KRAFT CONTINUOUS DIGESTER EFFECTIVE ALKALI CONTROL

Transcription

1 KRAFT CONTINUOUS DIGESTER EFFECTIVE ALKALI CONTROL BILL GOUGH MEMBER IEEE Universal Dynamics Technologies Inc International Place Richmond, BC Canada V6V 2X8 JOHN T. KAY MEMBER IEEE Universal Dynamics Technologies Inc International Place Richmond, BC Canada V6V 2X8 Abstract - Optimal control of a continuous pulp digester is a difficult problem. The objective is to achieve maximum pulp production at a specified Kappa number with a minimum of chemicals and energy input. Existing Kappa number control strategies focus on H factor control. These strategies attempt to model the relationship between Kappa number, H factor, sulphidity, and Effective Alkali. Reducing the variability of Effective Alkali through closed loop control contributes to smoother digester operation and reduced Kappa number variation. However, closed loop control of Effective Alkali is a significant control problem due to the long dead time that exists between changes in white liquor flow and measured residual Effective Alkali. This paper describes the application of a predictive adaptive process controller that was able to provide closed loop control of Effective Alkali and resulted in reduced Kappa number variability. The controller used was based on Dynamic Modeling Technology (DMT) and an introduction to DMT is provided. Following this the test results and the justification to purchase are presented. I. INTRODUCTION TO DMT Dynamic Modeling Technology (DMT) is a new approach for modeling process transfer functions, which reduces the effort required to obtain accurate process models. DMT is able to automatically determine the structure of the transfer function model as well as the values of the model parameters using an unstructured approach based on orthonormal Laguerre functions. DMT provides several advantages compared to classical S-Plane (Laplace Transform) frequency response methods such as the ability to easily model high order behaviour and process dead time. Although improved process control is an economical method to optimize product quality and achieve lower production costs, the requirement to reduce the cost of material and human resources needed to implement advanced process control on real world applications is an important factor in the realization of these savings. The benefits of process transfer function modeling using DMT will be discussed. II. PROCESS MODELING The first step in applying an analytical approach to process control is to obtain a mathematical model of the process transfer function. Without a mathematical representation of the process response characteristics, only ad hoc and heuristic methods can be used to implement advanced controls resulting in uncertain control performance. It is essential that the process can be accurately modeled with minimum effort in order to achieve consistent, optimized performance in a manner that is both practical and cost effective. A. S-Plane Models Conventional process modeling methods are based on frequency response using S-Plane (Laplace Transform) techniques. These process models describe transfer functions in terms of time constants (poles and zeros), gain, damping factors, and dead time. In reality, industrial processes are of high order due to the combined response characteristics of the sensor, process equipment, actuator, and delay time. This complexity makes deriving a complete model of the overall process response a difficult task. For practical reasons, the model is typically reduced to a simple first order (one time constant) or second order (two time constants) plus dead time structure. The simplified models are then fitted to the actual process response using manual techniques such as estimating model parameters from process bump tests or mathematical methods such as cross-correlation or least squares data fitting. The simplified models do not include the higher order components of the process response in the model structure so the resulting model is only an approximation of the true transfer function. The model infidelity caused by the unmodeled dynamics may or may not be significant depending on how well the chosen model structure approximates the plant. B. DMT Models Dynamic Modeling Technology (DMT) is a new method of process transfer function modeling developed at the University of British Columbia [1]. This method employs a set of orthonormal Laguerre functions that are used to approximate the process transfer function in a similar fashion to series expansion representations of mathematical functions such as Taylor series and Maclaurin series. A common function series expansion used in signal analysis is the Fourier series, which uses a Cosine function series to approximate periodic (sinusoidal) signals. In process control, most processes have an initial transient response that asymptotically approaches steady state. The Laguerre function series is based on exponential functions that are able to efficiently represent typical process transfer functions. P

