Close the ratio control loop and recopute the transfer function atrix, 5. Design the density controller based on the transfer function atrix of step 4. Repulper Tank Level PI Controller The repulper tank level is controlled by a PI controller coputing speed coands for the transfer pup otor. The two controller inputs are:. the pulp level h Rep as easured with an ultrasonic transducer, and 2. the level setpoint h Rep0.

8 The output of the controller is a correction ω p in pup otor speed, given by: It p = ph Rep0 Rep ih Rep0 Rep 0 ω ( t) K [ h ( t) h ( t)] K [ h ( τ) h ( τ)] dτ which is then subtracted fro the noinal speed ω p0 to for the speed coand. Figure 2 below shows a block diagra of the repulper tank level PI controller, where the Laplace operator /s represents an integrator. (7) level setpoint () pup otor speed (RPM) h Re p 0 ω p ω p ih Kph - K s - h Re p level easureent () ω p0 Figure 2: Repulper tank level PI controller Raglan to Strathcona Ratio PI Controller The R:S ratio is controlled by a PI controller coputing slurry valve opening coands (in %) for the Strathcona slurry line, fro a coputed error in dry ass flow rate of Strathcona. The three controller inputs are:. the dry ass flow rate of the ix at the output of the repulper as coputed fro agnetic floweter and density eter easureents, 2. the ass flow rate of Raglan going into the repulper, 3. the R:S ratio setpoint. The output of the controller is a correction x v in valve position, given by I x = K e K e ( τ) dτ v pr S ir S 0 where es: = ( R) is the error in Strathcona feed rate, and to which the rsp noinal valve opening x v0 is added to for the valve coand. Note that the first ter on the right-hand side of the last equation defining e S is the Strathcona dry ass flow rate setpoint. Figure 3 shows a block diagra of the ratio PI controller. The block with the sybol X siply ultiplies its two inputs. t (8)

9 r SP r SP x - x - K pr K s ir x v valve opening (%) v R x v0 Figure 3: Ratio PI controller Density PI Controller Density at the output of the repulper is controlled by a PI controller acting on the process water flowrate setpoint, based on the density error. An internal water flow control loop, not included in this study, ensures that the actual flow is close to the setpoint. The two controller inputs are:. density easureent f fro density eter at the output of the repulper, 2. density setpoint f 0. The output of the controller is a correction w in water flow rate, given by: It w( t) = Kpd[ f( t) f0( t)] Kid [ f( τ) f0( τ)] dτ (9) 0 to which the noinal water flow rate w0 is added to for the setpoint for the internal water flow control loop. Figure 4 shows a block diagra of the density PI controller. density setpoint (%) f 0 - K pd K s id w water flow rate w f density easureent (%) w0 Figure 4: Density PI controller

10 NONLINEAR CLOSED-LOOP SIMULATION The nonlinear odel of the feed blending syste was ipleented as a siulator using the software package MATLAB SIMULINK TM [THE MATHWORKS, 998]. The ain siulator block diagra is depicted in Figure 5. It cobines the nonlinear feed blending syste odel described above with the level, ratio, and density PI controllers (gray blocks). The siulator was built fro low-level continuous-tie dynaic function blocks to for an interconnection of the three ain coponents of the syste, naely: the repulper tank, the transfer pup, and the roaster feed tank. Each siulation run represented 2 hours of real-tie operation, and the tie unit used was the hour. A step size of 0/3600 hour (0 seconds) in the fifth-order Runge-Kutta integration routine was used to solve the nonlinear differential equations. Legend for Siulink Sybols var var output to variable var in Matlab workspace input fro variable var in Matlab workspace transport delay.0 gain ultiplying the input Mux ultiplexer block cobines its inputs to for a vector output 0.s u[2]/u[] transfer function block function block apping vector input into scalar output scope eter block to view variable trends during siulations saturation block

11 noise R:S PID.s /(u[]) (%) noise valve0 w0_dot ratio_sp valve_psn_nl valve_psn K valve gain f_dot R_dot w_dot water _dot_nl strathcona R:S ratio ix density filter raglan in ix raglan strathcona in ix water water in ix ix tank level Repulper tank oegap0 oegap_nl ratio_nl (RPM) R:S ratio ix density (%) density_nl.0 R_dot_nl rag in ix strath in ix S_dot_nl water in ix w_dot_nl () Rep. tank level hrep_nl level () hrep0 PID otor speed speed ixwater ixwater hrf_nl R:S ratio ix density SG (t/^3) SG tank level () Roaster feed tank level Transfer pup density_r_nl ixwater to roaster 00*u[2]/u[] density to roaster density fro repulper density to roaster Mux Roaster feed tank (%) RF_dot (%).0 density_sp notes: * All inputs to repulper are ass flow rates in etric tons per hour PID density * The "ix" input is the dry ass flow rate at the output of the repulper, * The ix density is expressed as a percentage solids/(solidswater) * The repulper and roaster feed tank levels are expressed in etres * PI controllers are in blue Figure 5: Main block diagra of closed-loop nonlinear siulator

