Multivariable Control and Energy Optimization of Tissue Machines

T87 Multivariable Control and Energy Optimization of Tissue Machines By S. Chu, R. MacHattie and J. Backström Abstract: The desire to increase profits by minimizing operating costs without sacrificing paper quality and runnability is a goal all papermakers strive for. Modern tissue machines are typically equipped with more than twenty low-level control loops and multiple sheet property measurements at various locations along the machine. It is a large and strongly coupled process that can be difficult for control engineers to optimize without advanced multivariable control techniques. This paper examines the process interactions and energy cost reductions using model predictive control (MPC) technology with an optimization layer that automatically drives the process towards the lowest cost while honoring hard process and quality constraints. The studied paper machine was equipped with a fast scanning moisture measurement before the Yankee dryer in addition to the measurements of a traditional reel scanner. raditional and through-air dried T (TAD) tissue manufacturing expends more resources removing water than any other function. Knowing the water content throughout the process and the efficiencies of the various water removal elements used, allows an advanced control system to control the process in the most economical manner. The studied paper machine was equipped with an ExPress Moisture scanner measurement [1] before the Yankee dryer in addition to the measurements of a traditional reel scanner. With these measurements along with advanced multivariable control, the economic efficiencies of each drying element and the optimization layer, it was shown that the advanced control system distributed the drying load such that significant economic benefits were realized. Several trials were run with different energy costs. It is given that energy costs change with time, so the cost of energy is updated in the advanced control system periodically, which can have a big impact on how the tissue machine is optimized. In all trials, the more expensive manipulated variables (MVs) were driven down to their lower operating cost limits and the cheaper MVs were driven to their higher operating cost limits. Significant energy cost savings were realized without sacrificing paper quality and machine runability. MACHINE OVERVIEW The paper machine studied uses two TADs and a Yankee dryer to dewater the tissue (Fig. 1). A traditional reel scanner measuring Dry Weight and Reel Moisture along with an ExPress Moisture scanner (located after TAD2) measuring TAD Moisture are the on-line measurements available. Before the optimization trials, the machine direction (MD) controls were multivariable but only Stock Flow and TAD2 exhaust temperature were used in cascade control. The setpoints for the rest of the manipulated variables (MVs) were fixed based on operator experience and previous operating conditions. A new multivariable control strategy was devised to take advantage of the economic optimization layer in the multivariable MPC. The control strategy was based on customer requirements, a benefit analysis of MPC MD controls [3], and a case study that was published [2]. Several new MVs were added to the control strategy with process upper and lower limits. The MVs added were Supply Temperature ( Supply Temp), dry end differential pressure ( DE DP), gap pressure ( Gap Pres), TAD2 dry end differential pressure (TAD2 DE DP) and TAD2 gap pressure (TAD2 Gap Pres). Furthermore, Machine Speed and Tickler Refiner were added as disturbance variables (DVs) to the control strategy. These provide feedforward information to MVs such that disturbances will be minimized before their impact on the controlled variables (CVs) is measured. Figure 1 shows the relative locations of the MVs and CVs and Fig. 2 shows the control matrix. Bump tests were performed to determine the transfer functions between the MVs and CVs. EXPRESS MOISTURE MEASUREMENT - TAD MEASUREMENT For moisture, traditional tissue machine MD controls almost always include controlling the S. Chu, R. MacHattie, J. Backström, 30 Pulp & Paper Canada November/December 2010 pulpandpapercanada.com