2 The Laguerre function series is defined as: pt i-1 li 2p e d = [ i-1-2pt t e ] i=1 to N (i-1)! i-1 dt where p Laguerre Pole A process transfer function can then be approximated using a Laguerre series representation by summing each function in the function series where each function is multiplied by an appropriate coefficient: i= g( t) = c i l i ( t) i= 0 where g(t) c Process transfer function ith Laguerre coefficient The DMT modeling method is able to represent higher order process transfer functions and is inherently able to model process dead time. The transfer function approximation is thus more accurate than conventional models based on S-Plane techniques. The orthonormal property of the Laguerre function set enables data fitting algorithms such as recursive least squares (RLS) to function efficiently with increased robustness. These properties enable the DMT models to be built on line in the presence of process disturbances and time varying dynamics. The user does not have to provide detailed knowledge of the process in order for an accurate transfer function to be obtained resulting in a great reduction in the effort required to model the process. Typically the model is produced automatically by the algorithm simply by observing the control actions and responses of the system during normal operation. Due to the simplicity of DMT modeling, it is possible for the algorithm to simultaneously develop models that describe the transfer functions of other variables and measured disturbances (feedforwards) which affect the controlled variable. The DMT method is able to automatically correlate observed data in order to determine the underlying transfer functions of the complete plant. This capability means that DMT modeling can be performed on line for processes with large disturbances that would normally inhibit S-Plane methods. III. PREDICTIVE ADAPTIVE CONTROL (1) (2) under various operating conditions. Commercially produced controllers of this type have commonly been called "model based" adaptive controllers. These schemes rely on the creation of an exact mathematical model of the process for each application of the controller. This requires a detailed knowledge of the transfer function (plant order, time constants, time delay), usually determined experimentally, before it is possible to implement the controller. This requirement limits the ability to transfer a single controller design from one process to another. Adaptive controllers are used extensively in aircraft and naval autopilots. The time invested to develop accurate mathematical models for these systems can be justified because the models can be reused on a number of identical aircraft or ships. Until now, commercially available adaptive controllers for use in industry have been based on general process models that do not always adequately represent the individual process characteristics. The degree to which the simplified model is able to represent the actual transfer function determines the accuracy of the calculated control actions and the resulting performance. These controllers are usually difficult to apply and have had varying degrees of success. A. DMT Adaptive Control The DMT adaptive controller is a breakthrough in adaptive control based on new theory developed by Dr. Guy Dumont and Dr. Chris Zervos at the University of British Columbia [1]. The unique feature of this scheme is the ease of implementation compared to the model based methods employed by previous designs. The advantage of the DMT approach is that it does not require a predetermined model of the process to be controlled. The use of orthogonal functions to model the process permits rapid transfer function identification with a minimum of prior process information. The controller is able to learn the process transfer function while it is controlling the process and is able to automatically adapt to changes in gain, time constants or time delay to maintain optimal control. This technique is used to learn the effects of measured process disturbances in order to incorporate adaptive feedforward compensation into the control strategy resulting in further performance improvements. The DMT controller uses its mathematical models of the process to forecast process response so that set point is attained as rapidly as possible with little or no overshoot, using a minimum of control effort (actuator manipulation). The basic algorithm steps used in the DMT controller are shown in Fig. 1. Adaptive control schemes provide the opportunity to achieve improved control performance by basing the control action on a mathematical model of the process, including time delay, that is used to forecast process response and subsequently calculate the actual control action required to obtain set point. The mathematical model is adjusted automatically to compensate for changes in the process characteristics so that the controller can maintain control P

