Application of Soft Sensors, Dynamic Simulation and Model Based Control to Digestion Charge Control
John Gorst, Process Modeling Engineer (email@example.com)
Terry Snow, Advanced Control Engineer (firstname.lastname@example.org)
Nabalco Pty. Ltd
P.O. Box 21, Nhulunbuy N.T.
On-line measurement of Liquor Conductivity has been successfully used in numerous Alumina Refineries to provide improved control of the molar ratio (MR) of liquors leaving digestion (DIS). Further improvements in Charge Control have been made at the Gove Refinery using techniques such as soft sensors and model based control. This paper describes the successful development and implementation of a model based control strategy and an Operator Decision Support scheme for Digestion Charge Control. The applications make extensive use of various forms of soft sensors and explicitly incorporate process dynamics in internal models.
The soft sensors, using Recursive Least Square (RLS) and Kalman Filter estimators, perform three distinct functions; continuous calibration of the conductivity instrument, reconciliation of a dynamic mass balance, and the continuous inferred measurement of Digestion Feed Soda from on-line density measurements. The Operator Decision Support system uses the soft sensors to provide continuous predictions of the DIS MR, complementing the 2 hourly Laboratory analysis. The Control Application uses the soft sensors to perform feed forward control and Internal Model Control on a continuously calibrated conductivity instrument.
Considerable quality assurance was provided on the control application with the use of dynamic simulation and advanced control rapid prototyping tools. A high fidelity phenomenological dynamic simulation of the process and control system was developed and used to tune and evaluate candidate control strategies. The advanced control prototype was trialled on the simulation before being placed on-line. The Digestion process was perturbed with a multi-input pseudo random binary sequence to calibrate the process model. The extracted dynamics of the process were inherently incorporated into the soft sensors and model based control strategy.
The operator decision support has been on-line since December 1997 and the control scheme has been on-line since July 1998. These systems resulted in reduced variations in DIS MR.
alumina, charge control, soft sensors, modelling.
Application of Soft Sensors, Dynamic Simulation and Model Based Control to Digestion Charge Control
John Gorst and Terry Snow
The Molar Ratio (MR = Na2O/Al2O3) of the liquor exiting the digestors (DIS) is one of the principal control parameters in the Bayer Circuit. The control is achieved by charging the appropriate amount of bauxite into the circuit given the current process conditions. Bauxite quality, liquor concentrations, extraction efficiency are some of the factors that affect what the appropriate amount of bauxite may be. Both under charging and over charging bauxite reduce plant productivity. The production penalty for over charge can be much more costly than under charge so conservative charge targets tend to be set.
Like many other Alumina Plants (Langa , Chin  and McIntosh ), the ability to control DIS MR at the Gove Plant was significantly improved with the installation of a conductivity instrument to provide a continuously measured value for feedback control. A conductivity based feed back control scheme has been operational since 1992. This scheme enabled the setting of considerably more aggressive charge targets than were previously possible. Charge targets were progressively made more aggressive until a spate of over charge incidents signalled the controllable limit of that scheme had been reached. A new control scheme was sought to take the plant to the next level of stable, aggressive DIS MR Control.
A systematic approach to controller design resulting in the effective implementation of an advanced charge control system has been described. The approach involved a series of key stages
A process flow-sheet for the digestion section of the Gove refinery is shown in Figure 1. Bauxite from a set of blended stockpiles is introduced to a combination rod/ball mill via a weigh-belt. To facilitate grinding, a portion of the Strong Feed Liquor (SFL) refered to as Mill Liquor (ML) is also fed to the mills. The ground mill slurry (MIS) is then passed to a relay tank where it is heated with contact steam before being fed to the digestion train. The stream from the relay tank is known as the Injection Flow and the ratio of Injection Flow to the liquor flow is known as Injection Ratio.
The digestion train consists of six digestors in series of which commonly 5 are online. These are sparged with 12 ATA steam to maintain the reaction temperature in the face of the highly endothermic dissolution reaction. The slurry exiting the digestors is then fed to 3 flash vessels in series to reduce pressure and recover heat. It is then diluted with weak liquor before being fed to the blow-off tank and thence on to the de-sanding process. The digestor vessels consist of a number of compartments, which are individually agitated.
The bauxite is analysed daily for alumina content, silica etc. Even though the stockpile is blended, disturbances to the control system can occur with changes in moisture content, particularly during the wet season. Step changes in bauxite quality also occur when the reclaimers change stockpiles.
