Injection process-oriented variable reference trajectory iterative learning linear quadratic control method

Abstract

The application discloses a variable reference trajectory iterative learning linear quadratic control method for an injection molding process, which firstly utilizes the tracking error of the last period in the injection molding process to construct a variable reference trajectory learning strategy; secondly, based on the variable reference trajectory learning strategy, a state space model with prediction ability between the controlled variables and the manipulated variables of the injection molding process is established; and finally, based on the state space model with prediction ability, a variable reference trajectory iterative learning linear quadratic control law is designed. The application avoids the burden of designing a state observer and enhances the control performance of the controlled variables of the injection molding process control system when facing time lag and reference trajectory change.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing technology and relates to a linear quadratic control method for variable reference trajectory iterative learning in the injection molding process. Background Technology

[0002] As a key polymer material, plastics are now widely used in packaging, storage and transportation, aerospace, mold processing, and many other fields. With continuous social development, the demand for plastic products is also constantly increasing. Injection molding machines are the core equipment in the plastic product molding process. With their ability to efficiently process products with complex shapes and stringent dimensional accuracy requirements, they have become the core carrier for achieving large-scale production of high-performance plastic products. Injection-molded products typically possess both scarcity and high added value, and the current market is placing even stricter demands on the quality standards of these products. Therefore, improving the control performance of controlled variables in the injection molding process has become a key technological direction for manufacturing enterprises to improve quality and efficiency and enhance their core competitiveness.

[0003] The injection molding process is characterized by periodicity and repetitive operation, resulting in time delays. Furthermore, the reference trajectory for each cycle changes with product model switching. Traditional iterative learning linear quadratic control methods primarily address time delay issues in two ways: the first relies on feedback mechanisms to passively mitigate the adverse effects of time delays on the control system. However, feedback mechanisms can only passively correct after the time delay has affected the control system, limiting further improvement in the control effect of the controlled variable. The second approach involves designing a Smith predictor to compensate for the impact of time delays on the control system in advance. However, this approach heavily relies on an accurate mathematical model of the controlled object. If there are modeling errors between the model and the actual injection molding process, it not only fails to improve control quality but also exacerbates system fluctuations and deteriorates control performance. Additionally, the injection molding process produces different types of products, and the reference trajectory for each cycle changes with the product type. Existing control strategies do not consider the characteristics of reference trajectory changes with product type, failing to effectively suppress steady-state errors caused by reference trajectory variations and making it difficult to adapt to complex and ever-changing actual production conditions. Therefore, there is an urgent need for a control method that does not rely on an accurate mathematical model of the controlled object, can actively suppress time delays, and can adapt to variable reference trajectories to improve the control performance of the controlled variable. Summary of the Invention

[0004] To address the shortcomings of existing iterative learning linear quadratic control methods in handling time delays and varying reference trajectories, this invention provides a variable reference trajectory iterative learning linear quadratic control method for injection molding processes, aiming to improve the control performance of the controlled variable in the injection molding process. First, based on the repetitive nature of the injection molding process, a variable reference trajectory learning strategy is developed to enhance the control system's ability to handle time delays and changes in the reference trajectory. This strategy uses the tracking error from the previous cycle to anticipate the dynamics of the injection molding system in the future and outputs a predicted reference trajectory. Second, the predicted tracking error is calculated based on the difference between the predicted reference trajectory and the controlled variable. Combining the predicted tracking error with the measured values ​​of the controlled and manipulated variables, a predictive state-space model of the injection molding process is constructed. Finally, based on this predictive state-space model, a variable reference trajectory iterative learning linear quadratic control law is developed.

[0005] The steps of the method of the present invention include: Step (1). Utilize the tracking error of the previous cycle during the injection molding process to construct a variable reference trajectory learning strategy.

[0006] Step (2). Based on the variable reference trajectory learning strategy, establish a predictive state-space model between the controlled variables and manipulated variables in the injection molding process.

[0007] Step 2.1: Describe the relationship between the controlled variable and the manipulated variable in the injection molding process, and convert it into a state-space model. Step 2.2: Define the prediction tracking error, select state variables, and construct a state-space model with predictive capabilities; Step 2.3: Combining a state-space model with predictive capabilities, design an iterative learning linear quadratic control law to obtain the current manipulated variable.

