Modeling and control of mill discharge pumps in the Aitik copper mine

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Modeling and control of mill discharge pumps in the Aitik copper mine

Tomas Vikner

External supervisors: Stefan Sjöström, Erik Klintenäs, ABB

Internal supervisor: Joakim Ekspong, Department of Physics, Umeå University

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39 million tonnes of ore was processed into concentrated copper, silver and gold. The distributed control system 800xA is provided by ABB, and this is what the operators use for process monitoring and control. Currently, the control of the mill discharge pumps operating to transport slurry from the mill circuit to the flotation system is not completely satisfactory. This leads to additional work for the operators, and can in worst case interfere with production.

This project has aimed to identify the problems with the existing control solution mainly from the operators and the engineers perspective, but also by looking at trend data. The discharge pump system has also been modeled, based on a combination of theoretical knowledge and real sensor data obtained from the process control system. The model has been implemented in a 800xA simulation environment, where alternative control solutions have been simulated and evaluated.

The modeling procedure has been limited by the lack of pressure, density and flow sensors in slurry flows, and this has lead to an increased uncertainty, in particular for the dynamic characteristics of the pump system. The static characteristics of the discharge pumps have been modeled by regression analysis of a large amount of steady state data over several months, and the dynamic characteristics have been identified from a step response experiment.

A cascade connection of proportional-integral (PI) controllers are used for pump control, where the primary controller uses parameter scheduling as a function of measured tank level.

This leads to smooth control during normal mill circuit operation, which is a benefit for the flotation process, but it can also cause problems such as flooding, in particular at mill circuit starts or when switching between pumps. According to simulations, it seems like some modifications in the PI control should make it possible to use smooth control around the reference level, and to still avoid flooding at the situations that appear to be problematic today.

The initial goal of this project was a live implementation of improved control, but this was not possible during the final weeks of this project. Instead, the simulation results should be used as support for future decision making and controller tuning.

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1 Introduction

Boliden Aitik is located south of Gällivare, and it is the largest open-pit copper mine in Sweden, and one of Europe’s largest copper mines as well. More than 39 million tonnes of copper ore was enriched into concentrated copper, silver and gold, during 2017 [1]. The development of min- ing automation is an interdisciplinary collaboration between several partners. The distributed control system 800xA is provided by ABB, and this is what the operators and engineers at the concentrator use for process monitoring and control.

Currently the control of the mill discharge pumps is not completely satisfying. To test new control directly in the live environment is not an option, as this would interfere too much with production. This project has therefore aimed to identify the problems with the discharge pump system, to build a model of the pump system and its surroundings, and to test and evaluate alternative control solutions in a 800xA simulation environment similar to the live environment control system.

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2 Background

2.1 Process overview

After drilling and blasting in the open-pit, large blocks of ore are transported on haul trucks to a crusher, where mechanical force and pressure breaks down the material into copper ore. Copper ore is transported to the concentrator on a conveyor, and this is where valuable minerals are extracted. The concentrator consists partly of a grinding hall and a flotation area.

As ore enters the concentrator, grinding is the first stage. Here ore particles are reduced in size by a combination of impact, chipping and abrasion. This is done in large rotating steel cylinders, or grinding mills, which are the main components of the mill circuits. One of the primary mills in the Aitik concentrator can be seen in Figure1.

Figure 1 – One of the primary mills (gearless mill drive) in the Aitik grinding hall. Courtesy of ABB and Boliden.

During the grinding process, the ore particles are also mixed with water. The mixture of water and the well pulverized ore particles forms a thick and abrasive fluid inside the grinding mills, referred to as slurry.

The next stage in concentration is flotation, where water repellant chemicals are added to modify the floatability of minerals in the slurry. This makes it possible to separate the bouyant minerals in various stages, by using a connected line of flotation tanks. Situated at the end of the mill circuit are the discharge pumps. These are centrifugal slurry pumps that operate to transport slurry from mill discharge to the flotation area.

2.2 Mill circuit

In the grinding hall there are two identical mill circuits, and each mill circuit has two grinding mills, known as the primary mill and the secondary mill. Ore that enters the concentrator goes

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directly into the primary mill drop, and from the primary mill, slurry goes directly to the secondary mill. In the mill circuit, there are however also water additions at various locations, and there is also recirculation of ore particles that are considered too large for flotation in two stages.

Recirculation after the primary mill is handled by a trommel classifier (a rotating cylinder that conducts slurry through the surface) and conveyors for ore transport back to the primary mill.

Recirculation before flotation is handled by a screw classifier (screws situated in a slurry container that pushes away rocks) where large particles falls back into the primary mill and slurry continues to flotation. A schematic of the mill circuit is seen in Figure 2, and note that screw classifer is just referred to as classifer, in accordance with the sites real control system.

Conveyor Primary mill Trommel Secondary mill

Classifier DB

Pumps DB

Discharge pumps Conveyors

Classifier Flotation

m

qin

qout

r_s

r_t r_t

Figure 2 – Schematic mill circuit description. Scale is (physically) not considered. Copper ore (m), which also is the primary mill feed, enters the concentrator on a conveyor. Recirculation of ore occur after the primary mill by a trommel (rt) and before flotation by screw classifers (rs).

Slurry initially produced in the primary mill is transported through the trommel, through the secondary mill, to the pump system distribution box (Pumps DB) and finally to the discharge pumps. The slurry inflow to the discharge pump system is denoted qinand the outflow is denoted qout. After the mill circuit comes the flotation system where minerals are separated.

Note that the water addition locations are not included in the schematic, but for the purpose of this project it is enough to consider the total amount of water added prior to the discharge pump system. Most of the water additions are measured, and the sum of the additions prior to the discharge pump system is calculated inside the control system.