Cleaning liquor from the Precipitator descaling process is stored in a 4500 m3 tank. This is periodically fed to the relay tanks. The flow of Cleaning Liquor is variable and dependent on Liquor inventory. The concentration of the Cleaning Liquor can vary considerably. The relay tanks are also fed with an un-metered flow from the Mill area sumps. These sumps collect hose water and Mill overflow and other slurry spills.
The Evaporation Area concentrates the Spent Liquor from Precipitation to become SFL, which is stored in 2000 m3 surge tanks buffering the feed to Digestion. SFL flow is normally stable but step changes of 5 to 10% are not uncommon. SFL concentration can vary depending on evaporation rates and precipitation conditions. Fresh Caustic (FC) makeup is periodically introduced to the SFL stream during periods of refinery inventory generation.
Process control is achieved via Baileys Infi 90 Distributed Control System (DCS). Process monitoring is available via OSIs PI process information database. The previous control scheme consisted of a Conductivity feed back controller with output cascaded to a ratio controller that sets the injection flow as a ratio of the SFL flow. The conductivity is measured using a Rosemount Toroidal device situated at the exit of the first digestor. A level controller on the relay tank adjusts the flow of Bauxite on the weigh-belt. A ratio controller maintains a constant ratio between the bauxite weigh-belt reading and the Mill Liquor flow.
Control of the process is monitored with regular Laboratory analyses. Digestion Slurry (DIS) is sampled from the bottom of the 3rd flash vessel just prior to the introduction of dilution liquor every two hours and analysed by Thermal Titration (TT) to determine the soda (as Na2O) and alumina (as Al2O3) concentrations. SFL soda and alumina concentrations are determined in the same way every 2 hours. SFL is sampled prior to the pumps following injection of fresh caustic soda. The Cleaning Liquor (CL) from precipitation is sampled every 12 hours.
2.1 The Strategy for the New System
Maintaining constant DIS conductivity has been a successful strategy due to the strong relationship between conductivity and MR. However, this relationship is not constant. Large changes in liquor soda concentrations are known to affect the relationship and the instrument itself was known to drift with scaling. Occasionally the flushing of the instrument resulted in an abrupt conductivity step change after the flushing was completed. This makes it difficult to determine an accurate conductivity set point . Adjusting this based on the Laboratory samples introduces considerable dead-times to the control system. Added to this, the instability of the liquor produces spurious Laboratory results, which are often interpreted as undercharges leading to unnecessary conductivity set point changes.
Reviewing the previous control strategy revealed a number of aspects that had significant potential to improve charge control.
Putting these symptoms into a control solution, it was evident that we required a more sophisticated feed forward controller to reject feed disturbances and to provide improved control in the absence of the conductivity instrument. We also needed to directly target DIS MR by closing the loop between the (outer) DIS MR target variable and the (inner) conductivity controller. If the operators were confident that an aggressive control scheme was not placing the process at risk, they would not intervene. Operator confidence could be greatly improved by providing a more frequent and accurate indication of their primary control variable, the DIS MR.
3.0 DYNAMIC MODEL OF THE PROCESS
3.1 Process Dynamics
An accurate dynamic model is the foundation for all aspects of the project; dynamic simulation, soft-sensors and control strategy. A reasonable structure for the digestion dynamics was formulated and then a set of System Identification Experiments were designed, conducted and analysed to establish the process dynamics, and to provide a data set for calibration of a dynamic simulation.
There were four sets of dynamics that were of interest to us
In good modelling practice we simplified the model structure as follows:
3.2 System Identification Experiment
Two trials were conducted on both Stage 1 and Stage 2 of the Gove refinery to determine the process dynamics. To maximize information content, the process was peturbed by a Pseudo Random Binary Sequence (PRBS) of injection ratio changes and fresh caustic addition to the SFL. The trials were run for 12 hours with the period of the PRBS signal being 20 minutes.
Samples of the DIS were taken from the exit of the 3rd flash vessel at 20 minute intervals. These were centrifuged and analyzed by TT. The response of the conductivity meter was logged on the plants PI system. A small time difference existing between the Bailey and the PI system was noted and all other timing was synchronized with the Bailey system.
The input and output trends of the Stage I trial are shown in Figures 2a and 2b. As can be seen the process fluctuations resulted in a significant variation of the DIS MR values over the course of the trial. The trial was analyzed with the System Identification Toolbox of Matlab. A number of input/output relationships were examined, of particular interest was the conductivity / DIS MR relationship due to its impact on the soft sensor and controller designs.