[0008] Step (3). Based on the state-space model with predictive capabilities in step (2), design a variable reference trajectory iterative learning linear quadratic control law, obtain the manipulated variables, and complete the variable reference trajectory iterative learning linear quadratic control for the injection molding process.

[0009] The variable reference trajectory learning strategy in step (1) is essentially a closed-loop feedforward control strategy. After the variable reference trajectory learning strategy is put into operation, it can improve the ability of the injection molding process control system to handle time delays. The specific principle is as follows: As can be seen from the reference trajectory learning strategy, the variable reference trajectory learning strategy can sense the dynamics of the injection molding process control system in advance and embed it into the state space model with predictive capabilities in the form of predicted tracking error, thereby driving the manipulated variable to take action in advance and reducing the impact of time delay on the injection molding process control system through feedforward. When the reference trajectory changes, the controlled variable of the traditional iterative learning linear quadratic control method will not be able to track the reference trajectory in the next few production cycles, resulting in steady-state error. After the variable reference trajectory learning strategy is put into operation, it can avoid the steady-state error problem caused by the change of the reference trajectory. The specific principle is as follows: When the cycle enters the cycle, the cycle and the reference trajectory of the cycle are known. If the reference trajectory of the cycle and the reference trajectory of the cycle are inconsistent, the reference trajectory has changed. At this time, it is not equal to 0, the predicted reference trajectory is equal to the current reference trajectory, the reference trajectory learning strategy is cut off, and relearning is performed to prevent the change of the reference trajectory from affecting the control system. If the reference trajectory of the period is consistent with the reference trajectory of the period, then the reference trajectory has not changed. In this case, it equals 0, the predicted reference trajectory equals the output of the reference trajectory learning strategy, and the reference trajectory learning strategy is put into operation.

[0010] To further verify the feasibility of its application in the injection molding process, the method of this invention needs to select an injection molding process as the controlled object, build a simulation test platform, and conduct simulation tests to fully verify the effectiveness and applicability of the method of this invention, considering the cases where there are model mismatches, interferences and changes in reference trajectories between the actual physical model and the theoretical model.

[0011] This invention proposes a variable reference trajectory linear quadratic iterative learning control method for injection molding processes, which has the following technical advantages and application effects: (1) Based on the repetitive nature of the injection molding process, a variable reference trajectory learning strategy is proposed to improve the ability of the injection molding process control system to handle time delays and reference trajectory changes by introducing the tracking error of the previous cycle. This variable parameter learning strategy can perceive the future dynamics of the injection molding process control system in advance by using the tracking error of the previous cycle and output a predicted reference trajectory.

[0012] (2) By introducing the predicted reference trajectory and the measured values ​​of the controlled variable to calculate the prediction tracking error, and combining the prediction tracking error with the measured values ​​of the controlled and manipulated variables, a state-space model with predictive capabilities is constructed. Unlike traditional state-space models, this model has a certain predictive capability, and each state component can be obtained in real time based on industrial sensors, avoiding the burden of designing a state observer.

[0013] (3) A variable reference trajectory iterative learning linear quadratic control law was developed based on a state-space model with predictive capabilities. This state-space model incorporates the variable reference trajectory learning strategy in the form of a predicted reference trajectory. Since the model state includes prediction and tracking errors, the variable reference trajectory iterative learning linear quadratic control method can reduce the impact of time delay and reference trajectory changes on the injection molding process, thereby enhancing the control performance of the injection molding process control system. Attached Figure Description

[0014] Figure 1 This is a structural diagram of the variable reference trajectory iterative learning linear quadratic control method for injection molding process described in this invention; Figure 2 The integral graph of the squared error of the cavity pressure under different cycles is given when the order of the controlled and manipulated variables in the injection molding process changes and there is a fixed disturbance. Figure 3 The optimal control effect of cavity pressure is determined when the order of the controlled and manipulated variables changes and there is a fixed disturbance during the injection molding process. Figure 4 The diagram shows the control effect of cavity pressure in several specific cycles when the reference trajectory changes in the 51st cycle. Figure 5 To test the trajectory changes in the 51st cycle, the integral graph of the squared error of the cavity pressure under different cycles is shown. Figure 6 The diagram shows the optimal control effect of the cavity pressure when the reference trajectory changes in the 51st cycle. Detailed Implementation

[0015] Taking the mold cavity pressure control during the holding pressure stage of injection molding as an example, such as Figure 1 The specific implementation steps of the present invention are shown in detail below: The injection molding process is mainly divided into four stages: filling, holding pressure, cooling, and product ejection. Among these, the control effect of the mold cavity pressure during the holding pressure stage directly affects the molding quality of the injection molded product. Therefore, improving the control performance of the mold cavity pressure is a core factor in stabilizing product quality. This patent uses a holding pressure regulating valve as the manipulated variable and employs a variable reference trajectory iterative learning linear quadratic control method to adjust the opening of the holding pressure regulating valve, maintaining the mold cavity pressure within the allowable range of the process.