In the mill circuit, there are no measurements of pressure, flow or density available for slurry

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transport at any location. Primary mill feed ore weight, m, and recirculation by the trommel are properties that also are measured. Recirculation from the screw classifier is not measured however, but the total recirculation r = rs+ rtof ore is known to be approximately 8-20 % of m.

Density and volume of the ore at the primary mill feed is not measured either, but the density of the ore is said to be approximately 2.8 ton/m³.

The slurry inflow qin from the secondary mill enters the pump system distribution box, and the slurry outflow qout from the discharge pumps enters the classifier distribution box, and none of these flow rates are measured.

2.3 Discharge pumps

Situated below the secondary mill discharge (both physically and in the schematic) is the pump system distribution box. It is basically a tank with four controlled valves, and below it there are two tanks to distribute slurry into, with one centrifugal pump per tank. During normal mill circuit operation, only one pump is active at a time, while the other pump serves as a backup.

The reason for this is to make it possible to perform a pump switch, that is, the backup pump should be able to intervene in case the active pump for some reason is interlocked, or is not working as intended. Figure 3 shows a schematic of the pump system, where the inflow to the system enters into the pump system distribution box, and the outflow from the active pump enters the classifier distribution box. The pumps are reffered to as P1 and P2, and there seems to be no particular priority as active and backup pumps.

Pumps DB Classifier DB

Tank 1 Tank 2

P1 P2

Figure 3 – Mill circuit discharge pump system. The pump system distribution box distributes the inflow between the slurry tanks by four controlled valves, and the discharge pumps (P1 and P2) operate to transport slurry to the classifier distribution box. During normal mill circuit operation, only one of the pumps are active at a time, while the other one serves as a backup pump.

The tanks are cylindrical at the upper half, with a more conical shape at the bottom half, to prevent slurry from accumulating at the bottom. They are 6.84 m high, but at 5.19 m height there is an opening, and as the slurry reaches this level, the ground starts to get flooded. The

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inner diameters are 4.18 m at the cylindrical part, and there seems to be no clear information about at what tank height the conical shape starts. This height was however estimated as 2.75 m based on visual inspection. A tank can hold about 55-60 m³before the flooding level is reached.

The pumps that currently are installed are Warman horizontal centrifugal slurry pumps of model 400 TU-MCR, with a nominal speed of 450 rpm and a nominal power consumption of 1428 kW.

The pumps are connected at the bottom of the tanks, and operate to transport slurry upwards to the classifier distribution box through a 150 m long piping system, with a total ascent of 35 m.

2.4 Control setup

The active pump is controlled against the slurry level in the corresponding tank. Ultrasound gives the measured level Lm, from a sensor positioned above the tank. The pump power Pm

and the pump speed nmis also measured at all times, and for the rest of this report, tank level, pump power and pump speed, will always be considered in units of %. For pump power, 100 % corresponds to 1428 kW and for pump speed, 100 % speed corresponds to 450 rpm, as these values corresponds to the upper limits in the control system.

The ultrasound sensor is calibrated to measure 100 % at a level slightly lower than the flooding level. The flooding level is said to be about 10 % or slightly higher above the 100 % mark, and based on this it is assumed that the 100 % level measurement corresponds to approximately 4.7 m. The 100 % level will still be referred to as the flooding level in this report, as there is risk for flooding as this point. The control solution currently in use is described in detail in Figure4.

LC JC VFD Pump motor

Ultrasound Tank

Pumps DB Lr

−

Le Pr Pe nr

Pm

−

w, V

q_in Lm

L Impeller

qout

Figure 4 – Control setup and connection to the discharge pump system. Note that in reality, the setup is more complex, but this is enough for the purpose of this project. The level controller (LC) sets a reference power (Pr) for the power controller. The power controller (JC) sets a reference speed (nr) for the variable frequency drive (VFD). The VFD controls the pump motor, and the pump impeller produces an outflow qout from the discharge pump system. Note that qout in this context does not flow into the tank, but out from the tank. This only demonstrates how the control setup is connected to the pump system (as input/output relations).

A reference level Lr is specified by the operators in the control system. The level controller (LC) takes the level error (Le= Lr− Lm) as input and sets a reference power Pr for the power controller (JC). The power controller takes the power error (Pe= Pr− Pm) as input and sets a

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reference speed nrto a variable frequency drive (VFD).

The VFD operates to increase power P consumed by the pump motor by varying the AC (alter- nating current) frequency w and voltage V in a controlled way, such that the impeller speed n follows the reference speed set by the power controller. This makes the pump impeller produce a flow qout that in turn controls the tank level L, as it rejects the inflow qinfrom the pump system distribution box.

Currently the level controller and the power controller are PI (proportional integral) controllers in a cascade connection. The theory explaining what a PI controller is can be found in Section 3.3.2, and the theory explaining a cascade connection can be found in Section3.3.4.

2.5 Problem identification

Controlling the level in a tank sounds like a straightforward task, and it typically is, at least for steady inflows. But somehow Boliden has been asking ABB for improved pump control of the discharge pumps for several years, and still, this issue has not been taken care of. The problem with the discharge pump system was not clear at first, and the problem has been identified mainly by communicating with site operators and engineers, but also by looking at long term sensor data. It seems like everyone can agree on what the problems actually are, but there have been a few different opinions regarding the magnitude of the problems.

2.5.1 Control problems

Pump control under normal circumstances and when there is a steady inflow to the pump system has never been a problem. The most common problem seems to be that the tank level sometimes reaches a higher level than 100 % when there is a sudden change in the inflow rate to the system, or when switching between the two pumps in the system. This often floods the ground, and leads to additional work for the operators and of course, a small waste of resources. The reference level in the tank is usually set to 75 %, which may seem like a high reference level if flooding is a problem. The reason for this is that a too low level is damaging to the pump (and this is expensive), and at 25 % level, the pump is interlocked. An interlock of the active pump can cause the entire mill circuit to interlock, unless the backup pump is activated shortly. To keep the mill circuit running is clearly a higher priority than to avoid flooding.

