An investigation on the application of predictive control for controlling screw position and velocity on an injection molding machine.

INTRODUCTION

The injection molding process, which consists of filling, packing, holding, and cooling phases, is widely used in plastics industries due to its ability to produce intricate shape products efficiently and effectively. The quality of the molded parts, particularly the mechanical properties, such as tensile and impact strength, is strongly affected by the nature of the polymer flow entering the mold cavity [1].

The dynamic characteristic of the filling phase is very complex as it is a function of several process variables, including material properties, melt temperature, and mold cavity geometry. Agrawal et al. [2] have shown that controlling the injection velocity is the most essential during filling and therefore, the entire phase can be regulated by controlling the speed of the ram to follow the desired trajectories. It has been confirmed that an accurate and tight closed loop control of injection velocity is vital and has a significant improvement in the overall product quality [3-5].

Many investigations have been conducted to improve injection velocity control performance by developing better plant models as well as controller algorithms. Wang et al. [6] derived a fourth-order transfer function for air-shot injection operations. However, this model did not reflect the real plant since the nozzle and mold resistances and their corresponding pressure functions were not considered. Pandelidis and Agrawal [7-9] performed a series of control simulations for injection velocity on an injection molding machine (IMM). A nonminimum phase self-tuner control was first implemented [7] utilizing the model developed in Ref. 6 and then followed by the application of optimal anticipatory control [8]. The effectiveness of the optimal deterministic observer and Kalman filter to estimate the state variables in the presence of disturbance and/or noise were discussed in Ref. 9. The simulation results showed that the controller was able to closely follow the setpoint profiles and provided better control performances than a PID controller.

Tan and coworkers [10, 11] conducted control simulations using a learning-enhanced PI controller and sliding mode control based on a nonlinear physical model given in Ref. 12. However, none of their work was tested experimentally and the nonlinearity characteristic of the injection velocity was ignored. Zhang et al. [13] proposed an adaptive control approach for tracking injection velocity, but no detailed design procedure or theoretical analysis of the proposed control scheme was provided. A fuzzy controller was designed and implemented [14] with good results, which accounted for the nonlinearity of the injection velocity. However, the controller design required extensive theoretical knowledge of the process, which may not be possible in many instances. Self tuning adaptive control was proposed by Yang and Gao [15] as an alternative for controlling a process that is both nonlinear and time varying. Consistent and good performances have been achieved; however, the controller was very sensitive to mismatch between the actual process delay and its estimation.

Yang and Gao [16] implemented a new adaptive controller based on a generalized predictive controller, which was more robust to the model delay mismatch. Fuzzy multimodel adaptive control, which represents the process dynamic over a wide operating range, was also developed and implemented for injection velocity control results in an improved closed-loop control of injection velocity [17]. Gao et al. [18] demonstrated robust iterative learning control as an effective and efficient control strategy for injection velocity control. However, the controllers in Refs. 16-18 were tested on a small range of injection velocity only, i.e. a maximum velocity of 40 mm/s. Dubay and Lakhram [19, 20] proposed a polymer and melt temperature dependent controller, which allow the dynamic matrix of the controller to be redefined online as changes in the melt temperature occurred. Although, an improved closed-loop performance was achieved, the controller was only implemented for simple injection velocity profiles.

Current IMMs have the ability to produce larger and more complicated parts and hence, the importance of good injection velocity profiling becomes more significant. Proper velocity profiling and its accurate tracking improve the product quality, reduce the number of rejects, increase the productivity (shorter injection time), and it is highly recommended for precision molding [21, 22]. A desired flow front velocity and advancement, which indicate whether the cavity is properly filled, are critical factors during filling and it can be achieved if good injection velocity control is available [23].

