PREEMPTIVE CONTROL OF MULTIPLY ACTUATED PROCESSES: APPLICATION TO MOISTURE CONTENT CONTROL IN PAPER MANUFACTURING USING SURROGATE MEASUREMENTS

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1 PREEMPTIVE CONTROL OF MULTIPLY ACTUATED PROCESSES: APPLICATION TO MOISTURE CONTENT CONTROL IN PAPER MANUFACTURING USING SURROGATE MEASUREMENTS Perry Y. Li Dept. of Mechanical Engineering Uniersity of Minnesota Minneapolis, Minnesota Petar J. Bjegoic Dept. of Mechanical Engineering Uniersity of Minnesota Minneapolis, Minnesota Shri Ramaswamy Dept. of Wood and Paper Science Uniersity of Minnesota St. Paul, Minnesota ABSTRACT Many manufacturing processes inole the successie processing of the substrate at multiple station on a transport medium, with the hope that at the end of the process, the product has the desired property. Paper manufacturing is an example in which oer 90% of the water from pulp is sequentially remoed through graity, acuum dewatering, pressing, and thermal drying. The consistency and uniformity of the moisture content at the end of process is important for paper quality. Current strategy for the control of moisture content uses a feedback sensor at the end of the process to adjust the dryers. This introduces a long deadtime and causes excessie use of the dryers, which translate to limitations in performance, robustness and inefficient energy usage. In this paper, we inestigate a new control approach in which in-process moisture contents are estimated using air-flow as surrogate measurements, and the pressure settings in the multiple acuum dewatering boxes are adjusted according to the surrogate measurements. A preemptie control algorithm is deeloped which has the ability to decouple and eliminate the effects of the disturbances that occur upstream in the process from downstream. Robustness analysis and simulation studies suggest that as long as the surrogate measurements are accurate, the proposed control scheme will be robust and accurate. 1 Introduction The paper industry in the U.S. alone consumes approximately 2.7 quadrillion Joules ( J) of energy eery year [1]. To be competitie, it is necessary to improe quality and to reduce cost. The two key quality measures are 1) moisture content; and 2) basis weight (weight of paper fiber / m 2 of paper). THIS RESEARCH IS SUPPORTED BY THE TAPPI FOUNDATION AND THE NATIONAL SCIENCE FOUNDATION. headbox graity drainage Figure 1. incoming slurry Circulating wire mesh... acuum dewatering Wet press Dryer section Dryer cans steam pressure Controller Moisture sensor Schematic of a water remoal processes in a paper machine and the current process control strategy These measures must be regulated at desired alues and must be uniform throughout the length and width of the paper produced. Paper manufacturing (Fig. 1) inoles the sequential remoal of water from pulp with 99.5% moisture by means of graity, acuum dewatering, mechanical press, and thermal drying in a paper machine, to form end product with moisture content of 4 8%. Of these, the dryer section is the most energy inefficient but is also currently utilized as the main moisture control actuator. Therefore, an effectie moisture control strategy with proper means can hae significant impact on energy utilization. Currently, acuum dewatering is not actiely inoled in closed loop process control. Rather, pressure settings are determined by operator based on isual inspection. The most important disturbances and uncertainties in the paper making process relate to the composition and the initial water content of the slurry entering the process at the headbox (Fig. 1). Composition in terms of basis weight, types of fibers and their treatments, and chemical addities affect the drainage property of the sheet, and hence the moisture content of the end product. The uncertainties of the composition become een more pronounced when recycled stock is used. Current process control strategy for moisture content makes