PEER REVIEWED T88 reel moisture only (i.e. the final product moisture). However, the final moisture is controlled by many elements far up the machine where the moisture levels are different, and there are drying elements between those locations and the reel that can further change the moisture [4]. The various drying elements that can manipulate moisture also have varying efficiencies and costs. These costs change with time. It has long been understood that better control will lead to better quality and cost performance and this can be achieved by measuring the moisture further up the machine, but this has not been practical, until recently [5]. With the ExPress Moisture scanner located after TAD2, moisture can now be measured upstream of the reel and closer to the critical drying elements. Combining this new direct moisture measurement with the reel moisture measurement via the Profit multivariable MPC along with the economic efficiencies of these various drying elements then makes it possible to truly optimize the energy consumption of the machine, since the control has direct feedback of process changes and true moisture levels going into various machine sections. As the cost of different energy forms change, the Profit controller with the optimization layer will automatically adjust and attain the lowest possible operating cost while maintaining the product quality. TAD REGULATORY CONTROL LOOPS Each TAD has several regulatory control loops that can affect TAD Moisture and Reel Moisture. The regulatory control loops have different efficiencies and costs because of the various forms of energy that each consumes. The temperature control loops consume natural gas and the pressure control loops consume electricity. By adding the temperature and pressure loops in the control strategy along with associating costs and defining upper and lower limits with each loop, the Profit multivariable MPC with the economic optimization layer can distribute the drying load in the TADs to minimize costs while not upsetting quality (i.e. maintaining TAD Moisture and Reel Moisture). Table I shows the TAD loops that affect the TAD Moisture and Reel Moisture. FIG. 1. Paper machine overview with Profit multivariable MPC. Dry Weight Reel Moisture TAD Moisture Exhaust Pressure Stock Flow Supply Temp DE DP TAD2 Exh TAD2 DE Gap Pres Temp DP LINEAR OBJECTIVE COEFFICIENTS The linear objective coefficients are parameters in the objective function of the optimization layer. The general form of the objective function is eq. 1: Minimize J = j b j MV j (1) TAD2 Gap Pres rofit Multivariable MPC Control Matrix FIG. 2. Profit multivariable MPC control matrix. Yankee Hood Temp Yankee Supply Fan Speed Machine Speed Stock Flow Gap Pressure Tickler Refiner table i. TAD Regulatory Loops with Linear Objective ficients MV Energy Fuel Units Linear Obj Cost/Eng Unit Supply Temp Gas deg F 0.680 DE DP Electricity Inch H 2 O 47.267 Gap Pres Electricity Inch H 2 O -0.030 TAD2 Exh Temp Gas Deg F 5.858 TAD2 DE DP Electricity Inch H 2 O 40.249 TAD2 Gap Pres Electricity Inch H 2 O -16.415 MV Energy Fuel Units Linear Obj Cost/Eng Unit Supply Temp Gas deg F 0.680 DE DP Electricity Inch H 2 O 47.267 Gap Pres Electricity Inch H 2 O -0.030 TAD2 Exh Temp Gas Deg F 5.858 TAD2 DE DP Electricity Inch H 2 O 40.249 TAD2 Gap Pres Electricity Inch H 2 O -16.415 where are the linear objective coefficients for the MVs representing the energy cost per engineering unit of the MVs. Bump tests were performed to determine the linear objective coefficients for each MV used in the Optimizer. Table I shows the linear objective coefficients for the MVs used in the Profit multivariable MPC with the optimization layer. pulpandpapercanada.com November/December 2010 Pulp & Paper Canada 31