A great deal of research effort has been devoted on finding "the optimal" injection velocity profile to minimize injection time while maintaining a uniform melt flow front velocity. These objectives cannot be readily achievable if the design of the controller does not provide robust and tight control. As discussed above, different types of controllers have been developed and implemented for injection velocity control. Dynamic matrix control (DMC) [24, 25], which belongs to MPC family, has been successfully applied not only on slow reacting processes but also fast reacting processes [26-30]. The simplified form of DMC known as simplified predictive control (SPC) [31] minimizes only one future error at a distance D on a prediction horizon to evaluate a single control move, results in reduced computational effort over DMC. In addition, SPC provides just as good robust stability as the DMC for a wide range of process uncertainties [32]. This article is focused on the development and investigation of control system for injection velocity during filling phase using SPC and DMC on an IMM.

EXPERIMENTAL

The experimental work was conducted on 150 tonne industrial scale IMM. The injection unit is equipped with a translational position transducer, having a DC voltage output of 0-10 V corresponding to a linear displacement of 0-200 mm. The transducer output is sent to 16-bit data acquisition (DAQ) board via a shielded cable and a field screw terminal. A control algorithm developed and written using Lab Windows CVI was used to measure, control, and display the controlled and manipulated variables in real-time. The control system includes an industrial control computer, sensors (translational potentiometers, pressure transducers, etc.), and actuators (proportional and servo valves, relays, etc.). The servo valve is used to control the injection screw position and velocity. Low density polyethylene and general purpose polypropylene were used in this investigation.

BACKGROUND

Injection Velocity

Velocity profiling can be used to achieve a constant melt flow front velocity that affects molecular orientation and internal stresses produced in the molded parts [2]. Experienced molders determine velocity profiles through an iterative trial and error method. General guidelines have been established for defining an injection velocity profile [33] and a typical multistep injection velocity profile for mold geometry with varying cross-sectional area is depicted in Fig. 1.

It is important to note that different injection profiles should be adopted for molds with different geometries and for different plastic materials being processed. In addition, the injection velocity profile to satisfy the given guidelines has to be achieved in the short duration of time available for high speed mold filling. These considerations impose stringent requirements on the control scheme to closely follow the desired injection velocity trajectory.

[FIGURE 1 OMITTED]

Predictive Control

The model predictive control (MPC) strategy comprises of controller variables predictor and optimizer. The predictor uses a process model, the past and future control moves to determine the controlled variable (in this case injection velocity) predicted trajectory over a prediction horizon P. The process model known as the dynamic matrix contains the normalized step response coefficients of the process parameters to be controlled, i.e. screw position or injection velocity. For a single-input-single-output system, the dynamic matrix is expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

The optimizer generates a sequence of optimal control moves to satisfy a predefined objective function J given by the following equation.

[J.sub.MPC] = min{[P.summation over (k=1)][y(t + k) - [^.y](t + k|t)][.sup.2] + [lambda][[n.sub.u].summation over (k=1)][[DELTA]u(t + k - 1)][.sup.2]}. (2)

The first term in Eq. 2 is defined as the future errors e, which represents the difference between the reference trajectory y, i.e. screw position or velocity, and its corresponding predicted outputs [^.y] over P. [^.y](t + k|t) is the value of the prediction k steps into the future given information up to time t. The length of P represents the number discrete sampling instants that the screw position or velocity trajectories are predicted in the future. The second term is the changes in the control moves or manipulated variables, which are to be evaluated over a control horizon [n.sub.u]. The move suppression coefficient [lambda] is introduced to avoid excessive changes in the manipulated variable (analog voltage to a servo-valve) due to the ill-conditionality of the system matrix [A.sup.T]A. Using the least squares method, Eq. 2 yields the DMC control law,

[DELTA]u = ([A.sup.T]A + I[lambda])[.sup.-1][A.sup.T](y - [^.y]) (3)

subject to the following constraints,

[u.sub.min] [less than or equal to] u [less than or equal to] [u.sub.max]. (4)

The prediction of the process output or controlled variable is calculated using

[^.y](t + k|t) = [^.y](t) + [k.summation over (i - k - [n.sub.u] + 1)] [a.sub.i][DELTA]u(t + k - i) + [k + P - 1.summation over (i=k - 1)] ([a.sub.i] - [a.sub.i - k])[DELTA]u(t + k - i) + [phi](t) for k = 1, 2,..., P; i > 0; [n.sub.u] < P (5)

with [phi](t) an adjustment parameter that accounts for process nonlinearities. Further details of the DMC control theory can be found in Refs. 24 and 25.