2 use of a single online moisture measurement at the end of a paper machine (typically 100m long) to monitor the moisture content of the end product. Based on this measurement, steam pressures in the thermal dryer cans are adjusted ia a ariety of possible control algorithms (e.g. P-I, adaptie [2], stochastic control [3], self-tuning LQ method [9], neuro-fuzzy control [15], self-tuning control [18], model algorithmic control [17], and arious robust control and model predictie control [13]) to remoe more or less water from the paper. This control topology itself presents the following fundamental limitations: 1. It would be too late to take any correctie action for any endproduct that already deiates from specifications. 2. Limited robustness and control performance due to the long deadtime (a few seconds) associated with the 30-60m distance between the actuator in the dryer and the moisture sensor at the output of the process. 3. The thermal dryers are more heaily utilized than are strictly necessary since they are the primary control actuators in the current control strategy. Water that could hae been remoed instead by the more energy efficient acuum dewatering process, is thermally dried instead. This is a major source of energy inefficiency. To oercome these limitations, we are deeloping a new approach to control moisture content, using the acuum dewatering boxes as process control actuators, and in-process estimation of the moisture content of the paper along the length of the paper machine, as the paper is being produced. Results in the literature [4], [16], ours and other s research in Through Air Drying (TAD) [12], [6], [10], [11], [14], and preliminary studies indicate strongly that the magnitude of the air-flow through the wet sheet and the dependence on moisture content contains adequate information to infer the moisture content of the sheet. We call such indirect measurements surrogate measurements. Based on these surrogate measurements, our proposed control strategy is to apply these for local feedback and preemptie feedforward control. Since the moisture content measurements and the actuation are nearly co-located, high feedback gain can be used. The use of preemptie feedforward control would allow us to effectiely decouple disturbances upstream from affecting the downstream process. The oerall potential benefits would be improed accuracy in moisture content control, and more efficient use of energy (since energy use in the dryers can be minimized). In this paper, we inestigate a preemptie control strategy based on the aboe approach to ealuate the usefulness and feasibility of using multiple acuum dewatering boxes and surrogate measurement feedback for the control of moisture content. Since the system inoles continuous process dynamics, described by partial differential equations, a suitable discrete dynamic model in the form of an interconnected system, is first deeloped for control design. Preemptie control law is then deeloped. It can effectiely decouple upstream disturbance from propagating downstream. In addition, local feedback, enabled by the in-process surrogate measurements, enhances robustness to uncertain system parameters. Similar to paper manufacturing, in many other manufacturing processes, e.g. thermal processing of composite material as in tape laying, a substrate is transported successiely to be processed at multiple stations. The product requirements are often specified for the property at the end of the process. Moreoer, the processes are often described by partial differential equations. The modeling techniques as well as the control philosophy enunciated in this paper should also be applicable to these. The rest of the paper is organized as follows. The deelopment of the control design model is gien in Section 2. Section 3 presents the preemptie control algorithm. Section 4 presents the robustness analysis of the control scheme to measurement and model parameter accuracies. Simulation results are presented in section 5 to illustrate the usefulness of the approach. Sections 6 and 7 contain discussion and concluding remarks. 2 Dewatering model for Control Design Following the classical work in acuum dewatering [5], the rate of water remoal is assumed to be proportional to the square root of the applied pressure (or acuum) and to the water content: q = K Pc (1) where q and c are the water remoal rate and the amount of moisture per unit length of the sheet, and K is the transport coefficient. Assume that there are N dewatering boxes, each with length B m, and the constant speed of the paper machine is m/s. Let c(x,t) be the moisture content per unit length of the sheet at location x and time t. This can be conerted to the normal definition of moisture content, which is the amount of moisture per unit total weight of the paper, if the basis weight of the sheet is also known. By incorporating transport into (1), we obtain, ia a mass conseration argument: t c(x,t) = x c(x,t) K(x,t) P(x,t)c(x,t), (2) where the first term corresponds to the transport effect, and the second term corresponds to dewatering. We can consider P(x,t) = P i (t) when x is in the domain of one of the N dewatering box with index i = 1,...,N, and K(x,t) will be the transport coefficient of the sheet at x. Remark 1 Eq.(2) can be generalized for other processes that inole a product quality measure c, whose dynamics without transport, are gien by: dc dt = K g(u) c, where u is the control

