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Injection molding quality control by integrating weight feedback into a cascade closed-loop control system.

INTRODUCTION

The quality requirements of injection-molded components have become more stringent because of growing plastics applications and increasing customer demands. The quality can be measured in many ways, such as part weight, mechanical properties, dimensional conformity, and aesthetic appearance. Among them, part weight is often selected as a measure of the quality because not only can it be measured precisely, but it is also an important criterion [1, 2]. Research has shown that the variation in part weight is due essentially to changes in part dimensions rather than variations in density [3]. Therefore, consistency of part weight is a good indicator of consistent part dimensions, which is important in precision manufacturing. As such, part weight is a commonly used criterion in quality control on the shop floor in industry.

To produce parts with high quality, considerable research has been conducted to address different aspects of the injection molding process. Some of the work has studied the control of machine components, such as the hydraulic system, injection ram, and/or heating bands of the injection barrel [4-6]. Because process variables (or polymer variables) are more closely related to part quality than machine variables [7], the control of process variables, such as cavity pressure, has received extensive attention [8-10].

However, part quality is a collective and lump-sum response to machine and process variables. The control of machine and process variables is not sufficient to guarantee the desired part quality in a consistent manner. Studies on machine performance revealed significant time-varying characteristics in the process (see e.g., [11]). Hence, quality control is needed to achieve quality consistency and accuracy. In general, there are two types of quality control schemes that have been investigated for injection molding: observer-based quality control and direct quality feedback control. The difference between these two schemes is how part quality is obtained. In the first case, a quality model, which estimates the quality from a set of machine and process variables, is used as a "soft sensor" while a real quality sensor is used in the second case.

The work reported in Refs. 12-14 falls into the category of observer-based quality control. Their common feature is that the control action is based on quality estimates rather than actual measurements. As a result, the control performance is highly dependent on the accuracy of the quality models no matter what constitutes the models. However, it is well known that the modeling accuracy is limited by many factors such as inevitable disturbances, incomplete knowledge, or limited resources. Strictly speaking, observer-based quality control does not close the quality loop; it is a comprehensive control of machine and process variables.

To overcome the deficiency in quality modeling and to achieve high performance in quality control, a direct quality feedback should be considered. Chen and Turng investigated online weight control through numerical simulation, combining feedback and feedforward based on a neural network model [15]. Havard et al. [16] proposed a direct weight feedback control with holding pressure adjusted for each shot. Their experimental results showed that the weight feedback control had a significant benefit on part weight stability over process control and machine control. In the above method, only cycle-to-cycle control was implemented; i.e., some selected machine variables could be changed once in a cycle to regulate the part weight, but there were no adjustments within a cycle to reduce the quality discrepancy. Long-term shift could be eliminated with such a method, because the average weight would be controlled to the preset value. Nevertheless, short-term consistency could not be improved because the machine performance was not changed within each shot.

In this paper, a cascade closed-loop system with direct quality feedback and disturbance feedforward for online quality control of injection molding is presented. Figure 1 shows the overall control system structure. At the outer loop, the part weight is regulated through manipulating the maximum mold separation (MS) from shot to shot. At the inner loop, the MS is taken as a signature of the process. The maximum MS specified in the outer loop is used to scale the whole MS profile, which covers the later filling and early holding stages. Then the profile, including the MS peak value, is controlled via two separate controllers: namely, cycle-to-cycle switchover control and within-cycle post-filling control. First, the switchover point is adjusted from shot to shot to achieve the required maximum MS value. After the switchover point, the holding pressure is adjusted to duplicate the desirable MS profile, which is normalized by scaling the maximum value to the required peak value. In this way, long-term disturbances are prevented in cycle-to-cycle control, and short-term disturbances are compensated by the within-cycle control. More details on injection molding control using MS can be found in Ref. 17. This paper concentrates on quality modeling, control, and related MS regulation.