Start of the mill circuit is a typical situation that causes a sudden change in the inflow to the pump system. Before the grinding mills are started, a pump is already controlling the tank level against a water addition of 200-300 m³/h. Considering that typical slurry flow rates are about 2800 m³/h, this is a large increase. Changes in the primary mill feed also causes a change in the inflow rate to the pump system, but apparantly not large enough to cause problems. When switching between pumps, there is no sudden increase in inflow to the discharge pump system, but it is a sudden increase to the backup tank, and this therefore leads to similar problems as a mill circuit start.

Initial conversation with the site operators made it seem like flooding was normal (something to typically expect) when starting the mill circuit, and that this lead to hours of additional work for the operators, who were manually flushing away the flooded slurry from the grinding hall. More experienced operators said they would set the pump control in manual mode when starting the mill circuit or when switching between pumps, to avoid flooding. These descriptions could not

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be verified clearly from the long term sensor data. It was noted that automatic control was most commonly used when starting the mill circuit, and the level seemed to stay below 100 % most of the time anyway. Later on, when presenting a few simulations to a group of engineers and operators, it seemed like most people agreed that flooding is not that common after all, and in their opinion, when flooding does happen, it is mostly water and does not take that much effort to flush away.

Even if the opinions seemed to differ along the way, it was decided that improved control was something considered worth looking into. And in particular, an improved automatic pump switch solution seemed to be of interest, and this may require the pump control to handle even larger sudden increases in the inflow rate in the near future.

2.5.2 Automatic pump switch

To switch from the active pump to the backup pump includes manual work by the operators today, even if there already is an existing implementation of an automatic pump switch solution in the control system. There seems to be two reasons why the automatic pump switch solution is not used today. First of all, there is a lack of a controlled cleaning devices (basically valves situated in each tank to flush away rocks), and second, according to the operators who have tried the automatic pump switch solution many years ago, it was not working as intended. Instead, it made the pump control go into some sort of back-and-forth behaviour, meaning that after an automatic switch between two pumps, the automatic control chose to switch back to the first pump once again.

Since the operators are not using the automatic switch solution today, there is no available data to identify the back-and-forth behaviour. The conditions that trigger an automatic switch can be seen inside the systems code, but today, the back-and-forth behaviour can not be explained from the code. However, according to the engineers, this code has been modified several times over the past years, and it is possible that the back-and-forth behaviour would not be present during an automatic switch today.

The installation of a controlled cleaning device seems to be the highest priority according to some of the operators. A pump switch often requires a lot of manual work from the operators today, and this takes a lot of time. More importantly, if one of the pumps for some reason suddenly is interlocked, the mill circuit will stop within 30 seconds unless the backup pump has taken over, and without an automatic switch solution, a stop in the mill circuit can be expected for such a situation.

An automatic pump switch that can handle an interlock also leads to a new control problem to consider. Such a situation would lead to an even larger sudden increase in inflow to the discharge pump system, that is more difficult to handle than the typical situations that causes problems today. Larger tanks would be the optimal solution rather than more aggressive control, with respect to both the pump system and to flotation, but replacing them is clearly not an option.

Improved control should be able to deal with those problems as well. But there will always be a trade-off here, since a more aggressive control solution will naturally cause larger disturbances in the flotation system.

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2.6 Goals

The long term benefits of this project is to make it possible for the operators to start the mill circuit and to switch between pumps, without manual interference in the pump control, and without the need to physically visit the grinding hall just to flush away flooded water and slurry, or to manually flush the pipes after pump operation. This requires both control optimization and mechanical installation of new controlled valves, used as cleaning devices.

This thesis has however mainly focused on building a model of the system, implement the model in a simulation environment, and to provide simulation results for various problematic situations that can be used as support for implementation of new control solutions and for tuning of controllers. This project has been based on three subgoals:

• The first goal of this project has been to model the discharge pump system, and the relevant surroundings, based on a combination of geometrical knowledge, theoretical knowledge and an analysis of sensor data. In particular, this goal has focused on identifying pump characteristics such as a power function and a flow function, to make it possible to simulate power consumption and flow rate delivered by the pump.

• The second goal has been to implement the model of the discharge pump system in a 800xA simulation environment that is based on a copy of the real control system environment, where the user instead can simulate an arbitrary inflow to the discharge pump system and evaluate control options.

• The final goal of this project has been to evaluate the currently implemented control solution and alternative solutions, both on situations that appear to be problematic for the control to handle today, and for problematic situations that can be expected in the future.

This goal has in particular been to produce simulation results that can be used as support for decision making in the real control system, and for controller tuning.

Implementation of improved control in the real system was meant to be the final goal of this project, but this would require assistance from ABB, and there was none available for implementation in the final weeks of this project.

The installation of controlled valves as cleaning devices required for an automatic switch solution was discussed with the operators and engineers of Boliden during this project, but it was decided that the installation will not be possible in the scope of this project. However, the control evaluation goal of this project has still considered new situations that can arise with an updated solution for automatically switching between pumps.

2.7 Limitations

As the initial plan was a live implementation in the scope of this project, and otherwise implementation of the solution in a simulation environment similar to the live environment, this project has only considered various forms of PID (proportional integral derivative) feedback control, and feed-forward control. Implementation of more complicated solutions in 800xA would most likely have been too time consuming, considering the lack of experience in 800xA Control Builder, where the control application is built.

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3 Theory

To model the discharge pump system, theory is combined with analysis of experimental data.

This section therefore first covers fluid mechanics and centrifugal pumps, and then modeling theory that is applied on experimental data. Finally, control theory is covered, which is necessary to understand the currently implemented control solution, and to motivate alternative solutions.