[0016] Step (1). Utilize the tracking error from the previous cycle during the injection molding process to construct a variable reference trajectory learning strategy: a. Establish the tracking error of the mold cavity pressure using the measured value of the current cycle mold cavity pressure and the reference trajectory during the injection molding process: ; in, The production cycle of the injection molding process, Represents discrete time; express cycle The measured value of the mold cavity pressure at any given time. express cycle The reference trajectory of the mold cavity pressure at any given time. express cycle Tracking error of the mold cavity pressure at any time.

[0017] b. Utilize the tracking error of the cavity pressure in the previous cycle to construct a reference trajectory learning strategy for the cavity pressure: ; ; in, for cycle Output of the reference trajectory learning strategy for the pressure in the mold cavity at any given time; and Represents the proportional learning factor and the integral learning factor; This indicates the time delay between the pressure regulating valve and the mold cavity pressure.

[0018] c. Construct a variable reference trajectory learning strategy for cavity pressure using the reference trajectories of the current cycle and the previous cycle: ; ; in, express Period and The sum of the differences in the reference trajectories of the cavity pressure at corresponding time points in the cycle. Indicates the summation symbol; This indicates the running time for each cycle. express cycle Predictive reference trajectory for mold cavity pressure at any given time.

[0019] In step (2), establishing a predictive state-space model between the mold cavity pressure and the pressure-holding regulating valve includes: a. An incremental two-dimensional ARIMA model is used to describe the relationship between the cavity pressure and the pressure-holding regulating valve: ; in, Indicates the first One cycle The measured value of the opening degree of the pressure-holding regulating valve at all times; and The parameters of the incremental two-dimensional ARIMA model, and These represent the orders of the controlled variable and the manipulated variable, respectively. This represents the difference operator along the time direction. ; ; b. Select the following state variables: ; Replace the incremental two-dimensional ARIMA model in step (2)a with a state-space model: ; in, ; ; c. Combine the predicted reference trajectory of the mold cavity pressure in step (1)c. Define the prediction tracking error of the mold cavity pressure. as follows: ; d. Combining the state-space model in step (2)b and the prediction and tracking error of the cavity pressure in step (2)c. We can obtain: ; e. Combining the state-space variables in step (2)b and the prediction tracking error of the cavity pressure in step (2)d. The state variables are reselected as follows: ; f. Combine the state-space model in step (2)b with the state variables in step (2)e. The predictive state-space model can be obtained as follows: ; in, ; ; ; g. Design cycle The linear quadratic control law is learned iteratively from the time-varying reference trajectory as follows: ; in, The linear quadratic control law is learned iteratively using a variable reference trajectory.

[0020] h. Multiply both sides of step (2) g by the left side simultaneously. By combining the state-space model with predictive capabilities in step (2)f, we can obtain: ; Because the model tracks the prediction error of the mold cavity pressure. The variable reference trajectory learning strategy is incorporated into the model state in this form, thus giving the model a certain predictive ability.

[0021] In step (3), the design of the variable reference trajectory iterative learning linear quadratic control law includes: a. Selecting finite-time domain performance indicators and Hamiltonian function as follows: ; ; in, for The weighted matrix, for The weighted matrix, For terminal weighting matrix, and Performance indicators The initial time and the terminal time, It is a Lagrange multiplier.

[0022] b. Based on the performance indicators and Hamiltonian function in step (3)a, we can obtain: ; ;

[0023] c. Let the step (3)b in If the value equals 0, then: ; This expression only Unknown, if it can be obtained This allows us to obtain the linear quadratic control law obtained through iterative learning of the variable reference trajectory. .