The computational effort for solving the above optimization problem depends on the magnitude of P and [n.sub.u]. Since this optimization problem needs to be solved at every sampling instant, the SPC algorithm [31] has been proposed to significantly reduce the computational effort. SPC minimizes only one error at point D on the prediction horizon and also uses D as its tuning parameter. As D increases, the control moves becomes smaller and the robustness of the system increases and vice versa. In SPC, the objective function of standard DMC given in Eq. 2 simplifies to [34]

[J.sub.SPC] = min{[summation][y(t + k) - [^.y](t + k|t)][.sup.2]}. (6)

The manipulated variable is given by

[DELTA]u = [y - [^.y]]/a(D) (7)

where a(D) represents the normalized open loop response coefficient at a distance D step ahead.

Further details of SPC theory can be found in Ref. 31 and 32.

System Identification

The most commonly used models to represent the relationship between inputs and outputs are difference equations, for example auto-regressive exogenous. The system linear difference equation can be expressed as

[psi]([q.sup.-1])y(t) = B([q.sup.-1])u(t) + e(t). (8)

Term e is an error term while [psi] and B are polynomials of the delay operator [q.sup.-1] expressed as

[psi]([q.sup.-1]) = 1 + [[psi].sub.1][q.sup.-1] + ... + [[psi].sub.n.sub.a][q.sup.-[n.sub.a]] (9)

B([q.sup.-1]) = [b.sub.1][q.sup.-(1 + d)] + ... + [b.sub.n.sub.b][q.sup.-([n.sub.b] + d)] (10)

where [[psi].sub.1] ... [[psi].sub.n] are the coefficients for past plant output or controlled variable and [b.sub.1] ... [b.sub.m] is the input or manipulated variable coefficients.

The variables [n.sub.a] and [n.sub.b] represent the orders of the model, while d represents the process delay. The [1 + d] term on the coefficient [b.sub.1] indicates that there is at least one interval of delay in addition to d time intervals.

SCREW INJECTION POSITION CONTROL

Position-Time Based Setpoint

The relation between translational velocity-position and position-time profiles for the IMM will be described here. A screw velocity setpoint profile is usually divided into several sections and inputted as machine setup data of velocity values v at corresponding screw positions x. The analyses begins with the continuous form of the fundamental rectilinear motion formulae [35], rewritten to evaluate the screw position and velocity at any ith section as a function of time. For any ith section of the maximum k, the acceleration [a.sub.i] can be expressed as

[a.sub.i] = [1/2] x [[[v.sub.ie.sup.2] - [v.sub.is.sup.2]]/[[x.sub.ie] - [x.sub.is]]]. (11)

Subscript i indicates the section number, while subscripts s and e indicate the start and the end of the ith section, respectively. Using Eq. 11 and the formulae in [35], the duration [T.sub.i] taken to complete each ith section can be evaluated using the following expression.

[T.sub.i] = [2([x.sub.ie] - [x.sub.is])]/[[v.sub.ie] + [v.sub.is]]. (12)

The instantaneous velocity [v.sub.i] and position [x.sub.i] is then

[v.sub.i](t) = [v.sub.is] + [1/2] x [[[v.sub.ie.sup.2] - [v.sub.is.sup.2]]/([x.sub.ie] - [x.sub.is])] x [t.sub.i] (13)

[x.sub.i](t) = [x.sub.is] + [v.sub.is] x [t.sub.i] + [1/4] x [[[v.sub.ie.sup.2] - [v.sub.is.sup.2]]/([x.sub.ie] - [x.sub.is])] x [t.sub.i.sup.2] (14)

for 0 [less than or equal to] [t.sub.i] [less than or equal to] [T.sub.i] and i = 1, 2, 3,..., k.

Here [t.sub.i] is the instantaneous time within the ith segment. It is to be noted that the start of the ith segment restarts at t = 0 and ends after [T.sub.i] has elapsed.