T89 Table II. MV Cost Ranking - Trial 1. Gain (Cost/% Optimization MV Energy Unit Low Limit High Limit Cost/Eng Unit (%Moi/Eng Unit) Moi) Rank Behavior Supply Temp Deg F 300.0 450.0 0.68-0.12 5.48 4 450 (max) DE DP Inch H 2 O 1.0 3.9 47.30-5.12 9.24 3 Controlling Moi Gap Pres Inch H 2 O 0.4 1.5-0.03 1.95 0.02 6 0.4 (max) TAD2 Exh Temp Deg F 175.0 250.0 5.86-0.45 13.02 1 175 (min) TAD2 DE DP Inch H 2 O 1.0 3.5 40.26-3.14 12.82 2 1 (min) TAD2 Gap Pres Inch H 2 O 0.2 1.5-16.40 4.25 3.86 5 0.2 (max) Fig. 3. TAD natural gas costs and electrical costs- Trial 1. Fig. 4. Total costs - Trial 1. Fig. 5. manipulated variables - Trial 1. Fig. 6. TAD2 manipulated variables - Trial 1. ECONOMIC OPTIMIZER - TRIAL 1 A trial was performed with the economic optimization layer turned on with the linear objective coefficients that are shown in Table I. To rank the cost of each MV, the linear objective coefficients must be converted to a relative cost in common units of Cost /% Moi. This can be accomplished by taking the linear objective coefficients and dividing by their respective process gains. Table II shows each MV along with their respective linear objective coefficients, process gains and cost rankings. The trial sequence was as follows: - Baseline data was collected between 8:30-9:30. o 100.0 relative cost units of energy. See Fig. 4. - Attempted to put optimizer on control between 9:30-10:44. Some windup errors were encountered with some MVs on the DCS that prevented the Profit controller from optimizing. This caused some abnormal behavior and hence higher energy costs. - 10:44-12:30 - all windup errors were cleared and optimizer on o TAD2 Exh Temp (rank 1) is driven to its lowest cost operating limit (175 deg F). See Fig. 6. o TAD2 DE DP (rank 2) is driven to its lowest cost operating limit (1.0 inch H2O). See Fig. 6. o To keep the Moisture the same, Sup Temp (rank 4), TAD2 Gap Pres (rank 5) and Gap Pres (rank 6) are driven to their maximum operating limits (450 deg F, 0.2 and 0.4 inch H2O respectively). These are the low cost MVs. See Figs. 5 and 6. 32 Pulp & Paper Canada November/December 2010 pulpandpapercanada.com

Figure 10: Manipulated Variables Trial 2 Table III. MV cost ranking - Trial 2. 5:00) = 99.4 relative cost units of energy, see Figure 9. The energy cost reduction Gain was 0.6%. (Cost/% Optimization MV Energy Unit Low Limit High Limit Cost/eng unit (%Moi/eng unit) Moi) Rank Behavior Supply Temp Deg F 300.0 450.0 1.41-0.12 11.40 2 Controlling Moi DE DP Inch H 2 O 1.0 3.7 55.64-5.12 10.86 3 3.7 (max) Gain (Cost/% Gap Pres Inch H 2 O 0.4 1.5-5.43 MV eng unit Low 1.95 Limit High Limit (Cost/eng 2.78 unit) (%Moi/eng unit) 6 Moi) 0.4 Rank (max) Behavior TAD2 Exh Temp Deg F 175.0 250.0 10.40 DE DP inch H2O -0.45 1.0 3.7 55.64 23.11-5.12 1 10.86 175 3 (min) 3.7 (max) Gap Prs inch H2O 0.4 1.5-5.43 1.95 2.78 6 0.4 (max) TAD2 DE DP Inch H 2 O 1.0 2.9 28.01 TAD2 Exh Temp deg F 175.0-3.14 250.0 10.40 8.92-0.45 4 23.11 2.9 1 (max) 175 (min) TAD2 DE DP inch H2O 1.0 2.9 28.01-3.14 8.92 4 2.9 (max) TAD2 Gap o Pres 100.0 relative Inch H 2 cost O units 0.2 of energy. 1.5 See -24.97 TAD2 Gap Prs inch H2O 0.2 4.25 1.5-24.97 5.88 4.25 5 5.88 0.2 5 (max) 0.2 (max) Figure 9. - The Optimizer was turned on at 3:25. Natural gas Controlled Variables usage decreased and electrical usage increased. See 12.7 25 Figure 8. 12.6 o Some sheet breaks and machine upsets were 12.5 20 encountered during the trial between 3:35 12.4 4:25. 12.3 15 12.2 o Machine settles down to steady state 12.1 conditions after 4:25. 10 12 o TAD2 Exh Temp (rank 1) is driven to its 11.9 lowest cost operating limit (175 deg F). See 5 11.8 Figure 11. 11.7 ReelDwt PV ReelMoi PV ExpressMoi PV o To offset the low TAD2 Exh Temp (rank 1), 11.6 0 DE DP (rank 3), TAD2 DE DP (rank Figure 9: Total Costs Trial 2 4), TAD2 Gap Pres (rank Time 5), and Gap Pres (rank 6) are driven to their maximum Figure Fig. 7. 7: CVs CVs undisturbed - Trial Trial 1. 1 Figure Fig. 8: 8. TAD natural Natural gas Gas costs Costs and and electrical Electrical costs Costs - Trial 2. operating limits (3.7, 2.9, 0.2 and 0.4 inch Trial 2 H 2 O respectively) to help dry the sheet. ECONOMIC These OPTIMIZER are the low cost TRIAL MVs. 2 See Figures 10 Since the energy and 11. costs change with time, the cost of energy is updated o in the control Sup system Temp periodically, (rank 2) is which within can its have a big impact operating on how the limits machine and therefore is optimized. performing Trial 2 shows that even though TAD Moisture different MVs and Reel were manipulated Moisture control. to minimize energy costs, See all Figure CVs remained 10. undisturbed. Throughout Natural the gas trial costs (3:00 varied 5:00) greatly all CVs in (Reel 2008. Dry The Weight, peak of the Reel Moisture natural gas and cost TAD was Moisture) in the summer were undisturbed, of 2008 and see it was Figure approximately 12. double the cost in trial 1. Trial 2 was performed Total energy with the costs cost during of natural steady gas state close optimization to its peak. (4:25 With the 5:00) = increased 99.4 relative price cost of units natural of gas, energy, the see natural Figure gas 9. costs The were energy higher cost reduction than the was electrical 0.6%. costs. This is reflected during this trial as natural gas usage decreased as electrical usage increased (Figure 8). Table 3 shows each MV along with their Table 3: respective MV Cost linear Ranking objective Trial coefficients, 2 process gains and cost Figure Fig. 9. rankings. 