3 input that affects the process rate and the process dynamics is linear in the quality measure c. 2.1 One-segment discrete model Although the partial differential equation description in Eq.(2) is complete, it is difficult to use for control design. Simplified discrete models will be more appropriate. To do this, we further assume that the transport coefficient K(x,t) = K i is constant for the i th acuum dewatering box. This is reasonable if the paper machine is operating at a nearly steady state condition. We further assume that the domain of each acuum dewatering box is represented by a single segment. Let c i (y,t) := c(x i + y,t) be the moisture content profile for dewatering box i, where x i is the location of the beginning of the i th dewatering box. Under steady state condition, the profile of the moisture content of the i th dewatering box is gien by c i (y, ) = c i (0, )e K i Pi ( ) y Our main assumption for the discretization of (2) is that within the segment that represents the dewatering box, the exponential profile in Eq.(3) holds at each instant of time. Based on this assumption, the total moisture content w i, defined below, can be used to describe the state of the segment. w i (t) is related to c i (0,t), and hence, to the moisture content profile (3) by B w i (t) = c i (y,t)dy = c i (0,t) 0 K i Pi (t) [ 1 e K i Pi (t) ] B. The state dynamics of w i, for i = 1,...,N (number of dewatering boxes) can now be deried using mass balance principle, which states that the rate of change of total water content within the segment must be equal to the net flow into the control olume. Thus, d dt w i(t) = [c i (B,t) c i 1 (B,t τ i )] K i Pi (t)w i (t), (4) where the first two terms correspond to the net flow due to the translation of the wet sheet and belt in the machine (process) direction, and the third term is due to acuum dewatering. τ i = L i / is the transit time for the sheet to trael between the i 1st and i th dewatering boxes which are L i apart. For i = 1, it is taken to be τ i=1 = 0. Notice that if we define (3) f i (t) := e K i Pi (t) B, (5) Headbox disturbances Wet sheet on translating wire Figure 2. W1 Cout2 W2 W3 Cout Box 1 Total water remoal Total air-flow Moisture content profile Cout1 Box2 Total water remoal Total air-flow Box3 Total water remoal Total air-flow To press s Schematic of the acuum dewatering section of the paper machine in which the one segment model is used to describe the dewatering boxes. we hae c i (B,t) = e K i where Pi (t) B c i (0) = K i Pi (t) f i (t) 1 f 1 (t) w i(t), so that d dt w i(t) = Ω i (t)w i (t) + c i 1,out (t τ i ), (6) Ω i (t) := K i Pi (t) 1 f i (t). (7) The exit moisture content is then related to w i 1 (t) by: c i 1,out (t) = K i 1 Pi 1 (t) f i 1 (t) 1 f i 1 (t) w i 1(t) for i > 1, (8) and c i=0,out (t) denotes the incoming moisture content entering the first acuum dewatering box from the headbox. If we had used n >> 1 (instead of 1) segments to represent each dewatering box, the equialent discretized model of Eq.(4) would become more and more accurate in approximating (2). For the purpose of control design, an adequately accurate model with fewest segments will be the most appropriate. Since the assumption in the model deriation is that the moisture content reaches steady state, it is expected that when the incoming moisture content c i 1,out or the pressure input P i are fast arying, modeling error would be worse. To assess to what extent this is the case, we hae conducted simulation studies comparing modeling errors (measured by the exit moisture content) between the models with arious number of segments and the model with n = 10 segments, which is taken to be the continuum model. Fig. 3 shows that, as expected, the percentage modeling error decreases as the number of segments n increases and for lower disturbance frequencies. Gien typical parameters of = 20m/s, B = 0.05m, and a 10Hz disturbances bandwidth in the incoming moisture content, the percentage modeling error of the one-segment model is less than 3%. Since the moisture content disturbances in the incoming slurry is expected to be only of the order of a few hertz, control design and analysis based on the one-segment model should be adequate.