3.1 Fluid mechanics

3.1.1 The Bernoulli equation

The Bernoulli equation applies to a fluid particle that moves along a streamline in a steady, inviscid and incompressible flow, and it states that

p ρ+1

2v²+ gz = constant, (1)

where p is pressure, ρ is density, v is velocity, g is the gravitational constant and z is elevation [2]. Note that every term in (1) has units of energy per unit mass. The terms p/ρ and gz are related to the work done by the pressure forces and weight respectively, and the term ¹₂v² is related to kinetic energy.

3.1.2 The centrifugal pump

A turbomachine is a mechanical device consisting of several blades attached to a rotor, and it is designed to extract (turbine) or to add (pump) energy to a fluid [2]. The centrifugal pump is one of the most common radial-flow turbomachines, and it has two main components. An impeller that is attached to a rotating shaft, and a stationary casing that encloses the impeller.

As a motor drives the shaft, the impeller adds pressure and absolute velocity to the fluid inside the casing [2]. The casing shape is designed to reduce velocity as the fluid leaves the impeller, and according to Equation (1), this increases the pressure on the discharge side of the pump.

The increase in pressure makes it possible for the centrifugal pump to lift fluid in the vertical direction.

3.1.3 Pump performance characteristics The power Pf transferred to the fluid is given by

Pf = ρgqha, (2)

where ρ [kg/m³] is density, g [m/s²] is the gravitational constant, q [m³/s] is flow rate and ha[m]

is the actual head in units of length supplied by the pump [2], and this can be derived from dimensional analysis. For a system with two tanks with fluid surfaces located at a lower height z₁ and an upper height z2, the actual head can be written on the form

ha= z2− z1+ kq², (3)

where k depends on pipe size, pipe length and friction factors [2]. The elevation difference z2−z1

leads to a hydrostatic pressure difference according to

∆p = ρg(z2− z1), (4)

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and the kq²term describes the pressure drop or head loss according to the Darcy-Wesibach equa- tion [2].

The overall efficency of the pump can be described as η = Pf

Ps

,

where Psis the power delivered to the shaft [2]. Now the efficiency for a pump is largely dependent ha and q, but by inserting Equation (3) into Equation (2), this leads to

Pf = ρgq(z2− z1+ kq²), or

Pf = ρgq(∆z + kq²). (5)

where ∆z = z2− z1 is the elevation difference. If the efficiency of the pump is not varying too much in an interval around an operating point, it is reasonable to assume that the power P consumed by the pump motor can be written as

P = aq∆z + bq³, (6)

if ρ and g are relatively constant, and are included in the arbitrary coefficients a and b. However, for a system of pipes with a significant ascent, a certain speed and power will be required just to overcome the hydrostatic pressure due to elevation. Until that, the overall efficiency can be seen as zero.

3.2 Modeling theory

3.2.1 Static and dynamic characteristics

A systems static characteristics are the properties that characterizes the system at a steady state.

The static gain for a process with input u and output y refers to the function y = f (u),

as the system has reached a steady state. A systems dynamic characteristics refers to the properties such as time delay and transient response.

3.2.2 First order system

A dynamic first order system refers to a process that can be described by a first order ordinary differential equation, according to

τdy(t)

dt + y(t) = Ku(t),

where K is the static gain and τ is the time constant of the system [3]. A first order low-pass filter is an example of such a system. The laplace transform of a first order low-pass filter is written as

1 τ s + 1,

where s = jw is a complex variable and j is the imaginary unit.

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3.2.3 Integrating process

An integrating process refers to a system where output in some way is the integral of the input [3]. An example of such a system is a tank with fluid, with tank level described as

A(L)dL

dt = qin− qout, (7)

where A(L) is the cross section area at fluid level L, and where qin and qout are inflow and outflow respectively.

3.2.4 Step response

A step response experiment considers the time evolution of y right after the system is subjected to a change in u, and it is a commonly used to determine a systems dynamic characteristics. For a first order system, the response to a step change ∆u in the input signal can be described as

∆y = K (

1− e⁻^τ^t )

∆u,

where K is the static gain, and τ is the time constant of the system [3].

3.3 Control theory

3.3.1 Feedback control

A control system is designed to control the behaviour of a system or a process in a controlled way, by using control loops. For continously modulated control, a feedback control loop is used to automatically control a process. The basic components in a feedback control loop can be seen in Figure5.

Controller u(t) Actuators System

Sensors

d(t)

n(t)

r(t) e(t) y(t)

− ym(t)

Figure 5 – Basic feedback control structure.

In feedback control, the control signal u(t) is based on a measurement ym(t) of the system output y(t), where

ym(t) = y(t) + n(t),

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and where n(t) is measurement noise at the sensors. A reference value r(t) is specified for the desired system output y(t), and the control signal is based on the deviation of the system output from the reference value, according to

e(t) = r(t)− ym(t),

where e(t) is referred to as the error, or the control input. The control signal controls the ac- tuator, and this could be for example a valve that is able to influence the system based on the control signal.

A feedback control loop can be said to have two main tasks. To reject disturbances d(t) that enters the system and affects the system output y(t) in an undesired way, and to track changes in the reference value r(t) [3]. A disturbance in this case is easiest explained by an example. If a control loop is designed to control level (y) in a fluid tank at constant reference level (r), the inflow to the tank is seen as a disturbance from a control perspective, as it makes the actual level deviate from the reference level. The control effort will be to produce an outflow from the tank that rejects the inflow such that the level remains around the reference level.

How the controller computes the control signal from the error depends on the control algorithm, and one particular control structure that has become almost universally used for industrial control is the proportional-integral-derivative (PID) structure [4].