The System ID Toolbox was used to perform a fit of the data to the following ARX model.
Here x is the conductivity reading and y is the DIS MR. The term nk is the dead-time in equivalent timesteps and the terms na and nb are the auto-regressive and moving average orders of the model respectively. For our purpose nb was set at one and the System ID toolbox was used to search for the best value of the parameter na as well as the weights a and b. In effect the value of na is the number of mixing effects in the system. The results of this exercise showed a significant improvement in increasing the order from 1 to 3. From 3 to 4 there was a slight improvement with little else to be gained from further increases. This is consistent with the argument proposed in the previous section for using 3 mixing effects.
Figure 2a Figure 2b
Input and Output trends for Stage 1 Trial
The model generated from the System ID acts as a filter. By passing the conductivity data through the filter, the direct conductivity/ MR relationship was able to be established. Results show that the correlation between DIS MR and conductivity improves greatly by filtering the conductivity in this way.
The information gained from these trials was used to assist in the design of the digestion soft sensors, calibrate the dynamic simulation, and design the model based control strategy.
4.0 SOFT SENSOR DESIGN AND IMPLEMENTATION
4.1 Kalman Filter
In simple terms, a Kalman filter is a dynamic model based data reconciliation technique. In accordance with the results of the System identification trial a Kalman filter was designed based on a model incorporating a steady state reaction followed by a series of 4 CSTRs (mixing vessels) with no reaction. A state vector was developed consisting of the exit concentrations of Soda and Alumina from each of these vessels. At 5 minute intervals the state is propagated in time using the dynamic mass balance. The exit concentrations of the last vessel serve as a prediction of the DIS Soda and DIS Alumina. At 2 hourly intervals the states are updated by laboratory measurements. The DIS molar ratio is determined directly from the soda and alumina estimates.
Comparison of kalman filter predictions against data from the Stage 1 system identification trial
It has been seen in practice that a systemic offset between the calculated DIS MR result and the Laboratory value develops. While an update of the states will account for this bias, between updates, the states will be effectively corrupted by the bad input. To account for this we introduce a phantom stream which appears as a state. This stream corrects for errors that may develop in the SFL flow meters or Bauxite weigh-belts. The only assumption we can make about the dynamics is that, being a systemic error, it is constant i.e the derivative is zero.
The performance of the Kalman filter is shown in Figure 3. In this figure, Kalman filter predictions are trended against the DIS MR measurements taken during the first system I.D. trial. To generate this data, the Kalman filter was allowed to run in for five days prior to and over the day of the trial. It should be stressed that during the trial, the regular 2 hourly samples were taken in addition to the trial specific 20 minute samples. It is these 2 hourly measurements that were used to update the Kalman filter states in Figure 3. Thus Figure 3 gives an indication of the performance expected when in normal operation. A comparison of the Kalman filter prediction in other trials gave comparable results.
4.2 Conductivity Soft-sensor
The results of the system ID trials showed that the correlation between DIS MR and conductivity can be improved greatly if the conductivity is passed through a filter representing the process dynamics. Such a soft sensor was implemented using the model given in Equation 2. In this expression y is the DIS MR and m is the conductivity passed through the auto-regresssive model determined from the system ID trial. A Recursive Least Squares (RLS) algorithm is used to determine the coefficients b1, b0
The performance of this soft sensor is shown in Figure 4. As with the Kalman filter, the soft sensor has been allowed to run for 5 days, including the day of the system ID trial, at the end of which its predictions are compared with the trial data. As can be seen the dynamics of the signal match that of the trial data but the amplitude of the response is under-predicted. This is a result of underestimating the slope of the relationship or parameter b1 in Equation 2 . This underestimation is a consequence of trying to fit the parameter while in closed loop control. Normally when trying to fit a linear relationship of the type shown in Equation 2, a large range of conductivity and DIS MR values would be desirable (as was achieved during the system ID trial). However in closed loop control the intention is to reduce the range, to a single point if possible. As would be expected, slope estimates from a single data point are very unreliable.
Given that the conductivity soft sensor tends to underpredict the slope of the MR conductivity relation, it was proposed that if the slope could be guaranteed to remain constant, a fixed slope could be used and RLS algorithm used to provide updated estimates of the intercept. The soft sensor then becomes effectively a bias estimator.