An example of a velocity vs. position setpoint profile for an IMM, which was divided into 10 stages is given by profile VP394 in Table 1 and illustrated in Fig. 2. VP394 and other labels in Tables 1 and 2 indicate the injection velocity profiles. Using the above procedure, the VP394 profile is then transformed into [x.sub.i](t) vs. time profile for position control, with the desired setpoint profile shown in Fig. 3.

Control Simulation and Real Time Applications

Open Loop Testing and Model Identification. To perform open loop tests in the vicinity of the setpoint trajectory, a mathematical equation relating the voltage input to the servo-valve and the screw injection velocity is required. Preliminary tests include sending several analog voltage values to the servo-valve and recording corresponding screw velocities. The mathematical equation is evaluated as

[u.sub.ol] = (1.46493 [10.sup.-5][y.sub.ss.sup.3]) - (4.04539 [10.sup.-5][y.sub.ss.sup.2]) - (0.06334[y.sub.ss]) + 0.29539 (15)

where [y.sub.ss] and [u.sub.ol] represent the open loop injection velocity (steady state) and its corresponding voltage signal to the servo-valve, respectively.

[FIGURE 2 OMITTED]

The open loop tests conducted for position control are categorized into two types, i.e. single-step change open loop (SCOL) and multistep change open loop (MCOL) tests. SCOL tests were conducted by sending a constant voltage signal to the injection servo-valve for the entire stroke and collecting position data with a sampling time of 10 ms. On the other hand, for the MCOL tests, there are more than one voltage signal sent to the servo-valve based on changes in the closed loop setpoint values. The voltages (manipulated variable) that are sent to the valve are obtained from Eq. 15.

For each SCOL test, only one model is derived, which represents the system dynamics corresponding to a certain injection velocity region. In this investigation involving SPC based on SCOL tests, the operating region was divided into two ranges, i.e. 0-50 mm/s and 50-100 mm/s. These regions correspond to two different step input values to the servo-valve, 30 and 70% of the maximum voltage input, which provide dynamic responses that fall within these two regions. All of the open loop tests were conducted using the correct shot size of molten plastic, which was injected into the mold in order to capture the true dynamic behavior of the screw motion. An example of a SCOL response corresponding to an injection velocity of 70 mm/s (where this velocity is the closed loop set-point steady state) is depicted in Fig. 4, and a 2nd order model identified from open loop data is given by

[G.sub.70] = [-0.0122[q.sup.-1]]/[1 - 0.7526[q.sup.-1] - 0.2464[q.sup.-2]]. (16)

[FIGURE 3 OMITTED]

[G.sub.70] represents the plant dynamics subjected to input to servo valve that give ~70 mm/s injection speed at steady state, while q represents the backward shift operator. These plant models obtained from the open loop tests were used to conduct the control simulations, and to construct individual dynamic matrices A required for practical implementation of the predictive controller.

[FIGURE 4 OMITTED]

In many instances, the molding of a part requires the screw to follow a multiple setpoint velocity profile and therefore, it is reasonable to conduct MCOL tests to formulate more than one dynamic matrix A. These tests were conducted by sending profiled voltage inputs to the servo-valve based on a desired setpoint trajectory, in order for the steady state open loop injection velocity fall within [+ or -]20% of closed loop steady state. Figure 5 shows a MCOL response test that closely follows the position set-point trajectory shown in Fig. 3 and the normalization process to construct the dynamic matrix A and to obtain the corresponding plant models or transfer functions. The dashed lines (constant slopes) approximate the open loop response of the screw position if the input voltages were not changed. With the screw initially at rest, the discrete response profile [A.sub.1] represents a 30% change in the voltage signal. [A.sub.2] and [A.sub.3] represent an added 60% change in the manipulated variable from [A.sub.1] and a -50% change from [A.sub.2]. From open loop data, the three normalized transfer functions corresponding to the open loop tests and injection setpoint changes were evaluated as

[FIGURE 5 OMITTED]