12 strathcona strathcona strathass filer cake 2 filter ix strath in ix ragass Strathcona in repulper 5 ix 3 raglan raglan ragass ix strathass raglan in ix Raglan in repulper 4 water water strathcona ix strathass ragass filter cake water in ix waterass water in repulper Notes: * All inputs are ass flow rates in etric tons per hour * The "ix" input is the dry ass flow rate at the output of the repulper, * Output 3, 4 and 5 are ass flow rates in etric tons per hour * The ix density is expressed as a percentage solids/(solidswater) * The repulper tank level is expressed in etres * Control inputs and easurable outputs are in blue strathass (t) ragass (t) (t) waterass Mux Mux /SGR /SGS u[2]/u[] 00*(u[]u[2])/(u[]u[2]u[3]) 4/(pi*DRep^2) (%) () R:S ratio 4 strathcona in ix 3 raglan in ix 5 water in ix 2 ix density 6 tank level Figure 6: Repulper tank Siulation Results We ran several siulation experients to test the following properties: Robustness and disturbance rejection Change in the incoing Strathcona specific gravity Change in the incoing Strathcona pulp density Change in the incoing Raglan specific gravity Change in the roaster feed rate (fro the operator) Noral lag ties and process dynaics typical in a ixing proble Manual change in the Raglan flow rate being fed to the syste

13 Tracking Change in the R:S ratio setpoint (fro the operator) Change in the density setpoint (fro the operator) Operation with filters Addition and reoval of filter(s) Due to space liitations, we present only one siulation case: a step change in the R:S ratio setpoint (fro the operator). The step change is fro the noinal r 0 = to r =. () (%) step change in desired R:S ratio (input) ix density at the output of the repulper tank () roaster feed tank level process water flow rate (USGPM) Raglan:Strathcona ratio Strathcona slurry pinch valve position (%) () repulper tank level (RPM) pup variable speed drive velocity tie (hours) tie (hours) Figure 7: Response to a 0.69 step change in R:S ratio setpoint

14 Based on the closed-loop siulation results, the following observations were ade: A decentralized PI control architecture was adequate The siulated control syste was robust to changes in Strathcona slurry density and specific gravity The siulated control syste tracked density and ratio setpoints adequately The addition or reoval of a filter had only a inor effect on density at the output of the repulper For very large additive disturbances and perturbations on the slurry valve odeling the effects of changes in Strathcona properties, the output pulp density was still aintained within % in ost cases. However, the R:S ratio started to vary significantly in soe cases. Setting the Raglan flow rate anually only had a inor effect on density and ratio at the output of the repulper (unless saturation occurred in the slurry valve). IMPLEMENTATION AND COMMISSIONING The density, ratio and level PI controllers were ipleented on the selter's Foxboro distributed control syste (DCS) using standard PID blocks. During coissioning, the calculated PI gains were tested, as well as other sets of gains to try to iprove the response further. After a few days of testing it was found that the calculated gains offered the best trade-off between perforance and robustness to variations in slurry and pulp density, which affect valve dynaics, transfer pup characteristics, etc. However, we decided to add a bit of derivative action to iprove the closed-loop daping, leaving the low frequency loop gain basically unchanged. CONCLUSION The feed blending control syste has been in operation since the spring of 998, producing a consistent pulp density that ultiately iproves the efficiency of Falconbridge's selting process. REFERENCES KUO, B. C., 985. Autoatic Control Systes. 5 th Edition, Prentice-Hall, New-Jersey, 720 p. THE MATHWORKS Inc., 998. Siulink User's Manual.

15 Sybol Variable APPENDIX A: NOTATION H Rep : Height of repulper tank () D Rep : Diaeter of repulper tank () V Rep : Active volue of repulper tank ( 3 ) S : Dry ass flow rate of Strathcona feed fro valve f S : Strathcona slurry density in % solids SG s : Specific gravity of dry Strathcona feed (t/ 3 ) x v : Strathcona slurry pinch valve opening (%) f : Dry ass flow rate of Strathcona feed fro filters f f : Density of Strathcona slurry fro filters (% solids) R : Dry ass flow rate of Raglan concentrate SG R : Specific gravity of Raglan concentrate (t/ 3 ) w : Mass flow rate of water h Rep : Pulp level in repulper tank () r : Ratio of dry Raglan/Strathcona ass flow rates in ix SR : Total ass of dry Strathcona in repulper tank RR : Total ass of dry Raglan in repulper tank wr : Total ass of water in repulper tank : Dry ass flow rate of ix out of repulper and into roaster feed tank f : Mix slurry density in % solids h RF : Pulp level in roaster feed tank w : Mass flow rate of ix (including water) out of repulper tank S : Dry ass flow rate of Strathcona in ix out of repulper tank R : Dry ass flow rate of Raglan in ix out of repulper tank w : Mass flow rate of water in ix out of repulper tank SG : Specific gravity of ix (t/ 3 ) ω p : Velocity of transfer pup variable speed drive (RPM)