9: Total costs As expected, Costs - Trial Trial 2. TAD2 2 exhaust temperature and Figure Fig. 10: 10. Manipulated manipulated variables Variables - Trial Trial 2. 2 Gain (Cost/% Optimization MV supply eng unit temperature Low Limit High Limit are ranked 1 and 2 respectively since both MVs o consume DE natural DP (Cost/eng gas. (rank unit) (%Moi/eng unit) 3) is within Moi) Rank ECONOMIC Behavior Supply Temp deg F 300.0 450.0 1.41-0.12 11.40 2 controlling Moi DE DP inch H2O 1.0 3.7 55.64-5.12 10.86 3 3.7 (max) OPTIMIZER - TRIAL 2 price of natural gas, the natural gas costs Gap Prs inch H2O 0.4 1.5-5.43 1.95 2.78 6 0.4 (max) TAD2 Exh Temp The limits deg F trial sequence and 175.0 controlling 250.0 10.40 was as follows: Reel Moisture -0.45 23.11 Since 1 the 175 (min) energy costs change with time, were higher than the electrical costs. This TAD2 DE DP inch H2O 1.0 2.9 28.01-3.14 8.92 4 2.9 (max) TAD2 Gap Prs and inch H2O TAD 0.2 Moisture. 1.5 See -24.97 Fig. 5. 4.25 5.88 the 5 cost 0.2 of (max) energy is updated in the control is reflected during this trial as natural - Baseline data was collected between 3:00 3:24. Throughout the trial (8:30-12:20) all system periodically, which can have a big gas usage decreased as electrical usage CVs (Reel Dry Weight, Reel Moisture impact on how the machine is optimized. increased (Fig. 8). Table III shows each 4 and Express Moisture) were undisturbed, Trial 2 shows that even though different MV along with their respective linear see Fig. 7. MVs were manipulated to minimize energy costs, all CVs remained undisturbed. cost rankings. As expected, TAD2 exhaust objective coefficients, process gains and 98.8 relative cost units of energy is achieved while the Energy Optimizer is Natural gas costs varied greatly in 2008. temperature and supply temperature are ranked 1 and 2 respectively since on, i.e. a 1.2% energy saving, see Fig. 4. The peak of the natural gas cost was in the In this trial, the cost of natural gas is summer of 2008 and it was approximately both MVs consume natural gas. less than electricity. Natural gas usage double the cost in Trial 1. Trial 2 was The trial sequence was as follows: increased and electricity usage decreased, performed with the cost of natural gas - Baseline data was collected between see Fig. 3. at close to its peak. With the increased 3:00-3:24. DW (lb/ream) 8:34:07 8:40:34 8:47:01 8:53:28 8:59:55 9:06:22 9:12:49 9:19:16 9:25:43 9:32:10 9:38:37 9:45:04 9:51:31 9:57:58 10:04:25 10:10:52 10:17:19 10:23:46 10:30:13 10:36:40 10:43:07 10:49:34 10:56:01 11:02:28 11:08:55 11:15:22 11:21:49 11:28:16 11:34:43 11:41:10 11:47:37 11:54:04 12:00:31 12:06:58 12:13:25 12:19:52 Moisture (%) Throughout the trial (3:00 5:00) all CVs (Reel Dry Weight, Reel Moisture and TAD Moisture) were PEER undisturbed, REVIEWED see Figure 12. Total energy costs during steady state optimization (4:25 Table 3: MV Cost Ranking Trial 2 Optimization Supply Temp deg F 300.0 450.0 1.41-0.12 11.40 2 controlling Moi T90 Fi Fi 5 pulpandpapercanada.com November/December 2010 Pulp & Paper Canada 33

T91 Fig. 11. TAD2 manipulated variables - Trial 2. Fig. 12. CVs undisturbed - Trial 2. o 100.0 relative cost units of energy. See Fig. 9. - The Optimizer was turned on at 3:25. Natural gas usage decreased and electrical usage increased. See Fig. 8. o Some sheet breaks and machine upsets were encountered during the trial between 3:35-4:25. o Machine settles down to steady state conditions after 4:25. o TAD2 Exh Temp (rank 1) is driven to its lowest cost operating limit (175 deg F). See Fig. 11. o To offset the low TAD2 Exh Temp (rank 1), DE DP (rank 3), TAD2 DE DP (rank 4), TAD2 Gap Pres (rank 5), and Gap Pres (rank 6) are driven to their