[FIGURE 1 OMITTED]

EXPERIMENTAL SETUP

Molding experiments have been conducted to validate the proposed quality control scheme. The experimental injection molding system consists of three components: an injection molding machine with a mold of two different cavity geometries, a mold temperature control unit, and an advanced control system based on computer networks, as shown in Fig. 2. The machine used in the experiments is a BOY 50T equipped with a Moog servo-valve. The mold temperature control unit is from Sterling (Model No. 8422). The advanced control system includes both hardware and software as follows: (1) data acquisition (DAQ) card (AT-MIO-16E-2 from National Instrument), (2) digital injection controller (DIC) that consists of Moog digital and analog modules and a digital signal processing (DSP) board that handles machine control during filling, packing/holding, and plastication, (3) signal conditioners (SCM5B series), and (4) control algorithms hosted on desktop computers connected through TCP/IP networks. An electronic balance (METTLER TOLEDO AG 104) with a repeatability of 0.1 mg is used to measure part weight.

Six signals are collected at machine side, namely, ram position ([Y.sub.r]), ram speed ([V.sub.r]), nozzle pressure ([P.sub.n]), melt temperature ([T.sub.m]), hydraulic pressure ([P.sub.h]), and servo-valve opening ([S.sub.o]). A configurable multicavity plate mold is used in this study. Figure 3 shows the schematic diagram of the plate mold geometry marked with different transducers and their positions. The mold has a tapered round sprue (the top diameter is 6 mm and the bottom diameter is 8 mm), trapezoidal runners (base dimensions are 4 mm and 5 mm with a height of 5 mm), and two rectangular cavities. The upper cavity is 120 mm long, 40 mm wide, and 1.73 mm thick with a rectangular gate (5 mm long, 3 mm wide, and 1 mm thick). The lower cavity has the same length and width as the upper one, but is 3.36 mm thick. It can be blocked by changing the layout of runners.

[FIGURE 2 OMITTED]

The mold is instrumented, as shown in Fig. 3, in order to collect process data. Four LVDTs, namely, M[S.sub.1] to M[S.sub.4] are mounted at the four corners of the mold along the parting line to measure the displacement, MS. The cavity pressures, P[c.sub.1], P[c.sub.2], P[c'.sub.1], and P[c'.sub.2] are measured by pressure transducers that are flush mounted inside the mold cavity near and far from the gates. The sprue pressure, [P.sub.s], and the runner pressure, [P.sub.r], are also measured at the sprue end and along the trapezoidal runner near the gate, respectively. The mold wall temperature, [T.sub.w], is measured by a J-type thermocouple mounted in the mold, 2 mm beneath the mold wall surface.

[FIGURE 3 OMITTED]

Two different types of resins are used in this study, namely, a semicrystalline polypropylene (PP, Exxon PP 7032 E2) and an amorphous polycarbonate (PC, Teijin Panlite AD 5503).

All the experiments are conducted through a custom-developed injection molding control program, which was coded jointly in Microsoft Visual C++ and Matlab. The program provides a human-machine interface (HMI) to set up the references, process conditions, control parameters, and other variables. Furthermore, it carries out the computation in quality control and process control, while the machine control runs in Moog DIC. The sampling periods are 0.2 and 2 ms, and one cycle, for machine level, process level, and quality level controls, respectively.

Before running the automatic quality control, a quality model and process model are obtained for the different combinations of molds and materials given the machine. The quality model is built on a design of experiments (DOE), and the process model is constructed in open-loop experiments. The model parameters are then read into the control program and used to tune control parameters. After the program starts and a part-weight reference is given, the system can automatically adjust process and machine parameters to achieve the target quality, based on the control algorithms in this paper.

Process and Quality Modeling

As shown in Fig. 1, the part weight is regulated through MS, and MS is regulated through switchover point and holding pressure. The holding pressure adjustment is implemented in the within-cycle control, which was published in Ref. 17, so it is not repeated in this paper. To properly design the control system, the process model, which describes the relationship between switchover point and MS, and the quality model, which describes the relationship between MS and part weight, are first obtained in experiments.