4 % error Figure 3. Frequency of incoming disturbance/(/b) Discrepancy between arious discrete models and the 10 segment model as a function of the frequency of the inlet water content. Error is measured by the exiting moisture content and is presented as percentage of the exit magnitude of the 10 segment model. 2.2 Surrogate measurement of moisture content For the purpose of this paper, which is to present the adantages of surrogate measurements in the control of moisture content, we assume that the relationship q a = f air (c) is known, where q a is the air-flow per unit length of sheet with moisture content of c. Our current research relates to determining experimentally, this complex function that depends on many factors. Assuming that this can be done, the total air-flow through the sheet in the i th acuum dewatering box is a function of the total moisture content: B Q a,i (t) = f air (c i (y,t))dy = F air,i (w i (t),p i (t)) (9) 0 for some static function F air,i (, ). Since P i is a known control input, using air-flow as a surrogate measurement of the moisture content consists in inerting F air,i (,P i (t)) : w i (t) Q a,i. We assume that this function is inertible for the type of basis weight paper that is being considered. This would be the case if air flow is indeed a alid surrogate measurement of moisture content. 3 Preemptie Control using Surrogate Measurements 3.1 Control problem formulation The objectie of the control algorithm is to adjust the pressure settings in the acuum dewatering boxes based on the feedback of a) the air-flow through the dewatering boxes, and b) the actual moisture content measurement at the output reel of the machine, so that 1) the paper leaing the paper machine has the desired moisture content (normally about 5-6%); 2) the energy used in the dryer cans is minimized; 3) the paper does not seal. The control system will be subject to disturbances in the consistency, material properties, basis weight of the incoming slurry. Uncertainties in plant dynamics and parameters are also expected. Since we desire to utilize the minimal amount of energy in the dryer, we can assume that there is a target moisture content n=1 n=2 n=3 n=5 n=7 alue for the sheet just about to enter the press / dryer section. This target alue should be as low as possible (to minimize energy use of the dryer). The objectie of the control system is then to regulate the moisture content of the sheet as it enters the press / dryer section at the desired alue. Our approach to this control problem is to consider the moisture content profile along the length of the machine. In other words, we specify either a desired total moisture content alue w i or a target exit moisture content alue for each acuum dewatering box i. For simplicity, we define the problem using the total moisture content. Then, the goal of the moisture content profile control is to ensure that the desired total moisture content at each box is attained: i.e. lim t w i (t) w i, i = 1,...,N. We assume that w i, i = 1...N hae been designed and a set of feasible nominal operating pressures P i, i = 1,...,N exists so that together with the nominal incoming moisture content c 0,out, the plant model (6) is satisfied: where Ω i := K i P i 1 f i 0 = ẇ i = Ω i w i + c i 1,out (10), f i := e K i P i B, and K i 1 P i 1 f c i 1 i 1,out = 1 f w i 1 if i > 1 i 1. c 0,out = nominal slurry moisture content if i = 1 Although the ultimate control objectie is at the last dewatering box, i.e. w N (t) w N, the adantage of controlling the profile of moisture content, instead of at the exit alone is that dewatering will be ensured to occur gradually. This in turn minimizes the risk of saturating the control effort in the acuum dewatering boxes, and of sealing. The moisture content profile control concept is similar to the control of traffic profile for automated highway systems [8], and to the problem of transporting cut sheet paper in a copier / printer along a multiplily actuated paperpath so that the sheet arries at the registration station at the correct time [7]. 3.2 Preemptie control law Let e i := w i (t) w i be the moisture content error for the i th dewatering box. It can be shown that ė i (t) = Ω i (t)e i (t) + (Ω i Ω i (t))w i + c i 1,out (t τ i ), (11) where c i 1,out (t τ i ) := c i 1,out (t τ i ) c i 1,out. Notice that Ω i (t) 0 defined in (7) is a monotone increasing function of pressures, so it is inertible for any non-negatie alues. Moreoer, c i 1,out (t τ i ) is aailable using Eq.(8) if w i 1 (t τ i ) and