3.3.2 Proportional-integral-derivative (PID) control

A PID controller considers the instantaneous error, the time integral of the error, and the derivative of the instantaneous error. The control signal can be computed as

u(t) = Kpe(t) + Ki

∫ t 0

e(ti)dti+ Kd

de(t) dt + i.c.,

where the parameters Kp, Kiand Kd are the proportional, integral, and derivative gains respec- tively, tiis the integration variable and i.c. are the initial conditions. For industrial use, the PID equation is typically written as

u(t) = K_p (

e(t) + 1 Ti

∫ t 0

e(t_i)dt_i+ T_dde(t) dt

)

+ i.c., (8)

where Tiis the integral time constant and Tdis the derivative time constant [4]. This is convenient for tuning with methods such as the lambda method described in Section6.3. When referring to the PI parameters or PID parameters in this report (or just PI parameters), it is assumed that the PID equation is written in the same form as in Equation 8, such that the parameters are K_p, Ti and Td. The procedure of specifying these parameters for a specific control application is known as tuning of the controller.

In the process industry derivative action is typically not used. This simplifies the PID equation to

u(t) = Kp

(

e(t) + 1 Ti

∫ t 0

e(ti)dti

) + i.c.,

and this is simply referred to as PI control. Without integral action as well, the equation can be simplfied to

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u(t) = Kpe(t),

such that proportional action only is used. However, proportional action only provides limited performance and nonzero steady state errors. The addition of integral action on the other hand slowly drives the steady state error to zero [4]. Further on, a lower Ti means a higher integral gain, and this in turn drives the error to zero more quickly.

Most commonly the parameters Kp, Ti and Td of PID controllers are specified as constants.

Otherwise, when the PID parameters are functions of sensor measurements, it is referred to as parameter scheduling in this report.

3.3.3 Integral windup

An actuator in a control system is always limited (physically) in some way. When a control signal reaches the actuator limit, the closed loop feedback control is broken, as an increase in the control signal will no longer have any effect on the system output. If a controller with integral action is used, the error may continue to be integrated even when the actuator is satured, and this is referred to as integral windup [5]. To avoid problems from such situations, PID controllers uses anti-windup compensation to prevent the integrator from excessively building up the control signal during actuator saturation.

3.3.4 Cascade control

An alternative feedback based architecture for dealing with disturbances when there are more than one measurement is cascade control. Cascade control uses at least two controllers and two sensors to control one actuator. The primary controller Cp, that controls the primary variable yp sets the reference value for the secondary controller Cs, that in turn controls the control secondary variable ys. This is seen in Figure 6, where Mp and Msare the sensors for yp and ys

respectively, such that ym,p and ym,s are the measured values.

− Cp

− Cs Ps Pp

M_s

M_p

ds dp

r_p e_p r_s e_s u_s ys

y_m,s

yp

y_m,p

y_p

Figure 6 – Cascade configuration feedback control structure.

The secondary variable is controlled by the inner loop and affects the primary variable. Cascade control is particularly useful when there are significant dynamics (e.g. time delays or long time

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constants) between the secondary variable and the primary variable [5].

The secondary controller should reject disturbances ds in the secondary process Ps before they affect the primary process Ppoutput. Cascade control is easier understood by an example. In the control setup described in Figure4, tank level is the primary variable and power is the secondary variable.

Tuning a PI cascade configuration requires tuning of the secondary controller to start with, and then, the primary controller can be tuned.

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4 Pump system modeling

This section covers both the procedure and the results of the development of the discharge pump system model. This section also explains how the model was implemented in simulation appli- cations. The modeling results are presented in this section and not at the end of the report, with the motivation that the content in the control simulations sections (the main results of this project) requires implementation of the modeling results.

This section has a few main objectives as listed below.

• To describe tank level as a function of inflow, outflow, and from geometrical knowledge.

This is done from Equation (7), and geometrical knowledge have been obtained from sheets and from a visit to the site.

• To relate system characteristics such as tank level, fluid density, pump speed, pump power and pump delivered flow rate.

Now there has been one particular complication for the modeling procedure, the lack of pressure, flow and density sensors for slurry flows. This motivates that the modeling procedure has been divided into identification of static and dynamic characteristics by two separate procedures. At a steady state, in a sense that measured signals such as primary mill feed, water additions, tank level and pump control all are relatively steady, it is reasonable to assume that

q_out= q_in,

that is, that the flow rate qout delivered by the active pump at a steady state is approximately equal to the sum of all inflows to the discharge pump system. This is one way of estimating the flow rate by the pump when there is a lack of flow sensors around the discharge pumps. This motivates the steady state analysis performed in Section4.1.1. A steady state analysis does however not give information about the dynamics of the system. Therefore, the modeling procedure is based on a combination of a steady state analysis part to identify the static characteristics, and a step response experiment part to identify the dynamic characteristics.

4.1 Static characteristics

The static characteristics describe the relationships between pump speed n, power P , flow rate q_out, density ρ and tank level L at a steady state. Steady state mean values are first obtained by the steady state analysis in Section4.1.1, and regression analysis is then applied to the mean value data sets in Section4.1.4to obtain the static characteristics.

4.1.1 Steady state analysis

By measuring conveyor weight and water flow rates at several locations in the mill circuit, the density inside the pump system and the flow rate delivered by the pumps can be estimated, but it must be considered that the mill circuit is physically huge, and this leads to large time delays between the sensor measurements.

Most of the water is added into the primary mill to produce slurry, but also in the secondary mill, and in the pump system distribution box. These water additions are controlled against the ore weight on the main conveyor to make sure that the slurry gets the correct concentration

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of coarse particles both inside the pump system but more importantly in the flotation system.

Smaller water additions are also located on the conveyors, and from several other locations in the concentrator. Sump pumps located on the ground in the grinding hall operate to remove waste water and slurry that for some reason has ended up on the floor, and these flows are not measured, but they end up in the pump system distribution box as well. Smaller water and slurry flows from other parts in the concentrator also goes into the pump system distribution box, and most of them are measured.