Process Modeling

A novel concept of mass-based switchover control is proposed and implemented in this study. The injected mass is calculated based on Eq. 1,

[m.sub.inj] = A([[l.sub.0]/[[v.sub.0](T, p)]] - [[l.sub.s]/[[v.sub.s](T, p)]]) (1)

where [m.sub.inj] is the injected mass, A is the area of the barrel's cross section, [l.sub.0] is the ram position at the start of filling, [l.sub.s] is the ram position at switchover, and [v.sub.0] and [v.sub.s] are the corresponding specific volumes at the start of filling and switchover, respectively. Parameters [v.sub.0] and [v.sub.s] are functions of temperature and pressure and can be calculated from the resin's pvT (pressure-specific volume-temperature) property given the melt temperature and pressure. In this study, the material's pvT property is modeled by a two-domain, modified Tait equation [18].

In contrast to the conventional, single switchover parameter, such as time, pressure, or ram position, mass-based switchover is determined based on multiple variables including pressure, temperature, and ram position. Note that the injected mass is the exact physical variable that needs to be controlled in the process. It provides more reliable control of the MS than do the conventional, single variable (i.e., time-, position-, or pressure-based) switchover method.

Conceivably, the mass-based switchover point affects the maximum mold separation in the current shot. Based on several independent experiments conducted using the same experimental set-up, the data points in the diagram of maximum MS versus injected mass at switchover roughly fall into a straight line, as shown in Fig. 4. Therefore, a pure proportional element is readily employed to model the effect of mass-based switchover on the maximum mold separation at an operating point, as shown in Eq. 2. The proportional gain, [K.sub.SM], can be obtained in open-loop experiments.

[DELTA]M[S.sub.max] = [K.sub.SM][DELTA][m.sub.inj]. (2)

Quality Modeling

As reported in Ref. 19, part weight is highly correlated with mold separation. However MS alone cannot account for all of the variations in part weight, which are a collective result of the process conditions. For example, additional experiments by the authors have revealed that melt temperature and mold temperature also affect the correlation between part weight and MS.

To obtain the quality model and investigate the temperature effects, a DOE was conducted. Three process parameters, namely, mold temperature, [T.sub.w], melt temperature, [T.sub.m], and holding pressure, [P.sub.p], are selected. In this DOE, all process parameters have two levels. The other important process conditions used in the experiments include: injection velocity at 35 mm/s, holding time at 5 s, cooling time at 25 s, and a position-based switchover point at 20.5 mm. The responses are maximum MS and part weight. The results of the full-factorial experiment with two replicates are given in Table 1.

[FIGURE 4 OMITTED]

From the experimental data, the coefficients in Eq. 3 are fitted, and the values are listed in Table 2.

[W.sub.t] = [Wt.sub.0] + [a.sub.1][MS] + [a.sub.2][[T.sub.m]] + [a.sub.3][[T.sub.w]] + [a.sub.4][MS][[T.sub.w]] + [a.sub.5][MS][[T.sub.w]] (3)

[MS] = [[MS - 35]/20], [T.sub.w] = [[T.sub.w] - 70/5], [[T.sub.m]] = [[T.sub.m] - 310/5]. (4)

Based on the fitted model, the temperature effects on the correlation between part weight and maximum mold separation can be visually examined in Fig. 5. It shows that the linear correlation between part weight and maximum MS still dominates. At the same time, the temperatures affect both the slope and the interception of the correlating line. This means that different maximum MS's correspond to the same weight at different temperatures. For instance, it requires a larger mold separation to achieve the same part weight when higher temperatures are used.

Controller Design

On the basis of the schematic closed-loop quality control diagram in Fig. 1, Fig. 6 shows the global nonlinear block diagram of the quality control system. Note that the within-cycle post-filling control is not included. Because the internal states of the post-filling control are not affected by any cycle-to-cycle updates, it is separable from the cycle-to-cycle control and designed independently as reported in Ref. 17. The design of the quality controller and mold separation controller are based on Fig. 6.