5 c_i-1,out incoming moisture content c_i-1,out estimated moisture content Smart Vacuum Dewatering Box pressure Figure 4. Controller Vacuum dewatering box Estimator Smart acuum dewatering box c_i,out outgoing moisture content c_i,out estimated outgoing moisture content P i 1 (t τ i ) are aailable. If surrogate measurements are aailable, w i 1 (t τ i ) can be estimated by inerting F air,i (,P i 1 ) in (9). The basic preemptie control strategy is to choose Ω i (t) as Ω i (t) = Ω i + 1 w i [λ f f,i c i 1,out (t τ i ) + λ f b,i e i (t) ] (12) where 1 λ f f,i 0 and λ f b,i 0 are the preemptie feedforward and feedback control gains respectiely. For i = 1, since measurement of the incoming moisture content is not aailable, λ f f,1 = 0. The resulting dynamics are then gien by: ė i (t) = { ( Ω i (t) + λ f b,i ) ei (t) + (1 λ f f,i ) c i 1,out (t τ i ) i > 1 ( Ω 1 (t) + λ f b,1 ) e1 (t) + c 0,out (t) i = 1. (13) Therefore, control law increases the conergence rate using local feedback and compensates for any discrepancy in the incoming moisture content to the present box. In particular, if λ f f,i is chosen to be 1, and λ f b,i 0, then the effect of any upstream disturbances hae been completely decoupled from the i-th box and ė i conerges to 0 exponentially. Using the relationship between the Ω i and c i 1,out in Eq.(10), the preemptie control law in Eq.(12) can be simplified: w i Ω i (t) = [ λ f f,i c i 1,out (t τ i ) + (1 λ f f,i ) c i 1,out] +λ f b,i e i (t). (14) incoming slurry from graity dewatering Smart V.D.box W Smart W Smart Smart... W W V.D.box V.D.box V.D.box W W W W Vacuum dewatering Figure 5. Press and Dryer Block diagram of the control scheme Moisture sensor W The bracketed term in Eq.(14) is a conex combination of the nominal and measured incoming moisture content. Thus, intuitiely, λ f f,i < 1 may be preferable if the estimate of c i 1,out (t) is inaccurate. Notice that for λ f f,i = 1, knowledge of neither Ω i nor of c i 1,out is necessary. Notice that in the control law (12), feedback information (i.e. the air-flow measurement) is utilized locally within the indiidual dewatering boxes and their immediate downstream neighbors. The localization can be conceptualized in terms of a Smart Vacuum Dewatering Box (Fig. 4) which has the ability to robustly control its own moisture content, and to proide an estimate of the moisture content to its neighbors. The complete control scheme which is made up of interconnected Smart Vacuum Dewatering boxes is shown in Fig Robustness analysis 4.1 Inaccuracy in w i estimation Our control scheme is based on the estimation of the moisture content using air-flow as the surrogate measurements. It is important to understand how accuracy in this estimation affects the performance of moisture content control. Assume that ŵ i is the estimate of w i and let w i = ŵ i w i be the estimation error. Then, using ŵ i instead of w i as feedback, the error dynamics become: ė i (t) = ( Ω i (t) + λ f b,i ) ei (t) + (1 λ f f,i ) c i 1,out (t τ i ) [ λ f f,i α i 1 (t τ i ) w i 1 (t τ i ) + λ f b,i w i (t) ] (15) where α i 1 (t) := K i 1 Pi 1 (t) f i 1 (t) 1 f i 1 (t). The ultimate error bound for e i is: e i (t ) (1 λ f f,i) c i 1,out + λ f f,i α i 1 w i 1 + λ f b,i w i where denotes the supremum of the magnitude of the argument, Ω i denotes the lower bound on Ω i (t). Based on typical operating ranges, we expect that 7.5s 1 K i Pi 125s 1, and the residence time B/ 0.003s. Hence, the ranges for B α i 1 (t) and for Ω i (t) are: 1 Bα i 1 (t) 0.7, and /B Ω i (t) 1.2/B. α i (t) generally are smaller and Ω i (i) are larger for boxes that are further downstream. Tighter bounds can be established if indiidual boxes are considered. Assuming that the estimation errors are the same for all dewatering boxes and is gien by w, we obtain e i (t ) (1 λ f f,i ) c i 1,out + B α ib λ f f,i + λ f b,i w (16)