[0024] d. Order , and Given the constructed coefficient matrix, we can obtain: ; e. Combine the predictive state-space model from step (2)h with the model from step (3)c. Substituting the expression into step (3)d, we get:

[0025] f. Take the steps in (3)e... Substituting the expression into (3)b The expression yields:

[0026] g. Compare step (3)d with the following. The expression can be used to obtain the finite-time optimization. The is: ;

[0027] in, ; ; h. Order The finite-time optimization in step (3)d tends towards infinity. Further transformed into infinite time-domain optimization as follows: ; in, This can be obtained by solving the following Riccati equation: ; i. The incremental iterative learning control law in step (2)g can be further written in the following form: ; The result obtained in step (3)h Substituting this into the formula, for the above formula, if it reaches... Period, then All information about the cycle, i.e. , , All of these are known. Therefore, the results obtained in step (3) are... Substituting this into the formula, we can obtain the manipulated variable. That is, the opening degree of the pressure-holding regulating valve .

[0028] Experimental section: Based on actual data, the model for the relationship between the mold cavity pressure and the opening of the pressure-holding regulating valve is as follows: ; The reference trajectory for mold cavity pressure is as follows: ; Various disturbances and uncertainties exist during the pressure holding process, leading to a mismatch between the modeled model and the actual process. The actual process between the mold cavity pressure and the opening of the pressure holding regulating valve is as follows: ; This indicates that the orders of both the controlled and manipulated variables in the actual process have changed, and a fixed disturbance exists. Note that the variable reference trajectory iterative learning linear quadratic control method is designed based on a modeling model and controls the actual process, keeping the cavity pressure within the process requirements.

[0029] The method of this invention is used to control the mold cavity pressure, and the control parameters are as follows: ; Figure 2 This paper presents the integral of squared error (ISE) curves of the cavity pressure at different cycles when the orders of the controlled and manipulated variables change and a fixed disturbance exists during the injection molding process. Figure 2 It can be seen that the integral of the squared error decreases as the cycle time increases. Therefore, under the control of the method of this invention, the control performance of the mold cavity pressure will improve with the increase of the cycle time until the optimal control effect is achieved. Figure 2 It can also be seen that after the production cycle exceeds 60, the integral of the squared error remains basically unchanged, which indicates that the control performance of the mold cavity pressure reaches the optimal control effect in the 60th production cycle. Figure 3 The diagram shows the optimal control effect of the mold cavity pressure. From Figure 3 It can be seen that the cavity pressure achieves excellent tracking performance. Although there is a time lag between the cavity pressure and the pressure regulating valve, the cavity pressure can still completely track the reference trajectory after the reference trajectory changes for the second time.

[0030] Because the injection molding process produces different types of products, the reference trajectory for a single cycle changes with the product type. To simulate this, in the 51st cycle, the reference trajectory for the cavity pressure becomes as follows: ; Figure 4 This diagram illustrates the control effect of the cavity pressure on several specific cycles after the reference trajectory of the mold cavity pressure changes in the 51st cycle, when the orders of the controlled and manipulated variables change and a fixed disturbance exists during the injection molding process. From... Figure 4 It can be seen that although the reference trajectory of the cavity pressure has changed, the cavity pressure can still track the reference trajectory. Figure 5 This paper presents the integral curves of the squared error of the mold cavity pressure in different cycles after the reference estimate changes in the 51st cycle, when the orders of the controlled and manipulated variables in the injection molding process change and a fixed disturbance exists. Figure 5 It can be seen that the integral of the squared error decreases as the reference trajectory changes. Therefore, under the control of the method of this invention, the control performance of the mold cavity pressure will improve with the increase of the cycle until the optimal control effect is reached. Figure 5 It can also be seen that after the production cycle is greater than 90, the integral of the squared error does not change much, which indicates that the control performance of the mold cavity pressure reaches the optimal control effect in the 90th production cycle. Figure 6 The diagram shows the optimal control effect of the mold cavity pressure. From Figure 6 It can be seen that the cavity pressure achieves excellent tracking performance.

Claims

1. A variable reference trajectory iterative learning linear quadratic control method for injection molding process, characterized in that, Includes the following steps: Step 1: Construct a variable reference trajectory learning strategy by utilizing the tracking error from the previous cycle during the injection molding process; Step 2: Based on the variable reference trajectory learning strategy, establish a predictive state-space model between the controlled and manipulated variables in the injection molding process; Step 3: Based on the state-space model with predictive capabilities, design a variable reference trajectory iterative learning linear quadratic control law to obtain the manipulated variables and complete the variable reference trajectory iterative learning linear quadratic control for the injection molding process.

2. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 1, characterized in that, The specific strategy for constructing a variable reference trajectory learning method is as follows: Step 1.1: Using the measured value of the controlled variable and the reference trajectory during the current cycle of the injection molding process, establish the tracking error for tracking the injection molding process: ； in, The production cycle of the injection molding process, Represents discrete time; express cycle The measured value of the controlled variable during the injection molding process at any given time. express cycle The reference trajectory of the controlled variable during the injection molding process at any given moment. express cycle Tracking error during the injection molding process; Step 1.2: Construct a reference trajectory learning strategy using the tracking error from the previous injection molding cycle: ； ； in, for cycle The output of the trajectory learning strategy is constantly referenced. and Represents the proportional learning factor and the integral learning factor; Indicates the time delay of the injection molding process; Step 1.3: Construct a variable reference trajectory learning strategy using the reference trajectory of the current period and the previous period: ； ； in, express Period and The sum of the differences between the reference trajectories at corresponding times of the period. This indicates the running time for each cycle. express cycle Predictive reference trajectory for the injection molding process at any time.

3. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 2, characterized in that, The specific implementation process of step 2 is as follows: Step 2.1: Describe the relationship between the controlled variable and the manipulated variable in the injection molding process, and convert it into a state-space model. Step 2.2: Define the prediction tracking error, select state variables, and construct a state-space model with predictive capabilities; Step 2.3: Design a linear quadratic control law, combined with a state-space model with predictive capabilities, to obtain the current manipulated variable.

4. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 3, characterized in that, The specific implementation process of step 2.1 is as follows: A two-dimensional ARIMA model in incremental form is used to describe the relationship between the mold cavity pressure and the pressure-holding regulating valve: ; in, Indicates the first cycle The measured value of the opening degree of the pressure-holding regulating valve at all times; and The parameters of the incremental two-dimensional ARIMA model, and These represent the orders of the controlled variable and the manipulated variable, respectively. This represents the difference operator along the time direction; ； ； The state variables are selected as follows: ； Replace the incremental form of the two-dimensional ARIMA model with a state-space model: ； in, ； ； 。 5. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 4, characterized in that, The specific implementation process of step 2.2 is as follows: Combined with predicted reference trajectory Define prediction tracking error as follows: ； Combining state-space model and prediction tracking error ,get: ;; The state variables are reselected as follows: ; Combining state-space model and state variables The resulting state-space model with predictive capabilities is as follows: ; in, ; ; .

6. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 5, characterized in that, The specific implementation process of step 2.3 is as follows: design cycle The linear quadratic control law is learned iteratively from the time-varying reference trajectory as follows: ； in, To iteratively learn a linear quadratic control law with a variable reference trajectory; Multiply both sides of the linear quadratic control law by the left side. By combining a state-space model with predictive capabilities, the state variables at the next time step can be predicted. : 。 7. The variable reference trajectory iterative learning linear quadratic control method for injection molding process according to claim 6, characterized in that, The specific implementation process of step 3 is as follows: Step 3.1: Select finite-time domain performance indicators and Hamiltonian function Down: ; ； in for The weighted matrix, for The weighted matrix, For terminal weighting matrix, and Performance indicators The initial time and the terminal time, For Lagrange multipliers; Step 3.2: Based on the performance metrics and the Hamiltonian function, we obtain: ； ； ； Step 3.3: Let Equal to 0, we can get ; Step 3.4: Let , and The constructed coefficient matrix can be obtained ； Step 3.5: Combine the predictive state-space model with the model from Step 3.

3. Substituting the expression into step 3.4, we get: ； Step 3.6: Take the contents of step 3.5... Substituting the expression into 3.2 The expression yields: ； Step 3.7: Compare with Step 3.4 The expression is used to obtain the finite-time optimization. : ； in, ； ； Step 3.8: Let Approaching infinity, finite-time domain optimization Convert to infinite time domain optimization as follows: ； in, This can be obtained by solving the following Riccati equation: ； Step 3.9: Iteratively learn the linear quadratic control law using the variable reference trajectory, and write it in the following form: ； The result obtained in step 3.8 Substituting into the formula, we obtain the manipulated variable. .

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