[G.sub.1] = [-0.3306[q.sup.-1]]/[1 - 0.5285[q.sup.-1] - 0.471[q.sup.-2]] (17)

[G.sub.2] = [-0.3951[q.sup.-1]]/[1 - 0.6279[q.sup.-1] - 0.3708[q.sup.-2]] (18)

[G.sub.3] = [-0.1707[q.sup.-1]]/[1 - 0.5337[q.sup.-1] - 0.4641[q.sup.-2]]. (19)

[G.sub.1], [G.sub.2], and [G.sub.3] represent the plant, i.e. the screw position dynamics for the sections 1, 2, and 3 as shown in Fig. 5, respectively. The models are used to conduct control simulations to determine the controller tuning parameters that are best suited for practical implementations on the injection screw. It is important to note that the setpoint velocity profile must be known prior to conducting the MCOL tests.

Practical Control on the IMM (SPC). A SPC controller was employed for control simulations of injection position using the plant SCOL model in Eq. 16 for profile VP6973 in Table 1, with controller parameter P = 200 and D of 5, 10, and 15. Good control performance was achieved and the result for D = 15 is shown in Fig. 6. Although the value D of 5 provides the closest response to the setpoint profile as indicated by the smallest IAE, the manipulated variable changes dramatically in the high velocity range. This can have significant effects on IMM during practical injection velocity control, resulting in dithering of the screw, which is harmful to the IMM components such as the hydraulic valves and injection cylinders. Therefore, a value of the tuning parameter D = 15 is best suited for real time applications without affecting the controller performance.

Control simulations for the same velocity setpoint profile VP6973 in Table 1 were conducted on [G.sub.1], [G.sub.2], and [G.sub.3] (representing the plant), given by Eqs. 17-19, respectively. The controller was tested using D values of 5, 10 and 15, and the result for D = 15 is depicted in Fig. 7. Prediction horizon P was set to 200 with the sampling time of 10 ms. The MCOL exhibited similar performance to the SCOL controller during the closed loop experiments where the IAE values increase as D increases. However, increasing D results in smoother closed loop responses with minimal oscillations in the manipulated variables, and hence, a higher value of D will be chosen in the real time applications.

The results of these control simulations using the plant models in Eqs. 16-19 indicated that SPC algorithm using SCOL and MCOL provide good closed loop control performance of injection screw position, which directly controls the injection velocity. Hence, the controller is expected to work well in real time applications on IMM. Control simulations also gave valuable insight into the dynamics of the system and the values of the controller tuning parameters to be used in the real time applications.

[FIGURE 6 OMITTED]

The controller developed in simulation using plant models in Eqs. 16-19 was then implemented on the 150 tonne IMM for profiled velocity closed loop control with tuning parameter D set to 15 for all applications. Using a setpoint profile VP394 in Table 1 with polyethylene material, good control performance was achieved for both SCOL and MCOL approaches controller. The closed loop responses and its corresponding manipulated variables are depicted in Figs. 8 and 9 for SCOL and MCOL, respectively. It can be seen that the manipulated variables in both instances are smooth showing a sharp increase with minimal oscillations when the setpoint is changed from 30 to 90 mm/s. Experiments were conducted using set-point profile VP6793 in Table 1 using polypropylene for both SCOL and MCOL with good results and corresponding IAE values of 122 and 180. These results indicated that SPC algorithm can effectively control various speed profiles for different polymers using the screw position feedback.

In most instances, the practical results showed larger IAE values when using the MCOL tuned controller in comparison to the SCOL case. Figure 10 shows a comparison between SCOL and MCOL tuned controller with set-point profile VP394. Using the same D = 15 and the same temperature conditions along the barrel zones, the IAE value of the SCOL tuned controller is smaller (25%) as compared with the MCOL tuned controller. In general, the differences in the IAE values are relatively small and therefore, there is no significant advantage of using the SPC controller tuned with the MCOL approach. The MCOL tuned controller can be made to have better closed loop performance than SCOL, if different D values are used during setpoint changes, which presents a future topic requiring further investigations.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