Figure 4 Figure 5
Conductivity soft sensor and Bias estimator soft sensor output vs data from Stage 1 system identification trial
A comparison of the system ID trials and data taken 18 months prior to these trials indicated that the slope does indeed remain constant. As a result, the conductivity soft sensor was altered to the following form.
The slope, m, was taken from the system identification trial and the RLS algorithm was used to estimate the bias b0. As before, the performance was tested by comparison with the trial data. This is shown in Figure 5 and as expected a clear improvement is evident.
5.0 CONTROL SYSTEM DESIGN, SIMULATION AND EVALUATION
5.1 Simulation Formulation
A dynamic simulation of the digestion train was produced using Matlab/Simulink. Simulinks standard functionality was considerably enhanced by the inclusion of customised (Sfunction) unit operations written in C++. The simulation performs a heat and multi-component mass balance around the digestion train. The main dynamic elements of the model occur after the reaction where the DIS is passed through 3 mixed tanks to simulate the lags in the digestor and flash vessel trains. In actual fact, there are 15 + mixing effects in the system. However, as verified in the system ID trial, if the process volume is constant the effect of going beyond 3 mixing effects is small.
5.2 Control System Design
The control system proposed is described graphically in Figure 6. It involves two parts. A feed forward controller utilising a mass balance of the digestion system to determine required Bauxite charge. A feed back system on the conductivity meter reading provides a trim to the demanded bauxite flow.
The feed forward controller incorporates the phantom stream estimates of the mass balance Kalman filter to adjust for offsets in the feed forward demand. The feedback controller uses the bias estimate in the conductivity soft sensor to determine a suitable conductivity set point based on the DIS MR target.
5.3 Simulation Results
A comparison of the simulation results with System ID Trial is shown in Figure 7. For these simulations the system was placed in open loop as it was during the trial. For this data the actual flowrates of SFL, CL, FC and Bauxite that were logged during the trial were used as inputs to the model. Laboratory analyses of the SFL and CL streams were kept constant but typical of the values sampled on the day. As can be seen the agreement between the model and the trial data is excellent. Only slight tuning of the process lag volume was required to match the trial data. The major dynamic element that was identified during this trial was the existence of a 45 minute dead-time in the process.
Having verified the fidelity of the model, the new controller design was tested in simulation against the existing controller. The existing control system elements were added to the Simulink Model and the soft sensors were written as Matlab SFunctions for inclusion in the Simulink model. A Laboratory sample model was also developed. A number of scenarios were developed to simulate actual plant disturbances. Plant disturbances were divided into two categories, deterministic and stochastic. The object of the deterministic disturbances was to test the controller under known, common plant disturbance situations. The object of the stochastic disturbances was to evaluate the controller performance in response to typical random process behaviour.
During the stochastic simulations the controller was tested against random process disturbances. The SFL flowrate remained steady but Cleaning Liquor flows and SFL and CL concentrations were subject to random variations. These random variations were determined from appropriate input models that generated deviations with the same frequency content and statistics as that seen in plant data.
The Cleaning liquor flow rate was assumed to be either 0 or at maximum flow and the switches were assumed to be Poisson distributed. The input models for the concentration variations were generated by taking historical data from the PI archive and fitting appropriate auto-regressive models using Matlabs system identification toolbox. These models were then driven by white noise. Laboratory analysis errors were sampled from uniform distributions.
The stochastic simulations were run for 20 weeks. The output from the stochastic simulations is a distribution of achieved DIS molar ratios. A cost function was developed to address the question of the gain associated with tighter control. This is a plot of lost production vs DIS MR setpoint and accounts for the loss of production due to overcharging and the loss of opportunity due to undercharging. This curve is shown in Figure 8. Point A defines the optimum operating point and the tighter the control, the closer we are able to operate to this point. The cost of operating at a specific target using a particular controller can be determined by multiplying the resulting DIS MR distribution from the simulation by the cost function. If this is performed at every possible DIS MR target the effect is a convolution of the two curves. This then becomes controller based cost function and the minimum of this curve is the optimal operating point given that controller. The better the controller, the lower this minimum.
Figure 8 shows the new and existing controller cost functions compared with the base cost function, which essentially indicates perfect control (i.e. delta distribution of MR). The difference in the optimal points gives an indication of the production increase to be gained by adopting the new control strategy. This was performed for all the scenarios listed above with the result that the new controller was expected to increase production by 10000 t Al2O3 /yr in all cases.