6 which can be used for the design of the feedforward and the feedback gains. For example, if the uncertainty in the incoming moisture content to the i-th box is B c i,out (t) M i w, then the right hand side of (16) will be minimized if and ˆf i (t) = e ˆK i Pi (t) B λ f f,i = { 1 if M i > B α i 0 if M i < B α i. Since α i B is of the order of 1, roughly speaking, if the uncertainty in the incoming moisture content is larger than the accuracy of the moisture content measurement, then preemptie feedforward control should be used. If the aboe preemptie feedforward gain policy is used, then Eq.(16) reduces to: e i (t ) B min( Bα i,m i ) + λ f b,i w. Since Ω i > /B and α i B < 1, λ f b,i should be set to zero! Howeer, for any alue of λ f b,i, the ultimate bound for e i approximately equals the accuracy of the estimate for w i. This means that the feedback gain cannot significantly degrade the accuracy either. We will now show that λ f b,i does play a positie role in combating the effect of model uncertainty. 4.2 Uncertainty in K i We analyze the effect of uncertainty in the dewatering transport coefficients K i. Based on the analysis aboe, we assume that λ f f,i = 1. We also assume that the measurements of w i are correct and estimation of the incoming moisture content for the first box is accurate (c 0,out (t) = c 0,out ). Let ˆK i be the estimate of K i. Let us use the notation ˆΩ i (t) to denote the expression for Ω i (t) in Eq.(7) with K i substituted by ˆK i (including inside f i ), and let ĉ i 1,out (t) denote the expression of c i 1,out (t) in Eq.(8) with K i 1 substituted by ˆK i 1. Then, the computation of the control effort P i will be based on: In the actual situation, the pressure P i (t) would be computed based on ˆΩ i (t) in (17), but applied to Ω i (t) in (7) and then in turn to the error dynamics gien by (10) and (11). Since ˆΩ i (t) and Ω i (t) are positie there exists s i (t) > 0 such that Similarly, we can define so that s i (t) := Ω i(t) ˆΩ i (t) = K i ˆK i 1 ˆf i (t) 1 f i (t). (18) g i (t) := α i(t) ˆα i (t) = s i(t) f i(t) ˆf i (t) = s i(t)e (K i ˆK i ) P i (t) B (19) ĉ i 1,out (t) = ˆα i 1 (t)w i 1 (t) = 1 g i 1 (t) c i 1,out(t). The error dynamics for i = 2,...,N then become: ė i (t) = [ Ω i (t) + s i (t)λ f b ] ei (t) + and for i = 1, ( 1 s i(t) s i 1 (t) e(k i 1 ˆK i 1 ) P i 1 (t τ i ) B ) c i 1,out (t τ i ), (20) ė 1 (t) = [ Ω 1 (t) + s 1 (t)λ f b ] e1 (t) + (1 s 1 (t)) c 0,out (t) (21) Under normal operating conditions, we expect that the exponents in f i (t) and ˆf i (t) are in the range [0.025,0.4], so s i (t) is gien approximately by: w i ˆΩ i (t) = ĉ i 1,out (t τ i ) + λ f b,i e i (t) (17) s i (t) K i [1 (1 + ˆK i Pi (t)b/)] ˆK i [1 (1 + K i Pi (t)b/)] = 1. where ĉ i 1,out (t) ˆα i 1 (t) { }}{ ˆK = i 1 Pi 1 (t) ˆf i 1 (t) 1 ˆf i 1 (t) w i 1(t) for i > 1, = nominal incoming moisture content for i = 1 c 0,out Therefore, the dynamics of e i, i = 2...,N and i = 1, due to uncertain K i and K i 1 are approximately gien by: ė i (t) [ ] Ω i (t) + s i (t)λ f b,i ei (t) ( ) + 1 e (K i 1 ˆK i 1 ) P i 1 (t τ i ) B c i 1,out (t τ i ) ė 1 (t) [ Ω 1 (t) + s 1 (t)λ f b,1 ] e1 (t) (22)

7 From (22), we can obsere firstly that uncertainty in K i only has a benign effect on the feedback action by changing the effectie feebback gain from λ f b,i to s i (t)λ f b,i. In particular, for i = 1, uncertainty in K 1 does not introduce errors. Secondly, unlike the case of uncertain measurements w i (t), the feedback gain λ f b,i can be used positiely to combat the aderse effect introduced by the uncertainty in K i 1. For example, we can see that e i (t ) c i 1,out( ) Ω i ( ) + s i ( )λ f b,i 1 e K i 1 Pi 1 ( ) B, where s i ( ) is the lower bound of s i (t 0). Thus, by increasing λ f b,i, the effect of the uncertainty in K i 1 will be decreased. Total moisture content m Actual and desired total moisture contents (without control) Box 1 Box 2 Box 3 Box 4 Box 5 Box 6 Box 7 Box 8 Box 9 5 Simulations The proposed control system is simulated for paper machine with N=10 dewatering boxes of length B = 0.05m and with machine speed of 20m/s. The transport coefficient K i decreases from K 1 = 0.6s 1 Pa 1/2 to K 10 = 0.1s 1 Pa 1/2, and the desired total moisture contents, which are designed based on increasing nominal pressures from 4500Pa to 70000Pa, decreases from w 1 = to w 10 = The nominal incoming moisture content c out,0 is 15kg/m. In all situations, λ f f,i = 1, λ f b,i = /B = 400sec 1. To be realistic, saturation limits (about ±10% of nominal alues) are imposed on the input pressures. Table lookup is used to inert the nonlinear function Ω i (t) (specified by the control law (14)) to obtain P i (t). First, we consider the situation when there are a 10Hz sinusoidal disturbance (10%) at the incoming moisture content, and a 7Hz sinuoidal disturbance (8%) before the 5th