SCREW INJECTION VELOCITY CONTROL

Multimodel Predictive Control

Unlike the above controller, multimodel predictive control (MMPC) uses the injection velocity as the controlled variable and DMC as the control methodology. The screw position signal is now used as an indicator to initiate an injection velocity setpoint change. The velocity signal was made available by the IMM manufacturer and was monitored and fed to the DAQ board as feedback. Injection velocity has been experimentally shown to be a nonlinear and time varying process, which makes it difficult to control especially when tracking a multi-setpoint profile [14]. Although it is assumed that the process to be controlled is linear and time-invariant, DMC has the ability to handle nonlinear process well by introducing an adjustment parameter in the process prediction. Eq. 5 [24]. However, the control performance decreases significantly when the nonlinearity becomes more pronounce. In this article, the application and ability of a MMPC to overcome the process nonlinearity during filling was investigated. The control strategy involves generating normalized open loop coefficients, i.e. dynamic matrices A, corresponding to the changes in the desired closed loop injection velocity setpoint profiles and the polymer materials. Therefore Eq. I can be rewritten and expressed as

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

where the operating regions b represent changes in the injection velocity setpoint profiles for different plastic materials r. Solving the objective function that is now region dependent, the DMC control law in Eq. 3 becomes

[b.[DELTA]]u = ([b.A.sup.T][b.A] + I[lambda])[.sup.-1][b.A.sup.T](y - [^.y]). (21)

From Eq. 21, the MMPC algorithm selects the corresponding dynamic matrix [b.A] seamlessly, when a setpoint change in injection velocity is encountered. This indicates that a new objective function is minimized the instant a setpoint change in injection velocity occurs. Furthermore, the future predictions of the controlled variable are now based on [b.A] as in Eq. 22.

[FIGURE 11 OMITTED]

[^.y](t + k|t) = [^.y](t) + [k.summation over (i=k - [n.sub.u] + 1)][b.a.sub.i][DELTA]u(t + k - i) + [k + P - 1.summation over (i=k + 1)]([b.a.sub.i] - [b.a.sub.i - k])[DELTA]u(t + k - i) + [phi](t) for k = 1, 2,..., P; i > 0; [n.sub.u] < P. (22)

Open Loop Tests and Real Time Applications

Multi-Steps Open Loop Test. Once the desired injection velocity profile has been defined, the controller is setup such that an open loop test corresponding to the velocity setpoint profiles is performed. This can be achieved by determining and sending the required voltages using Eq. 15 to the servo-valve such that the screw injection travels with an open loop velocity as close as possible to the profiled steady state setpoint velocities. Figure 11 shows an air-shot open loop response with the injection velocity profile VPA39273 in Table 2 and screw stroke of 200 mm (open loop response for VPA2479 not shown). Normalized multisteps open loop coefficients are then determined from the open loop responses and saved automatically to construct the dynamic matrices [b.A] in Eq. 20 with the selected values of P and [n.sub.u]. The number of dynamic matrices available to the controller depends upon the number of step changes in the setpoint profiles. For an open loop test shown in Fig. 11, there are five dynamic matrices corresponding to each of the step change. In this investigation, the value of P and [n.sub.u] were set to 300 and 2 respectively. A faster sampling interval of 4 ms was used since the rate of change of injection speed signal is much faster as compared with the position control, which uses 10 ms.

[FIGURE 12 OMITTED]

Practical Control on the IMM. The proposed approach was implemented on the IMM using several injection velocity profiles with different stroke sizes. Figure 12 shows that good control performance was achieved for air-shot with injection velocity setpoint profile VPA39273 in Table 2 and stroke size of 200 mm. It can be seen that the injection velocity reaches its setpoint values within ~0.3 s for both positive and negative setpoint changes without overshoot with the tuning parameter [lambda] set to 1.06. The MMPC algorithm allows different setting of [lambda] for each dynamic matrix.