maximum operating limits (3.7, 2.9, 0.2 and 0.4 inch H 2 O respectively) to help dry the sheet. These are the low cost MVs. See Figs. 10 and 11. o Sup Temp (rank 2) is within its operating limits and therefore performing TAD Moisture and Reel Moisture control. See Fig. 10. Throughout the trial (3:00-5:00) all CVs (Reel Dry Weight, Reel Moisture and TAD Moisture) were undisturbed, see Fig. 12. Total energy costs during steady state optimization (4:25-5:00) = 99.4 relative cost units of energy, see Fig. 9. The energy cost reduction was 0.6%. CONCLUSION New sensor technology now permits the placement of high precision moisture measurements at almost any location between the press and reel on tissue machines. This technology is well proven and reliable enough for continuous control, providing positive results for producers globally. When combined with multivariable control, it produces consistent drying along the length of the machine, increasing product quality and reducing manufacturing costs. With the addition of energy costs, the system is able to optimize the machine to stay within product quality requirements, while running at the lowest possible energy costs, balancing various energy forms and their associated costs as well as product quality. A 1.2% energy cost reduction was achieved with the energy optimization layer enabled. LITERATURE 1. F. Haran, R. Beselt, R. MacHattie, Embedded High-speed Solid State Optic Sensor, Pulp & Paper Canada, 108:12, pp.57-60 (2007). 2. J.U. Backström, P. Baker, A Benefit Analysis of Model Predictive Machine Directional Control of Paper Machines, Proceedings from 2008 Control Systems/Pan Pacific Conference, June 16-18, Vancouver, BC, Canada, pp. 197-202 (2008). 3. S. Chu, Wet End Control Applications using a Multivariable Model Predictive Control Strategy, Proceedings from PACWEST 2008, June 18-21, Jasper, AB, Canada, (2008). 4. T. Steele, R. MacHattie, A. Paavola, B. Vyse, Tissue & Towel Quality Measurement & Control Advances, Presentation from Tissue World America 2008 Conference, March 11-14, Miami, FL (2008). 5. P. Baker, R. MacHattie, B. Vyse, Early Measurement and Control of Paper Machine Moisture, Proceedings from 2008 Control Systems/Pan Pacific Conference, June 16-18, Vancouver, BC, Canada, pp. 105-110 (2008). Résumé: Les fabricants de papier visent tous à accroître leurs profits en réduisant les coûts d exploitation, mais sans sacrifier la qualité du papier et l aptitude au passage sur machine. Les machines à papier mince modernes sont en général dotées de plus de vingt boucles de régulation de faible niveau et de multiples éléments permettant de mesurer les propriétés de la feuille à divers endroits le long de la machine. C est un vaste procédé compliqué en raison de son important couplage et les préposés aux services techniques le trouvent difficile à optimiser sans avoir recours à des techniques de régulation multivariables perfectionnées. La présente communication évalue les interactions du procédé et les réductions du coût de l énergie possibles à l aide d un modèle prévisionnel de commande avec un module d optimisation qui entraîne le processus automatiquement vers le coût le plus bas, tout en tenant compte de la nature du processus et des contraintes de qualité. La machine à papier à l étude était dotée d un appareil de mesure de la teneur en eau à balayage rapide installé avant la sécherie monocylindrique (Yankee), en plus des mesures prises à l aide d un scanner classique à l enrouleuse. Reference: Chu, S., MacHattie, R., Backström, J. Multivariable Control and Energy Optimization of Tissue Machines. Pulp & Paper Canada 111(6): T87-T91 (Nov/Dec 2010). Paper presented at PacWest 2009, June 10-13, 2009 in Sun Peaks, B.C. and Control Systems 2010, Sept. 15-17, in Stockholm, Sweden. Not to be reproduced without permission of PAPTAC. Manuscript received January 01, 2009. Revised manuscript approved for publication by the Review Panel July 12, 2010. Keywords: Multivariable Control; Model Predictive Control (MPC) technology; Machine Direction (MD); Control; Energy Optimization; Economic Optimization; Tissue Machines; Maximizing Profit; Express Moisture Sensor; Moisture Control; Yankee Dryer Control; Through Air Dryer (TAD) Control. 34 Pulp & Paper Canada November/December 2010 pulpandpapercanada.com