[FIGURE 5 OMITTED]

In Fig. 6, [G.sub.1] ([z.sup.-1]) and [G.sub.2] ([z.sup.-1]) are the weight and MS controllers, respectively. The function f ([m.sub.inj],[P.sub.p]) models the dependence of the maximum mold separation on switchover point and holding pressure. The function g ([T.sub.m], [T.sub.w], M[S.sub.max]) expresses part weight in terms of mold temperature, melt temperature, and the maximum mold separation. The equation, M[S.sub.max] = h([Wt.sub.ref], [T.sub.m], [T.sub.w]) is converted from Wt = g([T.sub.m], [T.sub.w], M[S.sub.max]). The symbol [z.sup.-1] is the backward shift operator on the shot sequence.

Note that there is a one-cycle delay in the MS feedback loop due to the intrinsic nature of cycle-to-cycle control. A two-cycle delay exists in the weight feedback loop because of the need to measure part weight after the cycle. The whole system can be divided into several subparts as follows.

[FIGURE 6 OMITTED]

Weight controller:

M[S.sub.max_ref.sup.fb] = [G.sub.1]([z.sup.-1])[[Wt.sub.ref] - Wt[z.sup.-2]] (5)

where M[S.sub.max_ref.sup.fb] is the feedback component of the maximum MS reference.

MS controller:

[m.sub.inj] = [G.sub.2]([z.sup.-1])[M[S.sub.max_ref.sup.fb] + M[S.sub.max_ref.sup.did] - M[S.sub.max][z.sup.-1]] (6)

where M[S.sub.max_ref.sup.did] is the disturbance input decoupling or feedforward component of the maximum MS reference.

Disturbance input decoupling or feedforward compensator:

M[S.sub.max_ref.sup.did] = h([Wt.sub.ref], [T.sub.m], [T.sub.w]) - M[S.sub.max_ref.sup.0] (7)

where [MS.sub.max_ref.sup.0] is the maximum MS reference corresponding to the required weight under nominal conditions.

Process (MS) object:

M[S.sub.max] = f([m.sub.inj], [P.sub.p]). (8)

Quality (weight) object:

Wt = g(M[S.sub.max], [T.sub.m], [T.sub.w]). (9)

Equations 5 and 6 are already in linear form and Eqs. 7-9 can be linearized. Next, a linear operating point model can be obtained. It is expressed in Eqs. 10-14,

[DELTA]M[S.sub.max_ref.sup.fb] = -[G.sub.1]([z.sup.-1])[DELTA]Wt[z.sup.-2] (10)

[DELTA][m.sub.ing] = [G.sub.2]([z.sup.-1])[[DELTA]M[S.sub.max_ref.sup.fb] + [DELTA]M[S.sub.max_ref.sup.ff] - [DELTA]M[S.sub.max][z.sup.-1]] (11)

[DELTA]M[S.sub.max_ref.sup.did] = - [[^.b.sub.1]/[^.a.sub.1]] [DELTA][T.sub.m] - [[^.c.sub.1]/[^.a.sub.1]][DELTA][T.sub.w] (12)

[DELTA]M[S.sub.max] = [K.sub.SM][DELTA][m.sub.inj] + [K.sub.SP][DELTA][P.sub.p] (13)

[DELTA]Wt = [a.sub.1][DELTA]M[S.sub.max] + [b.sub.1][DELTA][T.sub.m] + [c.sub.1][DELTA][T.sub.w] (14)

where [^.a.sub.1], [^.b.sub.1], and [^.c.sub.1] are estimates of [a.sub.1], [b.sub.1], and [c.sub.1], respectively. The coefficient, [K.sub.SP], equals [partial derivative]f/[[partial derivative][P.sub.p]]. From these equations, the state block diagram of the operating point model for the closed-loop quality feedback control can be readily drawn in Fig. 7, which has the same structure as Fig. 6.