3 INPUT PROCESS TRANSFER FUNCTION IDENTIFICATION UPDATE CONTROL MODEL CALCULATE CONTROLLER OUTPUT PLANT SETPOINT PROCESS RESPONSE Fig. 1. Basic Steps in the DMT Controller 1. Process Transfer Function Identification: The process model is adjusted by relating observed process responses to past control actions. 2. Control Update: The previous control action is taken into account to produce a new prediction of future process response. 3. Control Output: The predicted process response is used to calculate the required controller output to bring the process variable to the desired set point with minimum control effort. B. Kraft Continuous Digester Cooking Control An important development in continuous digester control has been achieved at Skeena Cellulose in Prince Rupert, British Columbia. It is well known that the major factors which influence digester Kappa Number are H factor, sulphidity, and Effective Alkali. Existing control strategies focus on H factor control; control of Effective Alkali has been difficult due to long dead times and large disturbances. A possible explanation for this is that H factor control is primarily a model-based feedforward approach which avoids the control problems caused by the long pulp residence time in the digester. Model parameters are obtained through correlation over time with H factor, Effective Alkali, and Kappa Number. Controlling Effective Alkali is a difficult problem due to the long dead time that exists between changes in white liquor flow and measured residual Effective Alkali. This dead time can be in excess of three hours and is not suited to control with conventional Proportional-Integral-Derivative (PID) control-lers. A model-based predictive controller is required to close loops with such long dead times. Previous predictive controller designs have been inadequate due to their inability to adapt to variations in process dead time as well as the complicated setup and maintenance they required. A new predictive adaptive process controller capable of controlling processes with long dead time and automatically adapting to process changes was successfully applied to the problem of closed loop Effective Alkali control. The results of this application will be presented. 1) Background: The relationship of Effective Alkali to pulp Kappa Number was presented in work by Wallin and Noreus, who discovered two different reaction mechanisms in the digester. Initially, alkali concentration decreases rapidly due to a variety of physical and chemical mechanisms that depend on chip quality. After these initial reactions, bulk delignification begins. The reaction rate during this phase strongly depends on alkali concentration. The concentration at the start of this phase is called the residual Effective Alkali. Effective Alkali is defined as the sum of the sodium Hydroxide concentration plus one half of the Sodium Sulphide concentration expressed as grams of Na 2O per litre. Effective Alkali is difficult to measure because the liquor must be analyzed after initial reactions have occurred. In a single vessel Kamyr digester, initial reactions are complete in the lower cooking zone. The mill has installed an on-line Effective Alkali analyzer that provides measurements approximately every thirty minutes. However, even with the measurement problem solved, Effective Alkali control remains a problem. Effective Alkali is sensitive to variations in chip quality and this property is also difficult to measure and employ in a feedforward control strategy. At Skeena, chip moisture alone can vary from 40% to 60% during a day s production. Without the ability to implement open loop feedforward control, the only remaining option for Effective Alkali regulation is feed back control. The presence of a three and one-half hour dead time in this feed back loop must be addressed in order to achieve control of Effective Alkali and realize improved digester operation. 2) Control Strategy: The mill installed a Kappa Number control system in This system is based on a fixed model relating Kappa Number, H factor, sulphidity, and Effective Alkali. The model structure is fixed and the model coefficients are determined using laboratory Kappa Number tests. The target K# is 21.5 and the installation of this control system has reduced standard deviation from 4.0 to 2.5 despite wide swings in chip quality. Residual Effective Alkali set point is 0.7 pounds per cubic foot with a historical standard deviation of 0.08 Effective Alkali. Fig. 2 shows the historical performance. Reducing the standard deviation of Effective Alkali will help make it easier to determine accurate coefficients for the Kappa Number prediction model. Improvements in Kappa Number predictions would also be obtained as the model could be refined for a smaller range of operating conditions once Effective Alkali variations are reduced. With improved Effective Alkali control, changes in target H factor would also be smaller resulting in reduced temperature and steam demand swings. Stable digester operation would contribute to reduced pulp property variations and smoother operation of the bleach plant. P

4 Fig. 3. Effective Alkali Control Schematic P

5 The new Effective Alkali control strategy was implemented using a commercially available advanced predictive adaptive process controller based on Dynamic Modeling Technology (DMT). The controller runs in a personal computer and communicates with the DCS control system via a serial link. A diagram of the control strategy is given in Fig. 3. The predictive adaptive controller monitors the Effective Alkali measurement from the on-line analyzer and calculates the set point for the White Liquor/Wood Ratio controller. The ratio controller is used to compensate for short term variations in wood chip mass flow while the Effective Alkali controller adjusts the ratio target based on longer term changes in chip properties. The black liquor flow was initially incorporated into the Effective Alkali controller as a feedforward input to compensate for changes in Effective Alkali caused by black liquor used to clear chip hang-ups in the digester. However, the DMT controller was able to determine that this was not related to Kappa # and this feedback signal was removed. This ability to confirm relationships within the process has been a very useful control engineering tool. The predictive adaptive controller was installed and setup to observe digester operation for several weeks. During this time, the controller automatically constructed process transfer function models for the relationship between Effective Alkali and the White Liquor/Wood ratio target. Following this observation period, the controller was placed in automatic and adjusted the White Liquor/Wood ratio target as required to maintain constant Effective Alkali. While in automatic control, the predictive adaptive controller continued to update the transfer function models as required to compensate for changes in process operating conditions in order to maintain optimal control. Results: It was decided to carry out a three-month trial to see if the Kappa number did have a reduction in standard deviation. The economic evaluation was based on a Swedish paper [3] that gave the following costs per ton for various Kappa targets and standard deviations as shown in Fig. 4. Fig. 5 shows data collected with the new control system operating for a period of three months. From this information it was determined that with K# = 21.5, or the equivalent Kappa = 32, the SD was reduced from 3.76 to 3.40 (after conversion to Kappa 32). This results in a savings per ton of pulp of $0.60 USD. When this is converted to $CDN and in metric tonnes, the amount is $0.75. Once multiplied by the total annual output of one Kamyr digester for this mill, the result is a saving of $108,885 per year. This is a return on investment of less than five months! It should be noted that the calculations used were provided by the mill and are conservative calculations as the K# SD used are the average of daily averages for all cases, which will tend to understate the SD and hence understate the potential savings US $ PER METRIC TON (1988) Kappa Target = 26 Kappa Target = 28 Kappa Target = 30 Kappa Target = STANDARD DEVIATION Fig. 4. Production Costs USD/t of Scandinavian Pine Kraft Pulp [2] P