Figure 13 shows that good control performance with the settling time of ~0.3 s was obtained when the controller is subjected to setpoint changes given by profile VP158 in Table 1. In this test, polyethylene material was injected into the mold cavity with the stroke size of 84 mm. The tuning parameter [lambda] was set to 1.05 for the first step change and 1.08 for the successive increase in the setpoints. Lower value of [lambda] is necessary for the initial step since the screw is at rest, which requires more aggressive changes in the manipulated variable to overcome its inertia and viscous friction effects. Once the screw is moving, higher values of [lambda] were used to minimize or prevent overshoot. The controller was also tested by injecting polymer into the mold using a high injection velocity setpoint (SVP110, Table 1), i.e. 110 mm/s, with good result as depicted in Fig. 14. Figure 15 shows another multi-setpoint velocity profile VP253 (Table 1) with good control performance. These results indicate that the approach is well suited to control the screw injection velocity effectively for various velocity setpoint profiles.

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

The major challenge on the application of SPC and MMPC algorithms is that the open loop tests have to be conducted for various molds and polymer types in conjunction with specific setpoint trajectories. However, the main improvement in both algorithms is the application of multimodel DMC when changes in the setpoint in the screw position and velocity occur.

CONCLUSION

Two different predictive control approaches were investigated for controlling the screw injection velocity on a 150 tonne IMM. A position transducer and velocity information extracted via high speed analog processing of the position voltage signal were two forms of feedback that were available. An SPC screw position controller was developed demonstrating good control performance for all closed loop simulations and experimental tests. These results indicate that the SPC algorithm can effectively control various speed profiles for different polymers using the injection screw position feedback.

[FIGURE 15 OMITTED]

An MMPC for screw injection velocity control was developed and implemented with good results. This approach allows the controller to be updated automatically when changes in the velocity setpoint profile occur. This makes the method more capable of handling the inherent nonlinearities in the system. The control simulations and real-time implementations indicated that MMPC provides good control performance for multi-setpoint velocity profiles. The ability of the above mentioned control strategies to track closely various setpoint profiles during a very short time, demonstrates that wide ranging setpoints can be specified than currently possible. This in turn would provide tighter control over the filling phase and therefore lead to improved product quality. These control strategies can be applied to any size IMM and corresponding mold and material.

REFERENCES

1. H.W. Cox and C.C. Mentzer, Polym. Eng. Sci., 26, 488 (1986).

2. A.R. Agrawal, I.O. Pandelilis, and M. Pecht. Polym. Eng. Sci., 27, 1345 (1987).

3. C. Ou-Yang and G.P. Maul. Int. J. Prod. Res., 27. 1917 (1989).

4. Y. Yang and F. Gao, J. Reinforc. Plast. Compos., 20. 1160 (2001).

5. D.V. Rosato, D.V. Rosato, and M. G. Rosato, Injection Molding Handbook, 3rd ed., Kluwer, Boston (2000).

6. K.K. Wang, S.F. Shen, C. Cohen, A.C. Hieber. T.H. Kwon, and R.C. Ricketson. "Injection Molding Project Progress." Progress Report. No. 11. Cornell University. Ithaca, NY (1985).