The weight variation is related to the extra inputs through

[DELTA]Wt([1/[a.sub.1]] + [1/[a.sub.1]] [K.sub.SM][G.sub.2][z.sup.-1] + [K.sub.SM][G.sub.2][G.sub.1][z.sup.-1]) = [K.sub.SP][DELTA][P.sub.p] + (1 - [K.sub.SM][G.sub.2][z.sup.-1]) ([[b.sub.1]/[a.sub.1]] [DELTA][T.sub.m] + [[c.sub.1]/[a.sub.1]][DELTA][T.sub.w]) - [K.sub.SM][G.sub.2]([[^.b.sub.1]/[^.a.sub.1]][DELTA][T.sub.m] + [[^.c.sub.1]/[^.a.sub.1]][DELTA][T.sub.w]). (15)

Equation 15 shows that the temperature effects on weight variations can be eliminated entirely if the parameter estimates match their true values and if the MS controller, [G.sub.2], is selected as an integrator. Thus [G.sub.2] takes the following form,

[G.sub.2]([z.sup.-1]) = 1/[[^.K.sub.SM](1 - [z.sup.-1])] (16)

where [^.K.sub.SM] is the estimate of [K.sub.SM].

The weight controller, [G.sub.1], also needs to be an integrator to eliminate steady state errors. A proportional element is added to provide additional degrees of freedom to improve system performance. Thus, it takes the form of a PI controller, as

[FIGURE 7 OMITTED]

[G.sub.1]([z.sup.-1]) = [K.sub.P] + [[K.sub.1]/1 - [z.sup.-1]] (17)

where [K.sub.P] and [K.sub.1] are the proportional gain and integration gain, respectively. The characteristic equation of the system is

[z.sup.3] - (1 + [epsilon])[z.sup.2] + [([a.sub.1][K.sub.P] + [a.sub.1][K.sub.1])(1 - [epsilon]) + [epsilon]] z(1 - [epsilon])[a.sub.1][K.sub.P] = 0 (18)

where [epsilon] = 1 - [[K.sub.SM]/[^.K.sub.SM]]. The controller gains, [K.sub.P] and [K.sub.1], are determined under the nominal condition, [epsilon] = 0. Note that there are only two design parameters in Eq. 18, but it has three characteristic roots. Thus, not all characteristic roots can be freely placed. There is one constraint in this pole-placement, namely,

[z.sub.1] + [z.sub.2] + [z.sub.3] = 1 (19)

where [z.sub.1], [z.sub.2], and [z.sub.3] are the characteristic roots. It is still possible to put all three roots in stable positions (within the unit cycle on the complex z-plane) by selecting proper [K.sub.P] and [K.sub.1]. For instance, if the characteristic roots are 0.4, 0.3, and 0.3, the corresponding controller gains are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)

When [a.sub.1] is not available, it is replaced by its estimate [^.a.sub.1]. This method is used to determine the values of the controller parameters in the experiments.

With both controllers properly designed based on the process and quality models, the closed-loop quality control system performance, such as the dynamic stiffness and robust stability, can be readily analyzed. The analysis can be found in Ref. 20 and is not included in this paper due to its length. Instead, several molding experiments have been conducted to verify the performance of the proposed quality control scheme.

Experimental Results

Two resins and two different mold geometries were used in the experiments. The resins were polypropylene and polycarbonate and the tool was the configurable multicavity rectangular mold, both described previously in the Experimental Setup section. The performance of the closed-loop quality control is compared with that of the prevailing cavity pressure based control, which is regarded as the most advanced method in the industry.

The process conditions in the experiments, which are tabulated in Table 3 where the references for weight and cavity pressure are listed, were used in the closed-loop quality control and cavity-pressure based control. In the experiments with a two-cavity mold, the weight reference is the combined part weight, the cavity pressure reference is the threshold value for switchover from filling to holding, and the pressure measured by P[c.sub.1] is used in all cases. As shown in Fig. 3, the thickness of the two cavities is different, and thus the mold-filling process is not balanced. To reduce the effect of unbalanced filling, the injection speed was increased to 40 mm/s. The melt temperature was increased as well to achieve filling at high speeds. The second cavity and its large thickness, combined with the increased melt temperature, required a longer cooling time. As a counteraction, the mold temperature was decreased to shorten the cooling time.