6 14 PERCENT SD BEFORE UAC #1 Dig. %SD/Avg Avg %SD/ Avg K# Avg %SD/Avg K# UAC AFTER UAC May '93 Jul Sep Nov Jan Mar May Jul '94 Fig. 5. Digester K# Percent Standard Deviation with a UAC Dynamic Modelling Technology Controller IV. CONCLUSIONS The unique ability of Dynamic Modeling Technology to learn the process and feedforward variable behavior automatically and continuously enables the simple and cost-effective implementation of advanced controls. DMT techniques can be used to ensure optimum control system performance at all times with a reduction in the maintenance effort required to support advanced controls. The problems of long development time, long setup time, repeated tuning and poor reliability associated with other advanced controllers such as Smith Predictor and other model-based controller designs are solved with the DMT method. The superior control performance that can be achieved by controllers based on Dynamic Modeling Technology reduces process variability and enables the potential quality improvement benefits of supervisory and statistical process control systems to be realized. In addition, the cascade effects of many small improvements provided by tighter control on individual loops can improve the complete process or plant operation substantially. The DMT control approach is a new tool available to the process control engineer to implement the continuous improvement concepts advocated by Deming [3] and Juran [4] in their Total Quality philosophies. With improved Effective Alkali control, changes in target H factor are small. With smaller changes in H factor target, temperature set point variations are smaller. Reduced variations in temperature set point dampen steam demand swings, which reduces energy costs and smoothes out digester and boiler operation. With reduced swings in Effective Alkali, pulp properties such as viscosity will be more consistent. Once Effective Alkali is controlled, optimization techniques can be used to investigate the economics of several process units affected by digester operation. Lower variation in K number will smooth out bleach plant operation and reduce the load on the effluent treatment system. By reducing the alkali added to the digester, the load on the chemical recovery system is reduced. With both parameters affecting K number under control, the most economical mix of H factor and Effective Alkali for the target K number can be found. With variations in chip quality and lengthy and varying time delays, Effective Alkali presents a significant control challenge. However, the adaptive controller installed meets this challenge with superior dead time compensation and feedforward capabilities. Furthermore, the controller is very easy to install and learns the process model automatically. Adaptive, predictive control with feedforward capabilities and automatic process model building affords the opportunity not only to improve Effective Alkali control but also to improve it effortlessly. By controlling Effective Alkali, K number deviations can be reduced, resulting in a more uniform and salable product. With both Effective Alkali and H factor under control, optimization techniques can be used to find the most economical operating point for the digester, bleach plant, effluent treatment system and chemical recovery system. The mill has purchased the system and it has been controlling Effective Alkali since May Besides the excellent return on investment, the mill now found much less engineering was required to achieve good control of this difficult process. It is believed that even further improvement to the Effective Alkali control would be seen if chip level and steaming vessel amps were added to the control algorithm as additional feedforward variables. The DMT control strategy has been applied to a second Kamyr digester and effluent system ph control. The results from these will be discussed in the presentation. P

7 V. REFERENCES [1] ZERVOS, C.C. and DUMONT, G.A., Deterministic adaptive control based on Laguerre series representation, Int. J. Control, Vol. 48, No. 6, (1988). [2] TIKKA, P.O., KUUSELA, M.J., and SAARENPAA, M.S., New Methods to Master Continuous Digesters, Control Systems (1988). [3] DEMING, W.E., Out of the Crisis, M.I.T. Center for Advanced Engineering Studies (1989). [4] JURAN, J.M., Juran's Quality Control Handbook, McGraw- Hill (1988). P