Data from several months, with a sample time of one minute (averaged), have been extracted for both mill circuits, where all four pumps are included (two per mill circuit). These data include ore weight to the primary mill m, the sum of all water addition flow rates in the mill circuit wa, tank level, pump speed and pump power. At a steady state, the total inflow to a slurry tank (and therefore also the flow delivered by the pump) can then be estimated as

q_in= (1 + r_s)m

ρ_o+ w_a, (9)

where ρo is the density of the ore to the primary mill and rs is recirculation of ore that goes through the pump system again. These measured properties are previously seen in Figure2. Now a mistake was made where rs was used as 0.14, which is an estimate of the total recirculation in the system rather than the recirculation that enters the pump system again. The recirculation that reenters the pump system is expected to be approximately half of that, but this should only have a minimal impact on the power vs. flow model latter in the report, and even less impact on the final results. The slurry density in the tank can also be estimated as

ρ =(1 + rs)m + wa

qin

, (10)

where rswas used incorrectly as 0.14 here as well. This should not have any impact on the final results either however, since in the end, constant density was used during all simulations.

To automatically obtain the steady state data, all extracted data are divided into two hour intervals. Each interval is then classified as steady if every measured value varies less than 10 % during that interval. The steady state mean values are then used to estimate mean flow rate from Equation (9), and mean density from Equation (10). For regression analysis, mean values for tank level, pump speed and pump power are also used from the corresponding intervals.

4.1.2 Limitations in the steady state mean value data set

It must be noted that the limited variations in the steady state mean values limits the regression analysis as well. As an example, since the pump is controlled to control the tank at a certain reference level, most steady state mean values are very close to the reference level.

A better data set with more varying level measurements could have been obtained during the project by asking the operators if they could use a slightly lower or a slightly higher reference level for a while. However, a higher reference level increases the risk for flooding, and a lower reference level increases the risk that the pump is interlocked. Also, some variations in the steady state tank level is already available in the existing data, as it seems like the operators have been using lower reference levels previously for some time. Height can therefore be included as a predictor in the regression analysis, but the data are far from optimal.

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Variations in the density are even more limited, and trying to control the mill circuit water additions to modify the density at the discharge pumps is a bad idea, since this would have a significant impact on flotation. The water additions in the system are already controlled against ore inflow, such that the ore concentration in the slurry at various positions follows specified values. Therefore, including density as a predictor in the regression analysis is not possible.

Despite the limitations in the steady state data, it has been possible to obtain a large steady state mean value data set with enough variation in pump speed, power and flow rate. These are the most important variables to include for analysis, and they have produced useful results.

As motivated in Section 4.1.3, a more theoretical approach has been used to include density dependence, and as motivated in Section4.1.4, the level variations in the tank are so small in comparison to the constant elevation in the piping system, that tank level can be excluded from the regression analysis.

4.1.3 Customized regression functions

To obtain useful results from regression analysis on the steady state mean values, custom regression functions have been specified first, and then curve fitting have been applied to determine unknown parameters. The functions are based on theory in combination with knowledge about physical limits in the discharge pump system.

The pump characteristics are completely different below and above the zero flow limit, which is referred to as the limit in terms of speed and power that is required for the pump to start producing a positive flow rate. The pumps require a lot of speed only to produce the pressure to overcome the 35 m high slurry column, but it does not require a lot of power at this point and below, as the pump is not delivering any work at this point, it is only lifting fluid in the pipe. Where this limit is in terms of pump speed and tank level is not known exactly, but by analyzing the system for low water flows when the grinding mills are on standby, such a limit can be estimated.

The slurry flows are never near zero, and this makes it complicated to estimate this limit for slurry. However, it is assumed that this limit is approximately equal for slurry and water. This assumption is based on the fact that the hydrostatic pressure difference in Equation (4) increases linearly with density, and according to Matlab’s model of a centrifugal pump [7], the pressure differential delivered across the pump at a certain pump speed increases linearly with density as well.

At a tank level of 75 % which is the typical reference level, the zero flow limit is estimated to be at 75 % pump speed, based on analysis of required to speed to deliver small water flows of 200-300 m³/h. A typical power consumption at this point is estimated to 10 % for slurry. By combining these limits with Equation (6), customized regression functions for pump flow rate as a function of power, density and tank level can be derived prior to regression analysis.

4.1.4 Regression analysis

A lower level in the tank increases the elevation difference ∆z between the supply tank and the delivery tank, and therefore also the power required to produce a certain flow rate according to Equation (5). The tank level variations are however mostly within 1 m in the steady state data set, and this corresponds only to a small pressure difference in comparison to the 35 m ascent in the pipe system, and in comparison to the pressure losses due to friction in the 150 m long pipe system. In either way, by writing Equation (6) as

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P = (a− bL)qout+ cq_out³ , (11) such that elevation is ∆z = a−bL, where L is tank level, and a, b and c are arbitrary coefficients, a decrease in power consumption is expected for a higher tank level. Figure7shows the multivariate regression.

Figure 7 – Multivariate regression analysis of steady state mean values, with power P as depen- dent variable, and flow rate qout and tank level L as predictors.

Apparantly power consumption increases as the tank level increases, and this does not make sense according to theory. It is expected that uncertainties in the measurements most likely have a larger impact on power consumption than variations in tank level, and tank level is therefore neglected as a predictor for regression analysis hereafter. It could of course have been motivated that tank level should have been neglected already, considering the small variations. However, considering that the pump requires a speed of approximately 75 % only to produce a positive flow rate, it is reasonable that even small elevation differences could have had significant impacts on the system characteristics.

By assuming a slurry density of 1.65 kg/m³, it is then possible to use a single variable regression analysis on the steady state data, with power consumption as a function of delivered flow rate.