7. I.O. Pandelidis and A.R. Agrawal. SPE ANTEC Tech. Papers, 33, 235 (1987).

8. I.O. Pandelidis and A.R. Agrawal, Polym. Eng. Sci., 28, 147 (1988).

9. I.O. Pandelidis and A.R. Agrawal, Polym. Eng. Sci., 28, 157 (1988).

10. K.K. Tan and J.C. Tang. Eng. Appl. Artif. Intell., 15. 65 (2002).

11. K.K. Tan, S.N. Huang, and X. Jiang, IEEE Trans. Control Syst. Tech., 9, 4 (2001).

12. M. Rafizadeh, W.I. Patterson, and M.R. Kamal, Int. Polym. Process., 11, 352 (1996).

13. C.H. Zhang, J. Leonard, and R.C. Speight, SPE ANTEC Tech. Papers, 42, 593 (1996).

14. H.P. Tsoi and F. Gao, Polym. Eng. Sci., 39. 3 (1999).

15. Y. Yang and F. Gao, Int. Polym. Process., 14. 196 (1999).

16. Y. Yang and F. Gao, Control Eng. Pract., 8. 1285 (2000).

17. M. Li, Y. Yang. F. Gao, and F. Wang, Can. J. Chem. Eng., 79, 263 (2001).

18. F. Gao, Y. Yang, and C. Shao, Chem. Eng. Sci., 56, 7025 (2001).

19. R. Dubay and R. Lakhram, Polym. Eng. Sci., 44, 1925 (2004).

20. R. Dubay and R. Lakhram, Polym. Eng. Sci., 44, 1934 (2004).

21. R.G. Speight, A. J. Monro, and A. Khassapov, "Recent Advances in Ultrasonic Monitoring of the Injection Molding Process," paper presented in the SPE ANTEC Technical Papers, Atlanta (1998). No. 0785.

22. D.L. Smith, SPE ANTEC Tech. Papers, 21, 225 (1975).

23. S.L. Wen, C.K. Jen, K.T. Nguyen, A. Derdouri, and Y. Simard, "Benefits of Velocity Phase Profiles for Injection Molding." SPE ANTEC Tech. Papers, New York (1999). No. 0516.

24. C.R. Cutler and B.L. Ramaker, "Dynamic Matrix Control--A Computer Algorithm," in the Proceedings of the Joint Automatic Control Conference. San Francisco, CA, (1980).

25. C.R. Cutler, "Dynamic Matrix Control--An Optimal Multivariable Control with Constraints," PhD. Dissertation, University of Houston, Houston (1983).

26. S.N. Maiti, N. Kapoor, and D.N. Saraf, Ind. Eng. Chem. Res., 33, 641 (1994).

27. S.J. Qin and T.A. Badgwell, "An Overview of Industrial Model Predictive Control Technology," in the Proceedings of the Fifth International Conference on Chemical Process Control, Tahoe City, CA, 232 (1997).

28. M. Morari and J. H. Lee, Comput. Chem. Eng., 23, 667 (1999).

29. B. Pramujati and R. Dubay, J. Injection Molding Technol., 6, 247 (2002).

30. D. Dougherty and D. Cooper, Control Eng. Pract., 11, 141 (2003).

31. Y.P. Gupta, Comput. Ind., 21, 255 (1993).

32. Y. P. Gupta, Can. J. Chem. Eng., 71, 617 (1993).

33. D.B. Hunkar, SPE ANTEC Tech. Papers, 21, 161 (1975).

34. F. Zhao and Y. P. Gupta, ISA Trans., 44, 187 (2005).

35. F.P. Beer, E.R. Johnston, and W.E. Clausen, Vector Mechanics for Engineers: Dynamics, 7th ed., McGraw-Hill, New York (2004).

Rickey Dubay, (1) Bambang Pramujati, (2) Jianguo Han, (1) Franz Strohmaier (3)

(1) Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3

(2) Department of Mechanical Engineering, Sepuluh Nopember Institute of Technology, Surabaya, East Java 60111, Indonesia

(3) Engel Canada Inc., 545 Elmira Road, Guelph, Ontario, Canada N1K 1C2

Correspondence to: R. Dubay; e-mail: [e-mail]

Contract grant sponsor: National Sciences and Research Council of Canada, Engel Canada Inc., Ropak Canada Inc.

TABLE 1. Injection velocities (mm/s) and its corresponding screw
positions on IMM.

Profile  Screw position (mm)
name     84   75.6  67.2  58.8  50.4  42   33.6  25.2  16.8  8.4

VP394      0   30    30    30    90    90   90    40    40    40
VP6793    60   60    60    70    70    90   90    30    30    30
VP158     15   15    50    50    50    80   80    80    80    80
SVP110   110  110   110   110   110   110  110   110   110   110

TABLE 2. Injection velocities (mm/s) and its corresponding screw
positions on IMM (air-shot).

                         Screw position (mm)
Profile name  200  180  160  140  120  100  80  60  40  20

VPA39273      30   30   90   90   90   20   70  70  70  30
VPA2479       20   20   45   45   70   70   70  90  90  90