Figure 7 Figure 8
Comparison of dynamic model against trial data
Cost Functions for various control schemes. Points A B and C refer to optimum charging points for perfect, new and existing controllers respectively
Having verified the performance of the new controller in simulation the next step was to implement the controller on a real time control system. This involved two stages, implementation in UNAC and implementation in the Bailey DCS.
UNAC is an advanced control rapid prototyping system developed by CICS Automation Ltd. It has a simulink style interface and a library of control element blocks similar to Bailey function codes. UNAC resides on a PC and is able to communicate to the Bailey system via a serial cable connected to a Serial Port Module (SPM). UNAC can read the output of any block in the PCU containing the SPM. It can also write to constant blocks using the same protocol as a Monitor Tune. These constant blocks may then be used as set points for the Bailey system itself.
To verify that the Simulink control system was ported accurately to the UNAC environment, the UNAC system was used to control the Simulink simulation over a period of two weeks. Although Simulink is not a real time system, a sleep block was developed that synchronised the simulation time with the PC clock time. A serial communication program was also written that communicated with the UNAC system using the Bailey protocol. The trials on the simulation verified that the calculations were performing as expected and that controller performance was equivalent to that seen under simulation.
The system was then attached to the Bailey system. UNAC read required plant data from the PCU and wrote injection ratio set points to a constant block. A slight modification was made to the existing CAD to allow the operator to select normal control or the UNAC injection ratio setpoint. A series of trials were then run to prove stability under steady operating conditions and to verify performance against known disturbances.
Having proved the stability and performance of the system in UNAC the controller was implemented in Bailey CAD. Using Baileys Wintools, this process took about two weeks. During the process some modifications were added to improve system. These included fast initialisation and reset of the soft sensors and operator selection of different controller modes on the feedback controller. The system was then downloaded to an offline system and run in parallel with the UNAC controller. Neither controller was in control but crucial outputs of each system were logged on the PI system and trended to check the calculations were identical.
At the time of writing, the controller has been online and in control for 1 month. It has been successful in stabilising the DIS MR during this period effectively tracking the drift in the conductivity meter. A plot of the weekly averages for the deviation (Set Point - Process Variable) in DIS MR over the last 18 months is shown in Figure 9. The data in this figure has been filtered using a 7 day moving average. On this time line is indicated the point at which the soft sensors were introduced as well as the time at which the new controller was placed online. There is a clear improvement in performance since the introduction of the soft sensors and a further improvement since the introduction of the new controller. It should be noted that the introduction of the new controller occurred during the dry season in the Northern Territory. Historically, this is a period of improved charge control and it is too early to be able to separate controller improvements from seasonal effects. However, a comparison with the same time period 12 months ago does indicate an apparent improvement.
DIS MR deviation from Set Point, Trended over two nine month periods showing introduction of soft sensor and new controller
A systematic approach to controller design resulting in the effective implementation of an advanced charge control system has been described. The approach involved a series of key stages.
The review of the current control system isolated the weaknesses and provided a strategy for the new controller design. The process dynamics were determined by a series of trials involving perturbing the process with a Pseudo Random Binary sequence of injection ratio and fresh caustic addition changes.
Soft sensors were designed based on the dynamic models produced from the system identification trials. These soft sensors used RLS and Kalman Filter estimators to perform continuous calibration of the conductivity instrument and reconciliation of a dynamic mass balance. The soft sensors were used as an Operator Decision Support system complementing the 2 hourly Laboratory analysis.
The new controller involved both feedforward and feedback elements. The feedforward system performed a mass balance over the digestion train using the Kalman filter soft sensor to provide estimates of the feed forward offset. The feed back element used the soft sensor to provide continuous calibration of the conductivity instrument.
Since implementation the controller has stabilised DIS MR in the face of large drifts in the conductivity instrument. The period following the controller implementation has seen the most stable DIS control in the past two years. However, the controller was implemented during the dry season and there is not enough data to date to be able separate seasonal effects from controller effects.
Langa, J.M. " A Diagnostic Expert System for Bayer Digestion Ratio Control", Light Metals 1989, pp 9 19
Chin, L.A.D " The State-Of-The-Art in Bayer Process Technology", Light Metals 1988, pp 49-53
McIntosh, P. " Optimum Control of Bauxite Charge to High Temperature Digestion Units at QAL", Light Metals 1984, pp 27-38