During the molding experiments, the melt and mold temperatures were purposely varied to evaluate the performance of different control methods. That is why two values are listed in Table 3 for each temperature setting. Typical recorded temperature points in the experiments with PC using a single cavity and PP using the two-cavity configuration are shown in Fig. 8, where the melt temperature setting was decreased by 5[degrees]C after 50 shots, and then the mold temperature setting was increased by 5[degrees]C after another 50 shots.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

The process and quality models shown in Eqs. 2 and 3 were obtained in the modeling experiments. In the experiments with the single cavity, the MS measured by M[S.sub.2] was adopted for process-level MS control, while M[S.sub.3] was used for the same purpose in the experiments with the two-cavity configuration. The estimates of the important parameters, [K.sub.SM] and [a.sub.1], in the process and quality models are given in Table 4.

[FIGURE 10 OMITTED]

To favor robust system stability, slightly larger values than the estimates in Table 4 were used to calculate the controller parameters. The closed-loop poles were placed at 0.4, 0.3, and 0.3 for fast and stable responses. Even though two poles are at the same location, the root loci do not leave the real axis under small parameter uncertainty when a larger [^.K.sub.SM] value is used [20]. The resulting controllers in the different experiments are given in Eqs. 21 and 22.

[FIGURE 11 OMITTED]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)

In Figs. 9-11, the weights obtained using cavity-pressure based control, direct weight feedback control without disturbance input decoupling, and direct weight feedback control with disturbance input decoupling are shown sequentially in (a), (b), and (c), respectively, for comparison. In the direct weight feedback control without disturbance input decoupling, the path from the temperature disturbances to the MS reference was cut off. Thus, the only control action was from feedback. The same controller parameters were used for direct weight feedback controls with and without disturbance input decoupling. Table 5 summarizes the statistical information including the mean and standard deviation of the part weight in each of the experiments with different control methods.

The experimental results in Table 5 and Figs. 9-11 clearly suggest that the direct weight feedback controls achieved more consistent and accurate part weight, and thus part quality, than cavity pressure based control when encountering the same temperature disturbances. The direct weight feedback control can regulate the part weight to its reference, but the weight cannot be directly assigned in process-level cavity pressure based control. In the two investigated schemes of direct quality feedback control, the disturbance input decoupling further improved the performance by reducing both the transition period and the magnitude of weight variations when the melt or mold temperatures were changed. The benefit of disturbance input decoupling is gained by counteracting the temperature effects on the part weight before they take place. Additionally, the quality improvement obtained in all experiments with the different mold geometries and resins builds confidence in generalizing the proposed method.

CONCLUSIONS

A direct quality feedback control system has been proposed and implemented for injection molding in this paper. It had a cascade structure and combined both feedback and feedforward controls. At the outer quality loop, the quality index, part weight, was measured online and regulated by manipulating the maximum mold separation. Next, the mold separation was controlled at an inner loop by changing the mass-based switchover and holding pressure. Both cycle-to-cycle control and within-cycle control were adopted to eliminate long-term and short-term quality variations. The cycle-to-cycle control included updating the references for the maximum mold separation and mass-based switchover point in each shot. Corresponding weight and MS controllers were designed using the pole-placement method based on the resultant process and quality models. The details of these models, including structure and parameters, were also presented.

The proposed closed-loop quality feedback control was evaluated in experiments by using different resins and mold configurations. The experimental results showed that closed-loop quality control can achieve much better part quality in terms of weight consistency and accuracy than cavity pressure based control, which is regarded as the most prevailing and advanced method in the injection molding industry.

Compared with process and machine controls for injection molding, direct quality feedback control has additional benefits, such as 100% quality inspection and automatic process tuning. Its successful application on the shop floor will depend on the development of quality sensors and measurement equipment. There are on-going research efforts to develop and apply innovative sensors to monitor the process and detect part quality [21, 22]. It is desirable to see more automated devices, including robotics, machine vision, and nondestructive sensors, to be used in injection molding. In the face of extensive competition from the global market, the degree of automation has to be improved for injection molding.