Without variations in tank level, it is possible to write Equation (6) as P = 10 + aqout+ bq³_out,

for regression analysis, where 10 % corresponds to the power consumption corresponding to zero flow rate, as motivated in Section 4.1.3. This single variable model of order 3 is also simplified and compared to a similar second order model, according to

P = 10 + aq_out+ bq²_out. (12)

The single variable regression results for power vs. flow rate for the two models can be seen in Figure8.

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1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 30

35 40 45 50 55 60 65

Figure 8 – Single variable regression of steady state mean values (ssm), with power P as dependent variable, and delivered flow rate qoutas predictor, for customized models of order 2 and order 3.

The second order model has the advantage that it can be solved for flow by the quadratic formula.

The third order model requires a more complex implicit solver and this could be complicated to implement in Control Builder, and the SSE (sum of squares due to error) is lower for the second order model as well. There are therefore two reasons to prefer the second order model.

Now the flow rate can be obtained as a function of power in the simulation environment (by solving the 2nd order equation for power vs. flow). A relationship that includes pump speed is still needed. The VFD controls power based on the reference speed specified by the power controller, and a modelled function from reference speed to power remains to be found. In this analysis, speed has been used and not reference speed, but they are very much the same, and in particular at a steady state. The actual speed seems to track the reference speed extremely quickly in general.

Linear regression is used for power vs. speed. There is no theoretical relationship that supports a linear model, but apparantly the data look linear, and applying higher order regression could lead to high deviations far from the measurements. The regression function used is

P = 10 + a(n− 75),

for positive flow rate, based on the zero flow limits. The regression analysis for power vs. speed can be seen in Figure9.

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82 84 86 88 90 92 94 96 98 30

35 40 45 50 55 60 65

Figure 9 – Linear regression of steady state mean values (ssm), with power P as dependent variable, and speed n as predictor.

Below the zero flow limit, there is not any steady state data. But a linear model is used there as well for simplicity, leading to

P = (10

75 )

n.

The accuracy of this region is not considered important for simulations, as everything interesting happens above this limit, and it is only necessary that both power and speed have reasonable values above the limit, and not below.

4.2 Dynamic characteristics

From step response experiments it was noticed that the power dynamics was similar to the dynamics of a first order system. This motivates that a transfer function from speed to power should be written as

P =

( 1

τ s + 1

) (10 + a(n− 75))

, (13)

that is, the transfer function is a low-pass filter in combination with the static gain, above the zero flow limit, and

P =

( 1

τ s + 1 ) (10

75 )

n, (14)

below the limit, where the time constant τ can be estimated from step response experiment data.

It is also reasonable to assume that an increased power must accelerate the fluid mass inside the pump system before an increased delivered flow is noticed, and based on this assumption, the transfer function from power to delivered flow rate is modelled as

q_out= 1 (t− tm)

∫ t t_m

q_s(P ), (15)

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where qs(P ) is the static flow rate obtained by solving Equation (12) with the quadratic for- mula, that is, the actual outflow qout delivered by the pump is computed from the mean power over a short time interval of time tv = (t− tm). Determination of the dynamic characteristics corresponds to finding the time constant τ and the time interval length tv. Dynamic data used to obtain τ and tv has been obtained through a step response experiment, where the pump was controlled manually to produce the necessary data.

4.2.1 Step response experiments

The step response experiment was performed for large slurry flows of approximately 3000 m³/h.

The power controller (JC in Figure4) was set to manual model, and the controllers output signal nr was manually changed in large steps. The reaction from reference speed to power, and the reaction from power to flow rate, could then be estimated.

It must be noted that these experiments disturbs the flotation process significantly due to the sudden changes in flow rate delivered by the pump, and the accuracy of these dynamics are not considered to be that important either. Therefore, one experiment including a few steps was considered to be enough. Figure10shows the measured data from the experiment.

100 200 300 400 500 600 700 800 900 1000 1100 30

40 50 60 70 80

Figure 10 – Step response experiment conducted on large slurry flows. Data with one second sample time for measured power and measured tank level. Measured level is denoted Lm and measured power is denoted Pm.

Note that the control signal rn to the VFD is not included. This is due to a mistake with the 800xA data log that was configured prior to the experiment. Only interpolated 6 second data are available for the control signal, and this is useless for the purpose of identifying dynamic characteristics. However, it is clearly noted when the control signal was changed since this is when the measured power starts to increase/decrease. These data are therefore still useful to identify the dynamic characteristics, and a new experiment with a fixed log configuration is not necessary.

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4.2.2 Step response analysis

The simulated power consumption Psim was simulated with the already obtained static charac- teristics. Different values of the time constant τ were then tested such that τ approximately matched the data. Figure11shows how the simulated power based on Equation (13) compares to the measured power, for τ = 3 [s].

100 200 300 400 500 600 700 800 900 25

30 35 40 45 50 55 60 65 70

Figure 11 – Simulated power Psim and measured power Pmfrom step response experiments.

The flow rate qout was also simulated with the already obtained static characteristics. Different values of the time interval tv was tested such that the simulated data matched the measured data. Figure12shows how the simulated level based on Equation (15) compares to the measured level for tv= 5 [s].

100 200 300 400 500 600 700 800 900 60

65 70 75 80

Figure 12 – Simulated corrected level L_corr vs. measured level L_m from step response experiments.

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There is however a slight modification in the flow rate magnitude for the simulated level (therefore corrected), to make it fit better in the y-direction, to in turn make it possible to estimate tv. This can be motivated, since the purpose of this experiment was only to obtain the dynamic characteristics, and not to validate the static flow characteristics. Of course, the simulated flow rate could instead have been compared to a estimation of the flow rate from the measured level, but this requires filtering and this made it more difficult to get an accurate estimation of tv.