dewatering box. The latter simulates a leaking water pipe in the middle of the factory. Figure 6 shows the total moisture contents with and without the preemptie controller. Without control, moisture content deiation at box 10 is about 10%. With control, the moisture content w i conerges to the desired alues for the 4th and the last box. At the other boxes, the effect of the disturbances has been significantly attenuated. Conergence does not occurs for some of the boxes because of saturation at the upper pressure limits. Figure 7 shows the situation when 10% inaccuracy in moisture content measurements are introduced. Notice that the moisture content conerges to region close to the desired alue with an accuracy commensurate with the accuracy of the moisture content estimation. Thus, the accuracy of the moisture content estimation is ery important to the proposed scheme. Figure 8 shows the moisture content of the last dewatering box when all the transport coefficients are 10% different from nominal, with feedback (λ f b,i = 400/s) and without feedback (λ f b,i = 0). Een without feedback, only about 2% error is introduced. When feedback control is applied, the error is further reduced to 1.29%. Total moisture content m Box Time s Solid actual W i Dashed desired W i Actual and desired total moisture contents (with control) Box 4 Box 1 Box 2 Box 5 Box 3 Box 6 Box 7 Box 8 Box 9 Box Time s Figure 6. Desired and actual total moisture content (w i, i = 1,...,N) when a 10Hz, 10% ariation moisture content disturbance, and a 7Hz, 8% ariation disturbance are introduced at the first dewatering and the 5th box respectiely. Top: no control; bottom: with preemptie control. Wi Nominal and archieed Wi with 10% biased measurements Box 2 Box 5 Box Time(s) Figure 7. Time trajectories of total moisture content at boxes 2, 5, 10 when 10% error in estimation of the moisture content is introduced.

8 W Uncertain K, results for Box 10 with and without feedback without feedback with feedback Box 10 desired alue 7 Conclusions A new approach for the control of moisture content for paper manufacturing has been proposed. The approach makes use of acuum dewatering and surrogate in-process measurement of the moisture content based on air-flow measurements. Potentially, such an approach can compensate preemptiely for any upstream disturbances. A preemptie control algorithm for the interconnected acuum dewatering system based on a discrete control model has been deeloped. Analysis and simulations show that the algorithm is effectie and robust to measurement inaccuracy and to uncertainty in system parameters Figure 8. Time (s) Time trajectories of moisture content at boxes 2, 5, 10 with 10% error in the transport coefficients K i s. 6 Discussion Analysis and simulations in sections 4 and 5 suggest that if accurate in-process moisture measurements are aailable, moisture content can be quite accurately controlled such that the moisture content at the dewatering boxes downstream become decoupled from the upstream disturbances. In addition, certain amount of robustness to uncertainty in transport coefficients can also be tolerated, especially if the feedback gains λ f b,i s are increased. Direct adaptie technique based on (21) or (22) may be possible (especially for small uncertainty in K i ). The difficulty here lies in that K i is nonlinearly embedded in the error dynamics. The effect of control saturation, as demonstrated in the simulations, is that the disturbances cannot be eliminated completely by one dewatering box. Howeer, as the error is propagated downstream, the size of the disturbance also decreases so that the error can eentually be eliminated in the downstream boxes without saturating the control. Since the actual requirement is to control the moisture content at the last dewatering box, this may not pose a signficant problem. The question of whether to eliminate error using ery few dewatering boxes with little saturation limits, or using a larger number of boxes with stricter saturation limits is interesting. This is similar to the controllability analysis of a multiply actuated paper path of a printer / copier [7]. Since the aailability and accuracy of the moisture content estimates from air-flow measurement is critical to the success of our approach, our current research aims to experimentally deelop such a model. 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