ACKNOWLEDGMENTS

The authors thank Professor Kuo K. Wang of Cornell University and Dr. Daniel F. Caulfield of the Forest Products Laboratory, USDA-Forest Service, for their technical support.

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Zhongbao Chen, Lih-Sheng Turng

Polymer Engineering Center, Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1572

Correspondence to: Lih-Sheng Turng; e-mail: turng@engr.wisc.edu

Contract grant sponsor: National Science Foundation; contract grant number: EEC-0332696.
TABLE 1. DOE results for quality modeling (resin: PC).

[T.sub.m] [T.sub.w] [MS.sub.max]
([degrees]C) ([degrees]C) [P.sub.p] (MPa) Wt (g) ([micro]m)

315 75 5 10.1101 69.45
 10.0211 52.07
315 75 4 9.7185 21.33
 9.7097 15.18
315 65 5 10.0611 50.24
 10.0169 42.11
315 65 4 9.7472 16.51
 9.7372 13.75
305 75 5 9.8964 34.99
 9.9247 32.51
305 75 4 9.6509 5.01
 9.6797 10.61
305 65 5 9.8846 22.79
 9.9486 29.39
305 65 4 9.6436 1.14
 9.6789 5.51

TABLE 2. Coefficient values in the quality model built upon experiments.

[Wt.sub.0] 9.92888
[a.sub.1] 0.18818
[a.sub.2] -0.03621
[a.sub.3] -0.04112
[a.sub.4] -0.01408
[a.sub.5] -0.01412

Coefficient unit: gram.

TABLE 3. Process conditions in the closed-loop quality control
experiments.

 PP
Process conditions Single cavity Two cavity PC

[T.sub.m] ([degrees]C) 200, 205 210, 215 310, 315
[T.sub.w] ([degrees]C) 35, 40 30, 35 60, 65
[V.sub.r] (mm/s) 35 40 35
[P.sub.p] (Mpa) 5.0 5.0 4.5
[t.sub.pack] (s) 4.0 4.0 5.0
[t.sub.cool] (s) 20 25 25
W[t.sub.ref] (g)/ 7.05/18.5 20.35/11.5 9.80/13.5
 P[c.sub.ref] (MPa)

TABLE 4. The estimates of [K.sub.SM] and [a.sub.1] in the process and
quality models.

Experiments [K.sub.SM] ([micro]m/g) [^.a.sub.1] (g/[micro]m)

PC, single cavity 25.0 0.00941
PP, single cavity 38.0 0.00381
PP, two cavity 40.0 0.00927

TABLE 5. Comparison of the performance of different control methods.

Experiments Control method* [Wt.sub.ref] (g) Mean (g) StDev (g)

PC, one cavity Pc N/A 9.7878 0.0294
 Wt Fb 9.80 9.8001 0.0085
 Wt Fb+DID 9.80 9.8022 0.0058
PP, one cavity Pc N/A 6.9537 0.0119
 Wt Fb 7.05 7.0500 0.0070
 Wt Fb+DID 7.05 7.0525 0.0040
PP, two cavity Pc N/A 20.3686 0.0338
 Wt Fb 20.35 20.3518 0.0124
 Wt Fb+DID 20.35 20.3507 0.0096

Experiments Control method* Max (g) Min (g)

PC, one cavity Pc 9.8689 9.7410
 Wt Fb 9.8207 9.7716
 Wt Fb+DID 9.8150 9.7865
PP, one cavity Pc 6.9769 6.9308
 Wt Fb 7.0638 7.0265
 Wt Fb+DID 7.0611 7.0386
PP, two cavity Pc 20.4141 20.2773
 Wt Fb 20.3820 20.3167
 Wt Fb+DID 20.3719 20.3169

* Pc, Cavity pressure based control; Wt Fb, direct weight feedback
control; Wt Fb+DID, direct weight feedback control plus disturbance
input decoupling.
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Author:Chen, Zhongbao; Turng, Lih-Sheng
Publication:Polymer Engineering and Science
Geographic Code:1USA
Date:Jun 1, 2007
Words:5427
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