4.3 Model implementation

By combining the static and dynamic characteristics identified in the previous sections, it is possible to simulate power, flow and level, based on the power controller output, such that various alternatives for LC and JC can be tested. In Figure 13, the modeled version of the system described in Figure4 can be seen.

− LC JC Power TF

Flow TF Level TF

Lr Le Pr

−

Pe nr

P P

q_in

qout

L

Figure 13 – Schematic of the discharge pump system model, where only one tank and pump is included in the schematic, and qin comes from the pump system distribution box. Power P is computed from reference speed nr by the Power TF block, and outflow qout is computed from power by the Flow TF block. Tank level is computed from qinand qoutand tank geometry by the Level TF block.

In Figure13, the Level TF (transfer function) block corresponds to Equation (7), the Power TF block corresponds to Equation (13) and Equation (14) and the Flow TF block corresponds to Equation (15). The rest of the 800xA simulation environment is based on a copy of the site’s real control system environment. The controllers parameters, settings and connected signals are the same as in the live environment, and controller hardware is simulated as well, to get an even more realistic simulation. This is one significant advantage with simulating control in 800xA.

The 800xA lab environment includes the tank and pump system with the two tanks, the two pumps, the pump controllers and the valves connected between the distribution box and the tanks. A screenshot of the live pump system environment can be seen in AppendixA, and the simulation environment looks very similar.

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5 Control analysis

This section describes the currently implemented control solution in more detail, for a better un- derstanding of the control solution and its limitations, and to identify what parts of the control that should be improved and what parts that are working well and should remain the same as today. This also requires a better understand of the control sequences used in the problematic situations in particular.

In the real control system, the mill circuit is started with a group start control sequence, that in turn includes a group control start sequence for the discharge pump system. This section will however only focus on how the pump control behaves as the mills are started and when switching between pumps, as this is what is relevant for the control optimization in this project.

The control is limited entirely by the level controller, the power controller and the VFD. The pa- rameters Kpand Ti in the controllers are mainly of interest, but limitations inside the controllers and the VFD are also considered.

5.1 Controller settings

The level controller uses a parameter schedule, that is, the parameters Kp and Ti are functions of the measured level Lm. The current schedule with the PI parameters for the level controller can be seen in table1.

Table 1 – Current parameter schedule of the level controller.

L_m [%] K_p T_i

0 1.13 139

50 1.13 139

60 0.51 331

70 0.33 524

80 0.51 331

90 1.13 139

100 1.13 139

The parameters are specified as certain values corresponding to certain tank level measurements.

The values in between those points are obtained from linear interpolation. The purpose of the parameter schedule is to make it possible to smoothly control the tank level near the reference level when the inflow is steady, by using a low proportional gain Kp and a long integral time constant Ti near the reference level, and by at the same time make it possible to aggressively control the pump when there is a sudden change in the flow rate that makes the level deviate far from the reference level. The power controller uses constant PI parameters, with Kp= 0.14 and Ti= 2.

The VFD settings limits rate of change in the reference speed ^dn_dt^r. It is currently limited to

dnr

dt max = 10 %/s and ^dn_{dt min}^r = −5 %/s, and during the step response experiments, peaks in

dnr

dt could be seen to almost reach these level. During automatic control, however, when there is no reason to make extremely rapid changes in pump speed, these limits should clearly be more than enough. Therefore, there is no reason to reconsider the VFD limitations.

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5.2 Specific control sequences

Setpoint (reference value) ramping is used both for grinding mills and discharge pumps as they are started. This means reference speeds are increased towards final targets at predefined rates.

For the discharge pumps, the closed loop PI control has no influence over the pump control, until a minimum speed has been reached. For the grinding mills, the secondary mill reference speed is first ramped, and as the final target is reached, the primary mill reference speed is ready to be ramped. For simplicity, setpoint ramping will just be referred to as ramping, from now on.

5.2.1 Mill circuit start

Before the mill circuit is started, the active pump is controlling tank level against a small water addition. When the mill circuit is started, the secondary mill speed is first ramped. This empties the secondary mill, unless the ramping of primary mill is very well timed. When the primary mill is ramped, and if the primary mill ore feed is not activated yet, it is possible that the primary mill gets emptied as well.

Mill circuit starts may lead to a more complex flow sequence during a start of the grinding line than during a pump switch. The flow magnitude and character at a mill circuit start seems to vary a lot from time to time, as it is highly dependent on the amount of slurry inside the mills and on the control of the mills.

The density in the system is increasing in a way that is quite complicated to predict. A lower density in the system means that a lower power is required to produce a certain flow rate, and therefore too aggressive tuning of the power controller could be particularly risky for mill circuit starts.

From trend data it seems like mill circuit starts typically does not lead to flooding, but apparantly in some cases the level goes above 100 %. It seems like the inflow magnitude goes to approximately 2000 m³/h in these cases, but this is varying a lot. An example of a start of the secondary mill can be seen in AppendixB.

5.2.2 Switching pumps

When switching between pumps, the inflow magnitude does not differ from a steady state situation, but the valve control must instead be considered. During a planned pump switch, it is possible to control the distribution box valves to split the inflow between the two tanks, before the backup tank takes over the inflow completely. If the primary pump is interlocked and an unplanned pump switch is required, the distribution box should be able to distribute all of the flow into the backup tank immediately.

The two pump switch situations are however very similar from a control perspective, and the main difference is that an unplanned switch should cause a much larger sudden inflow to the backup tank as it is not possible to utilize both pumps for a while and split the inflow. Based on trend data, it seems like during a planned switch the flow is distributed to reach approximately 2000 m³/h in some cases when the level reaches 100 %. An example of a planned switch can be seen in AppendixC.

Modeling and control of mill discharge pumps in the Aitik copper mine